tag:blogger.com,1999:blog-74353910496793827342024-03-13T08:26:36.379-04:00DualnoiseOperations Research and AnalyticsUnknownnoreply@blogger.comBlogger221125tag:blogger.com,1999:blog-7435391049679382734.post-4399020737315566292015-08-25T09:02:00.001-04:002015-08-25T09:02:12.175-04:00The One-Dollar HaircutEvery year, I travel more than 9K miles to my <a href="http://www.dualnoise.com/2012/09/visiting-land-of-ramayana.html" target="_blank">native place</a> in Tamil Nadu, India, to get my $1 haircut.<br />
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<a href="http://jhingu.com/media/catalog/product/cache/1/thumbnail/600x/17f82f742ffe127f42dca9de82fb58b1/_/0/_0005_subraminion_2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://jhingu.com/media/catalog/product/cache/1/thumbnail/600x/17f82f742ffe127f42dca9de82fb58b1/_/0/_0005_subraminion_2.jpg" height="320" width="320" /></a></div>
(pic source: http://jhingu.com)<br />
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The local <a href="http://www.dualnoise.com/2010/11/or-practice-tip-find-and-eliminate.html" target="_blank">barber </a>is an expert and does it the old-fashioned way. A <a href="https://www.zib.de/groetschel/pubnew/paper/groetschelpadberg1979a.pdf" target="_blank">comb </a>to sift, and super-quick scissors acting as efficient <a href="https://en.wikipedia.org/wiki/Cutting-plane_method" target="_blank">cutting planes</a> to produce a nice, convex-hull hairdo. No fancy machinery, seating, lighting, or A/C in his environment-friendly shop, and not a single nick, or hair out of place when he's done. This keeps his customers happy and operating cost low. It's a dollar regardless of crop density. Perhaps the argument is that for the sparse-headed, the cost of searching goes up even as the actual cutting time reduces. If the shop is full, spill-over customers can sit in makeshift chairs outside the shop, and sip chai from the adjoining 'tea-kadai'.<br />
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The Indian barber shop is also an instance of the 'elastic' capacity model that is key to understanding how the Indian economy has chugged along. Here is what Prof. R. Vaidyanathan, Professor at the Indian Institute of Management, Bangalore, in his superb book '<a href="http://www.amazon.com/INDIA-UNINC-PROF-R-VAIDYANATHAN-ebook/dp/B00HQXUT32" target="_blank">India, Uninc</a>' has to say:<br />
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<a href="http://1.bp.blogspot.com/-A8ylefEDP8U/Vc3DAEH7LPI/AAAAAAAABmU/ThdBx1TvH-g/s1600/barberCapture.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="267" src="http://1.bp.blogspot.com/-A8ylefEDP8U/Vc3DAEH7LPI/AAAAAAAABmU/ThdBx1TvH-g/s400/barberCapture.PNG" width="400" /></a></div>
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Data shows that it this 'unincorporated' economy built from the ground-up by entrepreneurs that is responsible for much of India's GDP and employment, and not the stock market that grabs headlines. Despite the recent crash of the global markets, the Indian elephant is likely to remain solid, like it did after 2008.<br />
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The traditional Indian way of doing business may be initially bewildering to the external observer, which may have led to this 'Uninc' being categorized by Nehruvian India's west-educated officials as "unorganized". Actually, it is anything but, and appears to be based on balancing <a href="http://www.dualnoise.com/2013/04/the-chaos-of-india.html" target="_blank">constraint-enforcing 'order' and constraint-relaxing 'chaos'</a>. This traditional Indian approach, which I personally view as <i>dharmic optimization</i>, yields <a href="http://www.dualnoise.com/2015/03/mumbai-dabbawalas-operational.html" target="_blank">astonishingly high</a> and sustainable levels of quality and efficiency when done right, but can also be disastrous when either order or chaos is excessive.<br />
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End Note: Apparently, the global wig supply-chain sources much of its hair from India.Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-7435391049679382734.post-78487444700605138382015-07-22T00:39:00.000-04:002015-07-22T00:39:02.889-04:00How many songs does your favorite internet radio station hold?Can we even measure the number of songs 'stocked' by our favorite internet radio station (IRS) ? Douglas Hubbard who wrote "<a href="http://www.amazon.com/How-Measure-Anything-Intangibles-Business/dp/1452654204" target="_blank">How to Measure Anything</a>" would say yes. At least, we can get a reasonable and useful estimate. In fact, it may be tough to identify what an 'exact' answer is here since new songs may be continually added, and less popular ones deleted over time.<br />
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This problem appears to resemble another one: How many fish are there in a particular lake? As DH notes, just because we may never see all the fish the lake or hear every song in the IRS, it does not automatically mean that we cannot estimate its size. As part of my self-education in Indian logic, I understand this as follows: when we cannot directly perceive and verify (<i>pratyaksha pramaana</i>), we can try to infer this unobserved truth (~<i>anumaana</i>). Sometimes, we can use comparison (~<i>upamaana</i>) to solve this problem. Here are examples of historically significant events in India where estimating unobserved quantities turned out to be important:<br />
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1. Estimating the size of native volunteers ready to take on the occupying British Raj as part of '<a href="http://www.dualnoise.com/2012/11/operation-red-lotus-and-jules-verne.html" target="_blank">Operation Red Lotus</a>' in 1857 (covert sampling and proportions)<br />
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2. Estimating the <a href="http://www.dualnoise.com/2013/06/estimating-number-of-refugees-inside.html" target="_blank">number of refugees inside the Red Fort</a> (without entering) after the 1947 partition of India (comparison of proportions)<br />
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3. Estimating the <a href="http://www.dualnoise.com/2013/06/traveling-surveyor-contributions-of.html" target="_blank">size of jute crop</a> in 1930s Bengal (random sampling)<br />
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4. The <a href="http://www.dualnoise.com/2013/06/bengal-holocaust-analytics-of.html" target="_blank">number of civilians</a> killed in the Bengali holocaust of 1943 (random sampling). The blog carries excerpts, but you should read Madhusree Mukerjee's <a href="http://www.amazon.com/dp/B00B9ZO9LG" target="_blank">book</a> for an in-depth analysis.<br />
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Using the overlapping sample approach and the fish example in DH's book: catch some fish (say 1000), tag them, and let them swim happily around the lake. Again catch fish (say, 1000) and count the proportion of tagged fish (say 5%), indicating that we tagged roughly 5% of all the fish, giving us an estimate of about 20k. We can also calculate, say, a 90% confidence interval for the chosen sample size. Which brings me to the reason for this blog. I noticed that too many songs on the Ilayaraaja radio station offered by Google-music repeated during my office commutes last week. No problem re-listening to Ilayaraaja musical scores like this one (based on Shamukhapriya ragam is my semi-educated guess).<br />
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<iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/so9tDRC5its" width="560"></iframe>
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20 songs were mentally tagged on day-1 and released back into the radio station, and 20% of those tagged songs were streamed back to me on day-2. This experiment was repeated a couple of times, yielding similar results, indicating that Google-music's Ilayaraaja station roughly currently stocks about a hundred songs, and I will soon be hearing only repeats.<br />
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<br />Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-7435391049679382734.post-22545374862524855452015-07-05T12:59:00.000-04:002015-07-05T12:59:49.417-04:00Finding an optimal parking spot for shopping<a href="https://punkrockor.wordpress.com/2012/09/27/what-is-the-optimal-way-to-find-a-parking-spot/" target="_blank">Here </a>is the original discussion at 'Punk Rock OR'. The blog below studies a parking objective in the shopping context, and where the entrance to the shopping complex and the exit are at different locations. The cost to be minimized consists of at least two components:<br />
(objective-a) the 'work' done searching for a good parking spot, as well as<br />
(objective-b) the total physical work done after parking. This includes the work done while walking to the entrance, as well as the work done after shopping and exiting the building. Let's focus on objective-b here, given that objective-a has been analyzed before, using the following notation.<br />
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Parking coordinates (O, D), where<br />
O = walking distance from the parking spot to the entrance, and<br />
D = walking distance from the exit to the parking spot.<br />
M = mass of the person,<br />
S = expected mass of purchased items, and<br />
(<span style="background-color: white;">μ, g) = constants denoting the coefficient of friction during walking, and the acceleration due to gravity, respectively.</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Work done = force * distance = </span><span style="background-color: white;">μg * mass * distance (<a href="http://www.dualnoise.com/2013/12/optimize-your-in-store-holiday-shopping.html" target="_blank">A prior blog</a> shows how to optimize our in-store shopping route.)</span><br />
<span style="background-color: white;"><br /></span>Objective is to minimize: <span style="background-color: white;">M*O + (M+S)*D</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">A minimal work objective suggests these simple rules:</span><br />
<span style="background-color: white;">1) H</span><span style="background-color: white;">eavy shopping: park close to the exit. </span><br />
<span style="background-color: white;">2) Light shopping: park to minimize total walk.</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">Thus, the goodness of a parking spot depends on the shopping context. </span><span style="background-color: white;">Let us figure out a good parking spot for the shopping scenario below.</span><br />
<span style="background-color: white;"><br /></span>
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<a href="http://1.bp.blogspot.com/-pEcSamu6l4w/VZk4ny2T3aI/AAAAAAAABkQ/PlAr2I0f9FY/s1600/parking.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="168" src="http://1.bp.blogspot.com/-pEcSamu6l4w/VZk4ny2T3aI/AAAAAAAABkQ/PlAr2I0f9FY/s320/parking.png" width="320" /></a></div>
<b>Linear Store, Manhattan Distances</b><br />
<span style="background-color: white;">Consider a long, 'linear' store along the x-axis, with the exit @ x = 0, and entrance @ x = L. Assume </span><span style="background-color: white;">'Manhattan' walking distances (</span><i style="background-color: white; color: #252525; font-family: 'Nimbus Roman No9 L', 'Times New Roman', Times, serif; font-size: 20.6499996185303px; line-height: 11.9502305984497px; white-space: nowrap;">ℓ</i><sup style="background-color: white; color: #252525; font-family: 'Nimbus Roman No9 L', 'Times New Roman', Times, serif; font-size: 16.5200004577637px; line-height: 1; white-space: nowrap;"> 1</sup><span style="background-color: white;">) and that prior customers selected spots nearest the building</span><span style="background-color: white;"> along y-axis, and picked their spots along the x-axis based on individual preferences. </span><span style="background-color: white;">Given this, t</span><span style="background-color: white;">he distance we can expect to walk to/from the store along the y-axis is already (near) minimal. This leaves us with a (non-convex) one-dimensional search for open locations x(i) along the x-axis</span><span style="background-color: white;"> over three regions. Let us split this task into two steps. </span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;"><b>Step-1: Find the best spot within each region</b></span><br />
<span style="background-color: white;">A) x(i) </span><span style="background-color: white;">= -a </span><span style="background-color: white;">≤</span><span style="background-color: white;"> 0 </span><br />
<span style="background-color: white;">Minimize M(O+D)+S</span><span style="background-color: white;">*D = M(L+a +a) + Sa = ML + (2M+S)a*</span><br />
<br />
<span style="background-color: white;">B) 0 </span><span style="background-color: white;">≤ </span><span style="background-color: white;">x(i) = b </span><span style="background-color: white;">≤ L</span><br />
<span style="background-color: white;">Minimize </span><span style="background-color: white;">M(L-b + b) + Sb = ML +Sb*</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">C) </span><span style="background-color: white;"> </span><span style="background-color: white;">x(i) = L+c </span><span style="background-color: white;">≥</span><span style="background-color: white;"> L</span><br />
<span style="background-color: white;">Minimize </span><span style="background-color: white;">M(c+L+c) + S(L+c) = ML+SL + (2M+S)c*</span><br />
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<span style="background-color: white;"><br /></span></div>
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<span style="background-color: white;">T</span>he optimal x* within each of these regions is the one closest to the exit. This is independent of S and L, and identifiable by greedy search.<br />
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<b>Step-2: Finding the least cost spot among (a*, b*, c*)</b><br />
The worst spot in B is no worse than c*, independent of S and L, yielding a binary choice: pick a* or b*.<br />
x(i) <span style="background-color: white;">≤</span><span style="background-color: white;"> 0: incremental cost = </span><span style="background-color: white;">(2M+S)a*, a* </span><span style="background-color: white;">≥ 0</span><br />
x(i) <span style="background-color: white;">≥ 0: incremental cost = </span><span style="background-color: white;">Sb*, b* </span><span style="background-color: white;">≥ 0</span><br />
<br />
For small values of S, b* dominates and is optimal for light shopping or window shoppers. As S increases and becomes comparable to M, b* is preferable when:<br />
b*/a* <span style="background-color: white;">≤ 1 +</span><span style="background-color: white;">2(M/S)</span><br />
<br />
Even if we 'shop till we drop' and carry our own weight, b* can be as much as 3a* and still dominate.<br />
<br />
Practically speaking, b* is a solid bet, but when B is full, the shopper is forced to choose between disjoint regions A and C.<br />
x(i) <span style="background-color: white;">≤</span><span style="background-color: white;"> 0: incremental cost = </span><span style="background-color: white;">(2M+S)a*</span><br />
x(i) <span style="background-color: white;">≥ L: incremental cost = </span><span style="background-color: white;">SL + (2M+S)c</span><span style="background-color: white;">*</span><br />
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<span style="background-color: white;"><br /></span></div>
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<span style="background-color: white;">shoppers would prefer a* to c* unless:</span></div>
<div>
<span style="background-color: white;">(a*-c*) ></span><span style="background-color: white;"> L/[</span><span style="background-color: white;">2(M/S)+1]</span></div>
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Scenarios:<br />
i) <span style="background-color: white;">Between spots equidistant from the entrance and exit, a* dominates c*, independent of S and L.</span><span style="background-color: white;"> </span><br />
ii) For the 'carry our own weight' scenario, a* is preferable when<br />
<span style="background-color: white;">(a*-c*) </span><span style="background-color: white;">≤</span><span style="background-color: white;"> </span><span style="background-color: white;"> L/3</span><br />
<span style="background-color: white;">iii) For unmanageably large S, a* remains preferable if:</span><br />
<span style="background-color: white;">(a*-c*) </span><span style="background-color: white;">≤</span><span style="background-color: white;"> L</span><br />
<br />
<span style="background-color: white;">We can now draw some conclusions.</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;"><b>Finding a Minimum-Work Parking Spot</b></span><br />
<span style="background-color: white;">Preferred order of parking is:</span><br />
<span style="background-color: white;">b* > a* > c*</span><br />
<span style="background-color: white;"><br /></span>
<span style="background-color: white;">which is out of order. </span><span style="background-color: white;">The actual search pattern we employ may depend on whether the aisles in the parking lot are along the x- or y-axis. </span><br />
<span style="background-color: white;"><br /></span>
<u><span style="background-color: white;">Light/medium shopping context</span></u><br />
<span style="background-color: white;">Clockwise, starting from the exit, scan B, park if feasible. </span><span style="background-color: white;">Else scan C, and park</span><span style="background-color: white;"> if feasible. Else, turn around c</span><span style="background-color: white;">hoose a spot in A. </span><br />
<span style="background-color: white;"><br /></span>
<u><span style="background-color: white;">Heavy shopping context</span></u><br />
<span style="background-color: white;">Clockwise, starting from the exit,</span><span style="background-color: white;"> </span><span style="background-color: white;">scan B, park if feasible. </span><span style="background-color: white;">Else turn around, scan A, and park</span><span style="background-color: white;"> if feasible. Else, c</span><span style="background-color: white;">hoose a spot in C.</span><br />
<br /></div>
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</div>
Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-7435391049679382734.post-76027377207980097542015-05-16T21:24:00.000-04:002015-05-21T12:07:05.174-04:00Activity Tracker Analytics - Part 1: Fun with Fit-BitsI've been experimenting with fitness and activity tracking devices the last few months. Somehow, I ended up testing three of them (let's call them blue, red, and green), each from a different company, one of them being a 'fit bit'. Blue and red showed similar daily readings, which also seemed to tally with small manual walking samples I took. On the other hand, the cheap, low-end green device was way off and severely under-predicting. Rather than simply junk the green tracker, can we 'rescue' it by noting its measurements and then optimally re-calibrate it using a more accurate tracker? This is the simple idea of this blog.<br />
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Figure 1 shows a one-month sample of normalized daily step-count readings obtained from the three trackers.<br />
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Figure 1.</div>
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<a href="http://4.bp.blogspot.com/-XTO5mPlh9fk/VVfWe1TSujI/AAAAAAAABgA/oLOOkeEPjPU/s1600/fitbit1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="207" src="http://4.bp.blogspot.com/-XTO5mPlh9fk/VVfWe1TSujI/AAAAAAAABgA/oLOOkeEPjPU/s400/fitbit1.png" width="400" /></a></div>
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The blue and red represent the 'good trackers', and the green one, which we wanted to junk, is the green line. This plot shows that although trackers from different manufacturers can differ significantly in terms of the absolute number of steps they count, their relative readings between days is likely to be more consistent. If you walk more, it is quite likely that the tracker will count more steps. Comforting.<br />
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<a href="http://jama.jamanetwork.com/article.aspx?articleid=2108876" target="_blank">This </a>February 2015 JAMA article discusses the quality of readings from a variety of activity trackers. Here is a snapshot of a paragraph from the preview page of this journal article.<br />
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<a href="http://4.bp.blogspot.com/-im-V4EtzBoU/VVflQAjrnvI/AAAAAAAABhQ/VPCl_n08TsY/s1600/jama.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://4.bp.blogspot.com/-im-V4EtzBoU/VVflQAjrnvI/AAAAAAAABhQ/VPCl_n08TsY/s400/jama.PNG" width="257" /></a></div>
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(Picture source: preview page from http://jama.jamanetwork.com)<br />
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It appears that this paper also mentions good 'intra-device' repeatability. This <i>consistency of response</i> (something that is incredibly important to ORMS decision support systems) offers hope for our green tracker. However, there is also plenty of scope for noise. The counting is done based on an accelerometer/sensor, and therefore, acceleration is what it detects and translates into step counts. If you are not a smooth driver during your morning and evening commute, you will have 'walked' a lot. I've taken a lot of steps driving my lawn mower tractor for 45 minutes. Different trackers respond differently to specific types of activity. Exceptions aside, these devices are generally quite useful. Moreover, they do really tell us if our exercise levels have increased or dropped over time, which is a very useful and healthy thing to know. This second figure below shows the ratio of step counts between two successive days.<br />
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<div style="text-align: center;">
Figure 2</div>
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<a href="http://3.bp.blogspot.com/-jKTsVKDTH10/VVfZeJA0eLI/AAAAAAAABgQ/bUORYzaTiVs/s1600/fitbit2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="205" src="http://3.bp.blogspot.com/-jKTsVKDTH10/VVfZeJA0eLI/AAAAAAAABgQ/bUORYzaTiVs/s400/fitbit2.png" width="400" /></a></div>
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The green-tracker looks pretty reasonable compared to the other two when it comes to reporting the relative response over time. During peak days, it closely matches the blue tracker, while on other days, it sticks reasonably close to the blue and red lines. Therefore, the green tracker is not a total write-off. We can rescue it by re-calibrating it upward. For example, let us assume the average of blue and red as the 'true' reading and employ linear regression (minimizing sum of squared 'error') to identify the green correction, as shown in Figure 3 below.<br />
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<div style="text-align: center;">
Figure 3.</div>
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<a href="http://3.bp.blogspot.com/-_gNtXf4nloU/VVfdu9zc6TI/AAAAAAAABgg/_zZLltZAKYg/s1600/fitbit3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="227" src="http://3.bp.blogspot.com/-_gNtXf4nloU/VVfdu9zc6TI/AAAAAAAABgg/_zZLltZAKYg/s400/fitbit3.png" width="400" /></a></div>
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For this specific usage profile, scaling the green reading up by 12% and adding 0.32 gets us close to the red and green numbers. However, the presence of peak-days may have skewed our calibration, so this may not be an 'optimal' idea. Let us remove the peak-days, and also swap the X and Y axes to get a 'normal day' recalibration. The result is shown in Figure 4 below.<br />
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<div style="text-align: center;">
Figure 4.</div>
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<a href="http://3.bp.blogspot.com/-NyxxIiK7ppo/VVfg1fdP0NI/AAAAAAAABgw/kHqLSlJZwVg/s1600/fitbit4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="235" src="http://3.bp.blogspot.com/-NyxxIiK7ppo/VVfg1fdP0NI/AAAAAAAABgw/kHqLSlJZwVg/s400/fitbit4.png" width="400" /></a></div>
<br />
Aha! This regression equation is interesting. The R-squared value drops a bit, but more importantly, it suggests that we may do not need to do scaling. We can do something as simple as adding 0.36 to the green reading. Of course, the relative response plot in Figure 2 should have given us that clue. Did the green-tracker company engineers miss a trick here: Do these missing '0.36 steps' represent a default 'idle' activity level that they forgot to account for? If the green engineers spread the 0.36 over 16 waking hours, their final readout would be in good shape. Let us compare the output of this (0.36 + green) with the blue-red plot in our last and final figure.<br />
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<div style="text-align: center;">
Figure 5.</div>
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<a href="http://2.bp.blogspot.com/-SIW8auVEB7k/VVfijjvlYXI/AAAAAAAABhA/ixdTbHy8Em8/s1600/fitbit5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="222" src="http://2.bp.blogspot.com/-SIW8auVEB7k/VVfijjvlYXI/AAAAAAAABhA/ixdTbHy8Em8/s400/fitbit5.png" width="400" /></a></div>
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By simply adding 0.36 to the count of the cheap tracker, we have obtained a good daily step count that compares well with the more expensive 'blue-red' trackers. Go Green!Unknownnoreply@blogger.com4tag:blogger.com,1999:blog-7435391049679382734.post-65851873805091838442015-03-24T19:06:00.002-04:002015-03-25T13:49:21.273-04:00Mumbai Dabbawalas: Operational Excellence Based on Trust Chains and dharmaMost business case studies, research papers, and news articles on the Mumbai dabbawalas (MD) focus on, and rightly marvel at the fact the MDs were awarded a remarkable '<a href="https://en.wikipedia.org/wiki/Six_Sigma" target="_blank">six sigma</a>' western certification based on the less than one-in-million statistical error rate in their daily delivery of home-cooked meals to many thousands of Mumbai workers for over a <i>hundred </i>years now. As background,<b> </b><a href="http://www.rediff.com/money/2005/nov/11spec.htm" target="_blank">here </a>is one of the earlier articles, written ten years ago, on this astonishing team. Please read this article first, since the remainder of the discussion will assume familiarity with the MD supply chain. The MDs have built a zero carbon-footprint, health-enhancing, almost perfectly-reliable, organically sustainable, hyper-personalized<b> </b>supply chain. Profitably achieving even one of these objectives would be considered a victory for modern day supply chains. Rather that again focus on what they achieved and how (and both questions are of great interest to the Operations Research and business analytics community), the more interesting questions for me as I began learning about the dabbawalas were:<br />
how can they <i>sustain </i>this? and <i>why do they</i>?<br />
<br />
Business case studies and news articles skip these questions. Luckily, I found at least two sources of information that I could tap into to try and answer these questions to my own satisfaction. We'll start with the 'how', and then the deeper, related question of 'why'.<br />
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<b><span style="color: #351c75;">How do they sustain it?</span></b><br />
We turn to Prof. P. Kanagasabapathi's gem of a book "<a href="http://www.amazon.com/Indian-Models-Economy-Business-Management/dp/8120345630" target="_blank">Indian Models of Economy, Business and Management</a> (3rd Edition)", and see what he has to say about MDs. I must add this: I have come to learn, over the last few years that the Indian economy is like a complex number. It has a real part and an imaginary part. The latter is covered by CNBC, Bombay Stock analyses, and Ivy-league university economic theories faithfully imported and regurgitated in Indian colleges, and gobbled up by students and economists. If we want to understand how the <i>real </i>part works, read this book, and Dr. R. Vaidyanathan's equally brilliant '<a href="http://www.amazon.com/INDIA-UNINC-PROF-R-VAIDYANATHAN-ebook/dp/B00HQXUT32" target="_blank">India, Uninc</a>'. Both are <i>data-driven</i> books, and offer us the reality based on deep insights into how the Indian society and mind actually function. They are available in paper and Kindle editions, and ridiculously under-priced.<br />
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Let us see what Prof. PKS has to say (emphasis in bold / square bracket is mine):</div>
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"...<i>the dabbawala business in Mumbai is an innovative business designed and executed by a group of uneducated and undereducated people from the ordinary classes to suit the local conditions. The business plan is so designed to make it perfectly functional, while at the same time keeping it cost effective</i>.</div>
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<i>"...<span style="color: #990000;">.<b>see how the supply chain management works</b></span>. The dabba-wallas are semi-literate people, with rural backgrounds from Pune district. They belong to the warrior </i>[clan]<i> of Malua, which fought for </i>[the great Indian king Shivaji]<i> in the earlier days. In the 1890s, one Mahado, a migrant from their area started the supply of lunch boxes. Today under the banner of Nutan Mumbai Tiffin-box Suppliers Association, more than 4500 of them are involved in supplying nearly 2,00,000 boxes every working day. Braving Mumbai weather conditions and difficulties involved in multiple transfer points, these `ordinary' people make <b><span style="color: #990000;">only one mistake for eight million deliveries</span></b> "I.It is no wonder that the Forbes Global Magazine gave them a Six Sigma efficiency rating on par with multinational companies such as Motorola and General Electric. In fact, the efficiency of dabbawallas is much better than the Six Sigma levels fixed by the experts for world class performances. As a result they are now admired as the model for the global corporations...While mega corporations use the most modern technologies and employ highly qualified technical and management experts to reach higher levels, <b><span style="color: #990000;">how could these ordinary people from village backgrounds with only their common sense and limited resources better the benchmarks fixed for the most efficient companies in the world</span></b>? Is it not due to the effective teamwork and most efficient planning? Are these people not practising the most effective methods to serve their customers? In the case of modern corporate sector, they search for different methods to sell their products. In some cases, the products may not be essential to the customers. But still they try to look for different ways to attract customers and sell their products. In the case of dabbawallas they have devised a way to serve the customers who would like to eat home-made food, and in the process they have made it so well that they have become world-class service providers.</i><br />
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We start to get some answers above on the 'how'. Now we turn to find answers for how they're able to sustain this:<br />
<i>".. <b><span style="color: #990000;">community relationships</span></b> provide certain benefits and cost advantages in business. <b><span style="color: #990000;">One is trust, which is very important for business</span></b>. Communities generate high levels of trust due to their close-knit relationships. Second is the lower transaction costs compared to the rates determined by the markets. As a result, efficiency is increased and costs are reduced..."</i><br />
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<b><span style="color: blue;">Trust</span></b>. It can dramatically reduce costs and boost efficiency. Every multinational company's employee brochure strongly emphasizes the importance of 'trust' and 'teamwork'. However, it is not easy build a high degree of cross-organizational trust in today's western workplace. why? Dr. Kanagasabapathi quotes Francis Fukuyama:<br />
<i>"The ability to associate depends, in turn, on the degree to which communities share norms and values and are <b><span style="color: #990000;">able to subordinate individual interests to those of larger groups</span></b>. Out of such shared values comes trust, and trust, as we will see, has a large and measurable economic value." <b><span style="color: #990000;">Trust results in `social capital.</span></b>'"</i><br />
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Trust can arise out of that bi-directional relationship called mutual respect. This <a href="http://www.dualnoise.com/2012/01/working-multicultural-model-necessary.html" target="_blank">blog </a>I wrote a few years ago views mutual respect as a necessary and sufficient condition for building trust in a workplace. If one party dilutes its commitment, and merely tolerates rather than respect, this trust is broken. The modern workplace is contractual. Order is enforced, and chaos is contained by a variety of standard background checks, zero and non-zero tolerances, and legal penalties. One of India's most important thought leaders, S. Gurumurthy has pointed out that 'Capitalism requires employers, Communism banks on employees. Traditional Indian economies are entrepreneurial and require neither'. Rather, they rely on trust chains built upon mutual respect, which produce social capital. To learn more about social capital, Dr. P. Kanagasabapathi turns to Aiyer:<br />
<i>"From time immemorial, groups of people have created strong communities, based on commonly observed rules and <b><span style="color: #990000;">mutual self-help</span></b>. These social links discourage deviant behaviour through ostracism and other social penalties, create a climate of trust in which agreements are honoured and grievances redressed, and facilitate collective action against threats from outsiders and risks from natural disasters. This is social capital..."</i><br />
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Thus, the MDs have been able to sustain their dizzying levels of operational reliability and quality levels by achieving a high degree of trust within their organization and the mutual respect between self and customer. <br />
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<b><span style="color: #351c75;">Why do they?</span></b><br />
The 'why' takes us even deeper. For this, I'm indebted to the head of the Indian embassy in Vancouver, Canada. Listen to his brief talk about the MDs in this You Tube video (watch from 9:33)<br />
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<iframe allowfullscreen="" frameborder="0" height="510" src="https://www.youtube.com/embed/Z88bIk-9HQc" width="854"></iframe>
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The Dabbawalas are doing their <i>dharma</i>, their cosmic duty. This idea of cosmic/sanctity implies an unmanifest motive to their duty. The <b><span style="color: #990000;">effect </span></b>that dharma has on the dabbawala output is real, measurable, and has made him go far beyond the so-called 6-sigma level of quality. As the consular head points out in his talk, when the Dabbawalas handle, deliver, and serve food, they also perform a sacred service, a <i>seva</i>. As mentioned in a previous blog here, an Indian business model seeks not unconstrained profit maximization, and nor is it non-profit, for neither are sustainable, but it <a href="http://www.dualnoise.com/2013/11/optimizing-shubh-laabh-harmonious.html" target="_blank">shubh laabh</a>, or auspicious profitability. There is a harmonious balance between the worldly and the unmanifest. The Indian idea of seva is different from the western conception of service. As Gurumurthy once pointed out (via the wonderful anecdote of Swami Vivekananda and the philanthropist Rockefeller), the Indian giver thanks the receiver, not the other way around. While the manifest, material benefit does indeed go to the receiver, the higher, unmanifest benefit from this good Karma accrues to the giver. Who, then is the giver, and who is the receiver? The entrepreneurial Dabbawala will continue to serve, innovate, and sustain operational excellence provided there is: demand for his service, trust at every point of interaction in the supply chain, and he chooses to do his dharma.<br />
<br />Unknownnoreply@blogger.com8tag:blogger.com,1999:blog-7435391049679382734.post-71077531485342620442015-02-24T23:02:00.003-05:002015-02-24T23:02:44.244-05:00Hunting for OptimalityOK. Sometimes, we really do need to find 'the' answer. Recall the scene from <i>Jaws</i>: "It's a shark, not <i>the </i>shark". But in general, seeking 'the' one and only, true, unique, prophetic optimal solution to real-life decision problems is an exercise in futility. It makes sense to talk about the best practically achievable solutions given resource constraints, costs, and priorities, which can then be iteratively refined over time. While filling out a <i>healthcare </i>quiz about better nutrition and weight management, I was delighted to see this question.<br />
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<a href="http://2.bp.blogspot.com/-JjkWa5pTTFc/VOtB-LdkerI/AAAAAAAABc4/TZ1INKb86eE/s1600/weight_loss_question_Capture.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-JjkWa5pTTFc/VOtB-LdkerI/AAAAAAAABc4/TZ1INKb86eE/s1600/weight_loss_question_Capture.PNG" height="250" width="400" /></a></div>
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The health-care researcher who designed this quiz deserves a round of applause.<br />
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But how do Operations Researchers find such solutions? Sometimes, the problems are provably cute (journals love to publish these).<br />
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<a href="http://3.bp.blogspot.com/-q4mkRTN3kTg/VO07l3UPntI/AAAAAAAABd8/yLzvy8zkQk4/s1600/cartoon-goldfish.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-q4mkRTN3kTg/VO07l3UPntI/AAAAAAAABd8/yLzvy8zkQk4/s1600/cartoon-goldfish.jpg" /></a></div>
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But very often in practice, you end up dealing with this:<br />
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<iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/2I91DJZKRxs" width="560"></iframe>
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No fear. Well-designed practical algorithmic approaches employing robust, industrial-strength optimization tools like CPLEX can help OR'ers recover high quality solutions to challenging, seemingly intractable, messy-data riddled, real-world decision problems.<br />
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Losing out on the perfectly good in a quest for the perfect seems pretty silly.Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-7435391049679382734.post-22470745256937008212015-02-08T22:52:00.003-05:002015-02-09T09:21:01.488-05:00RT if you agree, FAV if you don't: Does it work?A simple way of binary polling on twitter that reaches a large number of voters, especially if the polling handle (@H) is sufficiently popular, is to get followers to re-tweet (RT) the message if they agree with the proposition P, and 'favorite' (fav) it if they disagree.<br />
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<a href="http://2.bp.blogspot.com/-6f5PK8h5SSw/VNi_fZNBj-I/AAAAAAAABcY/ddvvIcd55ms/s1600/twitter_poll2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-6f5PK8h5SSw/VNi_fZNBj-I/AAAAAAAABcY/ddvvIcd55ms/s1600/twitter_poll2.png" height="400" width="396" /></a></div>
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In the above poll, while Kejri is as phoney as they come, the result shouldn't be this skewed.<br />
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(This is just a cursory analysis)<br />
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Suppose <i>m</i> followers of @H RT, and <i>n </i>fav. This gives us a <i>m</i>/<i>n</i> ratio among @H's followers. Next:<br />
a) The message gets forwarded to the followers of the <i>m </i>"RT" handles<br />
b) The message is not forwarded to the followers of <i>n</i> "fav" handles<br />
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and this RT'ing process continues. As long as the 'agree' nodes in RT chain via (a) represent random samples, this poll can work reasonably despite only the ayes propagating the message. i.e., the RT probability of the followers of an 'agree' handle (@YES) should not be influenced by @YES' RT (i.e., there are no significant 'vote-banks'). If birds of the same feather flock together, this assumption may not hold, and we are likely to see a disproportionate number of 'agree'. On the other hand, if the poll reaches any 'disagree' handle whose followers are also likely to disagree, the poll does not reach any of these followers, skipping many of the 'disagree' nodes of the social network. The final result may be skewed favorably toward 'agree'. Of course, the nays need not just 'fav'. Then can create their own separate tweet that links this poll, and share this with their followers. Perhaps @H can send out a modified tweet:<br />
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'Proposition P: RT if agree. Fav and<i> </i>share this msg if u don't'.<br />
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This additional step may restore some balance. However, the burden of extra work falls on the 'fav' group, and only the enthusiastic 'fav' folks are likely to oblige. <span style="color: blue;">The final result may remain skewed in favor of 'agree'</span> but could yield a better result compared to the unmodified polling tweet.<br />
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Alternatively, @H could send out two independent tweets, the first requesting an RT for agree, and the second, an RT for 'disagree'. Will this 'RT competition' work better? (RT if you agree, RT if you don't :)Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-7435391049679382734.post-46140943291785701712015-01-18T16:17:00.000-05:002015-01-18T16:41:03.561-05:00Strike Rate Analysis of AB de Villiers' Innings of 149(44)A quick blog on today's amazing knock by AB.<br />
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<a href="http://www.espncricinfo.com/south-africa-v-west-indies-2014-15/engine/match/722341.html" target="_blank">Here's </a>the archive of Cricinfo's online commentary for the cricket match where South African batsman <a href="http://www.espncricinfo.com/southafrica/content/player/44936.html" target="_blank">AB de Villiers</a> scored the <a href="http://www.espncricinfo.com/south-africa-v-west-indies-2014-15/content/current/story/821839.html" target="_blank">fastest ever ODI cricket century</a>. Here are the <a href="http://www.espncricinfo.com/south-africa-v-west-indies-2014-15/content/story/821895.html" target="_blank">stats</a>. He batted just 44 balls for his 149 runs that included 16 sixes. Here's a graph of his cumulative strike rate throughout the innings in runs per 100 balls.<br />
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<a href="http://1.bp.blogspot.com/-A5QFGSVxDGA/VLwXubgO79I/AAAAAAAABb8/ac0wa45qds4/s1600/ab%2Bstrikerate.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-A5QFGSVxDGA/VLwXubgO79I/AAAAAAAABb8/ac0wa45qds4/s1600/ab%2Bstrikerate.png" height="286" width="400" /></a></div>
His highest cumulative strike rate was 400 after the first ball, and thereafter, the lowest it ever reached was 200, after 4 balls. His first fifty took 16 balls, and his second fifty was even faster, coming of just 15 deliveries, giving him the record 31-ball century. He scored no runs of the last two balls he faced, causing his final strike rate to dip below 350 and end at 339.<br />
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AB was at the crease for just 44 minutes. In comparison, the <a href="http://stats.espncricinfo.com/ci/content/records/283006.html" target="_blank">slowest</a> international hundred (in test cricket, which can be very different) in history consumed 557 minutes.<br />
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As far as instantaneous strike rates throughout the innings, we can observe a 13-ball stretch (28th to the 40th ball) where he scored 63 runs to move from 82 to 145, at a strike rate of 485 - suggesting that in that period, like Viv Richards, AB was in two minds - whether to hit the bowler for a 4 or 6.<br />
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Here's a grainy YouTube video of today's innings.
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<iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/hJ0q8SsgJqo" width="420"></iframe>
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The previous fastest ODI century consumed 36 balls, which yields a strike rate of less than 300. AB's final strike rate in this innings is higher than the expected <a href="http://dualnoise.blogspot.com/2012/10/analytics-and-cricket-ix-book-cricket.html" target="_blank">book-cricket team strike rate</a> of around 325.<br />
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7435391049679382734.post-4887451902977587662015-01-06T17:50:00.001-05:002015-01-06T17:50:38.654-05:00Some OR aspects of Hidden-City Airfare TicketingRead <a href="http://dealnews.com/features/What-is-Hidden-City-Airfare-Ticketing-and-is-it-Legal/1242755.html" target="_blank">this </a>interesting discussion and reader comments on "Hidden city" airfare ticketing (HCAT)<br />
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(picture is linked from this <a href="http://dealnews.com/">dealnews.com</a> post)<br />
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The article quotes a NY times post that explains HCAT nicely and ends like this: "<span style="background-color: white; font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.25px; line-height: 21.125px;">If you want to travel to Dallas, the best way to get a reasonable fare is to book the flight to Los Angeles instead, and simply get off the plane at Dallas."</span><br />
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The passengers don't appear to be doing anything illegal by getting off. Nobody has been arrested yet, at least. The airline is within its rights to employ all legal means to curb this practice. UA is <a href="http://money.cnn.com/2014/12/29/news/united-orbitz-sue-skiplagged-22/" target="_blank">suing </a>a 22-year old for his website that seems to help people with HCAT. Some of the reader comments in response to these HCAT articles are interesting.<br />
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Is this seemingly weird pricing structure a rare but predictable outcome of optimally managing fares for a hub-spoke network? Or is it due to some less-than-realistic assumptions underlying the combinatorial optimization formulations within their revenue management, fleeting, and schedule planning models? <br />
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Consider the hotel analogy: Do hospitality RM systems create situations where one can purchase a cheaper hotel stay for 3 nights including a weekend but check out on Friday night? Surely one would expect a price consistency-check layer in place that would prevent such a scenario. Of course, when one has to consistently price to maximize revenue expected from predicted demands for millions of different itineraries, it can get quite complicated.<br />
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In OR revenue management practice, we have had to build pricing engines to manage request-for-quotes (RFQs) for a bunch of items that often involve complex demand interactions. If the customer is allowed to cherry-pick and is not bound to an all-or-nothing type bundle deal, the pricing optimization analytics we develop will naturally have to account for this. While life would be so much more easier if customers did not cherry-pick, explicitly blocking cherry-picking is not a great idea since it completely eliminates customer flexibility. Customers will simply take their business elsewhere. Thus, one option is to manage cherry-picking using 'soft' constraints.<br />
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Economics can make companies adopt seemingly strange pricing and assortment management practices. The rough equivalent of HCAT for Starbucks is 'the case of the missing short coffee cup' discussed in Dr. David Simchi-Levi's <a href="http://slevi1.mit.edu/books/designing-and-managing-the-supply-chain" target="_blank">book</a> on Supply Chain Management (SCM):<br />
"<i>they will serve you a better, stronger Cappuccino if you want one, and they will charge you less for it</i>"... <i>but why does this cheaper, better drink ...languish unadvertised?</i>... <i>Businesses try to discourage their more lavish customers from trading down by making their cheaper products look or sound unattractive...the bottom end of any market tends to get distorted"</i> As far as I know, Starbucks has not blocked the book authors.<br />
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The book mentions how & why, in the early days of the railway, in some places, a 3rd class carriage was deliberately left roofless even though it was pretty cheap to build one. The customer utility of the least profitable option is (ruthlessly) reduced, enough to discourage trade-downs but not bad enough to lose their economy customer segment to competitive options. Thus, if you want to deplane at Dallas, it seems that you will have to take your chances and not make it a habit. If we try to advertise or game this, it is apparent the companies are SCM-bound to come after us and make HCAT a most unattractive option.<br />
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Happy New Year!<br />
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<span style="font-size: x-small;">(views expressed in this blog are personal)</span>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7435391049679382734.post-47905606520218985492014-11-29T22:06:00.000-05:002014-11-29T22:06:23.670-05:00Calvin and Hobbes TSPEven if Calvin finds the correct, feasible tour traversing the 23+ 'cities', it is never going to be Hobbes-optimal.<br />
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(pic source: <a href="https://twitter.com/Calvinn_Hobbes/status/538882694130974721" target="_blank">twitter</a>)Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-7435391049679382734.post-1974354275718505432014-11-20T19:07:00.001-05:002018-10-07T09:54:41.182-04:00The Contextual Optimization of SanskritI'd written a <a href="http://dualnoise.blogspot.com/2014/10/lassoing-exponential.html?q=contextual" target="_blank">blog </a>for the INFORMS conference earlier this month based on my practice perspective, which emphasized the importance of contextual optimization rather than despairing over the 'not infallible' theoretical worst-case nature of certain mathematical problems. This is something well-internalized by those in the large-scale and non-convex optimization community, where '<a href="https://en.wikipedia.org/wiki/NP-hard" target="_blank">NP-Hardness</a>' is often the start, rather than the end point of R&D.<br />
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The wonderful '<a href="http://meetings2.informs.org/sanfrancisco2014/plenary.html" target="_blank">Philip McCord Morse Lecture</a>' at the recently concluded INFORMS conference in San Francisco by Prof. Dimitris Bertsimas of MIT touched upon this point, and the 'conclusions' slide in the talk explained this idea really well. To paraphrase, 'tractability of a problem class is tied to the context - whether the instances you actually encounter can be solved well enough'. I mentioned the Sulba Sutras in that blog - a well known body of work that epitomizes the Indian approach to mathematics as Ganitha - the <i>science </i>of computation. The genius, Srinivasa Ramanujan, was a relatively recent and famous example of a mathematician hailing from this tradition. The Indian approach is often algorithmic and more about rule generation than infallible theorem proving. Not that Indians shied away from proof ('Pramaana'. For example, see 'Yuktibhasa'). As I understand it, this sequential process of discovery and refinement does not lose sleep over theoretical fallibility, and consists of:<br />
a) in-depth empirical observation of, and a deep meditation on facts,<br />
b) insightful rule generation,<br />
c) iterative, data-driven refinement of rules.<br />
This quintessential Indian approach is applied not just to math, but to practically <u>every </u>field of human activity, including economics, commerce, art, medicine, law, ethics, and the diverse dharmic religions of India, including Hinduism and Buddhism. Panini's Sanskrit is a great example of this approach.<br />
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Panini, the famous Sanskrit grammarian (along with Patanjali) is perhaps the most influential human that much of the world does not know much about. His fundamental contributions to linguistics more than 2000 years ago continues to transform the world in many ways even today. Noted Indian commentator, Rajeev Srinivasan, has recently penned a <a href="http://www.firstpost.com/india/the-sanskrit-non-controversy-why-it-is-indeed-a-superior-language-1813201.html" target="_blank">wonderful article</a> on Panini and Sanskrit. You can learn more about Panini's works by reading Dr. Subhash Kak's (OK State Univ) research papers (samples are <a href="http://www.ece.lsu.edu/kak/bhate.pdf" target="_blank">here</a> and <a href="http://arxiv.org/pdf/physics/0411080.pdf" target="_blank">here</a>). This blog was in part, triggered by this article, and talks about Sanskrit and its contextual optimizations.<br />
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<b>Abstract:</b> Sanskrit recognizes the importance of context. Two examples that show how Sanskrit is optimized depending on the context, in two entirely opposite directions, is shown below.<br />
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<b>Optimization-1</b>. The grammar is designed to be entirely context-free as Rajeev Srinivasan's article explains, and anticipated the 'grammar' of today's high-level computing language by more than 2000 years: precise with zero room for ambiguity of nominal meaning. To the best of my knowledge, punctuation marks are not required, and order of the words can be switched without breaking down, although there may be personal preferences for some orders over the others, and the sentence remains unambiguously correct. An optimization goal here therefore is to generate a <i>minimum </i>(necessary and sufficient)<i> </i>number of rules that result in an maximally error-free production and management of a maximal number possible variations of Sanskrit text. In this case, Panini appears to have achieved the ultimate goal of generating a minimal set of rules that will produce error-free text, forever. There are other well-known optimizations hidden in the structure and order of the Sanskrit alphabet - more on that later.<br />
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<b>Optimization-2</b>. The final interpretation of many keywords in Sanskrit ARE contextual. Which means there are multiple, related interpretations for some words that have a nominal/generic meaning, but you have to optimize the final interpretation at run-time by examining the context of usage, to recover the most suitable specific choice. If the first optimization helped eliminate fallibility, this second optimization in a sense re-introduces a limited fallibility and a degree of uncertainty and freedom by design! This feature has encouraged me to <i>reflect </i>(recall <a href="http://dualnoise.blogspot.com/2014/08/the-best-decisions-are-optimally-delayed.html" target="_blank">Ganesha and Veda Vyasa</a>), develop a situational awareness while reading, pay attention to the vibrations of the words, and grasp the context of keywords employed, rather than mechanically parse words and process sentences in isolation. A thoughtful Sanskrit reader who recognizes this subtle optimization comes away with a deeper understanding. For example, Rajiv Malhotra, in his book '<a href="http://beingdifferentbook.com/" target="_blank">Being Different</a>' (now in the top-10 list of Amazon's books on metaphysics) gives us the example of 'Lingam'. This can mean 'sign', 'spot', 'token', 'emblem', 'badge', etc, depending on the context. Apparently, there are at least 16 alternatives usages for 'Lingam' of which one best suits a given context is picked, and <u>not</u> simply selected at random. And of course, the thousand contextual names ('Sahasranamam') for Vishnu is well known in India. Some well-known western and Indian 'indologists' have ended up producing erroneous, and often tragic translations of Sanskrit text either because they failed to recognize this second optimization, or because they misused this scope for optimization to choose a silly interpretation, leading to comic or tragic conclusions.<br />
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Again, this contextual optimization approach by the ancient Indians is not just restricted to Sanskrit, but is employed gainfully in many areas, including classical arts, management, healthcare, ethics, etc., and of course dharmic religion. This contextual dharmic optimization has perhaps helped India in getting the best out of its diverse society, as well as keep its Sanskriti refreshed and refined over time. For example, the contextual ethics of dharma (ref: Rajiv Malhotra's book) has a universal pole as well as a contextual pole that allows the decision maker faced with a dilemma, to not blindly follow some hard-wired ideological copybook, but contemplate and <u>wisely</u> optimize his/her 'run-time' choice based on the context, such that <a href="http://dualnoise.blogspot.com/2013/11/optimizing-shubh-laabh-harmonious.html" target="_blank">himsa is minimized</a> (dharma is maximally satisfied). Some posts in this space has tried to explore <a href="http://dualnoise.blogspot.com/2013/03/conflict-resolution-3-contextual.html" target="_blank">the applications of this idea</a>'.<br />
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An <a href="http://dualnoise.blogspot.com/2013/09/sine-generator-in-aryabhatiya-1500.html" target="_blank">earlier blog</a> discussed a related example of seemingly opposite goals for contextual optimizations. When it came to mathematical algorithms, data, and linguistic rules in Sanskrit, a goal was to be brief and dense, minimize redundancy, and <i>maximize</i> data compression, so that for example, an entire Sine-value table or generating the first N decimals of <i>Pi</i> can be both encoded and decompressed elegantly using terse verse. Panini's 'Iko Yan Aci' in the Siva Sutras is a famous example of a super-terse linguistic rule. On the other hand, when it comes to preserving long-term recall and accuracy of transmission of Sanskrit word meanings <i>as well as</i> the precise vibrations of mantras (e.g. <a href="http://dualnoise.blogspot.com/2011/07/error-reduction-codes-hidden-in-vedic.html?q=chants" target="_blank">Vedic chants</a>) that are critically linked to the 'embodied knowing' tradition of India, the aim appears to be one of re-introducing controlled data redundancy to maximize recall-ability, and error-reduction. This optimization enabled Sanskrit mantras to be accurately transmitted orally over thousands of years.<br />
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To summarize, contextual optimization is a powerful and universal dharmic approach that has been employed wisely by our Rishis, Acharyas, Gurus, and thinkers over centuries to help us communicate better, be more productive, healthier, creative, empathetic, scientific, ethical, and interact harmoniously with mutual respect.<br />
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update 11/22/2014: 'optimize the final interpretation at parse-time / read-time' is the intent for optimization-2, rather than the computer-science notion of 'interpretation at run time'.Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-7435391049679382734.post-55319168355950206702014-10-25T17:13:00.000-04:002017-12-15T10:29:55.867-05:00Lassoing the Exponential<div style="color: #333333; font-size: 12.731481552124px; line-height: 19px;">
<span style="font-family: inherit;">An abbreviated version was blogged for the INFORMS 2014 annual conference as '<a href="http://meetings2.informs.org/wordpress/sanfrancisco2014/2014/10/25/not-particularly-hard/" target="_blank">Not Particularly Hard</a>'.</span></div>
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<span style="font-family: inherit;">While working on a new retail optimization problem a few weeks earlier, a colleague was a bit disappointed that it turned out to be NP-Hard. Does that make the work unpublishable? I don't know know, but unsolvable? No. The celebrated Traveling Salesman Problem (TSP) is known to be a difficult problem, yet Operations Researchers continue to <a data-mce-href="http://www.math.uwaterloo.ca/tsp/concorde.html" href="http://www.math.uwaterloo.ca/tsp/concorde.html">solve incredibly large TSP instances</a> to proven near-global optimality, and we routinely manage small TSP instances every time we <a data-mce-href="http://dualnoise.blogspot.com/2012/05/optimal-shoelacing.html" href="http://dualnoise.blogspot.com/2012/05/optimal-shoelacing.html">lace our shoes</a>. Why did I bring up laces? In a moment ...</span></div>
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<span style="font-family: inherit;">Hundreds of problems that are known to be difficult are 'solved' routinely in industrial applications. In this practical context it matters relatively less what the theoretical worst-case result is, as long as the real-life instances that show up can be managed well enough, and invariably, the answer to this latter question is a resounding YES. The worst-case exponential but elegant 'Simplex method' continues to be a core algorithm in modern-day optimization software packages. </span></div>
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<span style="font-family: inherit;">This issue of contextual optimization is not a new one. For some ancient people who first came across 'irrational' numbers, it was apparently a moment of uneasiness: how to 'exactly' measure quantities that were seemingly beyond rational thought. For some others, it was not much of an issue. Indeed, there is an entire body of <em>Ganitha</em> (the science of calculations, or mathematics) work in Sanskrit, the '<em>Sulba Sutras</em>', almost 3000 years old, where irrational numbers show up without much ado. 'Sulba' means rope or lace or cord. If we want to calculate the circumference of a circle of radius r, we can simply use (2πr) along with an approximation for 'π' that is optimally accurate, i.e., good enough in the context of our application. If we we did not have a good enough value for π, we could literally get around the problem: simply draw a circle of radius r, and line up a Sulba along its circumference to get our answer. For really large circles, we can use a scaled model instead of ordering many miles of Sulba. Not particularly hard. Encountering </span><span style="font-family: inherit; font-size: 12.731481552124px;">a really difficult optimization problem can be a positive thing, depending on </span><a href="http://dualnoise.blogspot.com/2012/07/ekthetikophobia-fear-of-exponential.html" style="font-family: inherit; font-size: 12.731481552124px;" target="_blank">how we respond to it</a><span style="font-family: inherit; font-size: 12.731481552124px;">. </span><span style="font-size: 12.5714282989502px;">Often, there are alternative approaches to business problems that at first glance, appear to have insufficient data: this tempts us to throw in the towel and send the problem back to the customer and say "infeasible" or "unbounded".</span><span style="font-size: 12.5714282989502px;"> Instead, we can </span><span style="font-family: inherit; font-size: 12.731481552124px;">use a S</span><span style="font-size: 12.731481552124px;"><span style="font-family: inherit;">ulba and Lasso our decision variables. This could well be an ORMS motto:</span></span></div>
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<span style="font-family: inherit;">"When the going gets NP-Hard, Operations Researchers get going" :)</span></div>
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Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-7435391049679382734.post-33883790563811434972014-09-06T11:52:00.002-04:002014-09-06T11:56:16.291-04:00Jugaad for Moto-E Video chatI recently got a family member in India a really cheap but very useful smartphone, the Motorola <a href="http://www.motorola.com/us/consumers/shop-all-mobile-phones/Moto-E/moto-e.html" target="_blank">Moto-E</a>.<br />
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<iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/v5Asedlj2cw" width="560"></iframe> <br />
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A problem is that this phone only has a front-facing camera. Moto-E holders have to turn the phone around for us to see them during a video chat, depriving them of a view. Of course, if both callers are using Moto-Es, video-chats get a bit more frustrating. A simple <a href="http://dualnoise.blogspot.com/2013/05/jugaad-innovation-stuck-in-local-optimum.html" target="_blank">Jugaad </a>to fix this is to have the Moto-E holders sit in front of a dressing mirror during the video-chat. I'm sure somebody figured this out long ago but I got a small kick out of it.<br />
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7435391049679382734.post-65048457585229973802014-08-30T12:10:00.001-04:002014-08-30T12:10:52.414-04:00The Best Decisions are Optimally DelayedThe lessons learned from the last few years of practice have convinced me that analytics and OR (OR = Operations Research), or at least MyOR is mainly about learning the art and science of engineering an optimally delayed response. Good analytics produces an optimally delayed response.<br />
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<script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>But why introduce a delay in the first place? Isn't faster always better? 'Science of better' does not always mean 'science of faster'. From age-old proverbs we find that in between 'haste makes waste or knee-jerk reaction' and being 'too clever by half' lies 'look before you leap'. If we view Einstein from an OR perspective: "Make things as simple as possible, but not simpler", the reason seems clearer. We must make situation-aware and contextually-optimal decisions as fast as possible, or as slow as necessary, but not faster, or slower, i.e., <span style="color: blue;">there exists a nonzero optimal delay for every response decision</span>. A middle path in between a quick-and-shallow suboptimal answer, or a slow-and-unwieldy 'over-optimized' recipe. Of course, one must work hard during this delay to maximize the impact of the response, and put <a href="https://en.wikipedia.org/wiki/Parkinson's_law" target="_blank">Parkinson's law</a> to good use, as suggested below:<br />
<blockquote class="twitter-tweet" lang="en">
<a href="https://twitter.com/hashtag/orms?src=hash">#orms</a> methods often *delay* product response to find superior answers. Tricky to pick optimal (delay, improvement) pair :)<br />
— (@dualnoise) <a href="https://twitter.com/dualnoise/statuses/495239957779206144">August 1, 2014</a><br />
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See <a href="http://dualnoise.blogspot.com/2013/01/being-optimally-sorry.html" target="_blank">this </a>old post on 'optimally delaying an apology' to maximize benefit to the <u>recipient</u>, or recall the best players of every sport being able to delay their response by those few <a href="http://dualnoise.blogspot.com/2009/05/longest-millisecond.html" target="_blank">milliseconds </a>to produce moments of magic, or Gen. <a href="http://www.americaslibrary.gov/aa/eisenhower/aa_eisenhower_dday_2.html" target="_blank">Eisenhower </a>delaying the call to launch D-Day. In the same way, a good OR/analytics practitioner will instinctively seek an optimal delay. For an example of this idea within an industrial setting, read <a href="https://www.ibm.com/developerworks/community/blogs/jfp/entry/optimizing_real_time_decision_making?lang=en" target="_blank">this excellent article</a> by IBM Distinguished Engineer J. F. Puget on taxicab dispatching that he shared in response to the above tweet. Implication: If your analytics system is responding faster than necessary, then slow it down a bit to identify smarter decision options. The 'slower' version of this statement is more obvious and is a widely used elevator pitch to sell high-performance analytics and optimization tools.<br />
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The history of the 'optimal delay' is many thousand years old, going back to the writing of the world's longest dharmic poem, the Mahabharata, which also includes within it, the Bhagavad Gita, one of the many sacred texts of Hinduism.<br />
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(pic link: http://www.indianetzone.com)<br />
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The story about how this epic came to be written is as follows:<br />
Krishna Dvaipana (the Veda Vyasa) wanted a fast but error-free encoding of the epic that could be told and re-told to generations thereafter. The only feasible candidate for this task was the elephant-faced and much beloved Ganesha, the Indian god of wisdom and knowledge, and remover of obstacles. The clever Ganesha agreed to be the amanuensis for this massive project on the condition that he must never be delayed by the narrator, and must be able to complete the entire epic in ceaseless flow. Veda Vyasa accepted but had his own counter-condition: Ganesha should first grasp the meaning of what he was writing down. This resulted in a brilliant equilibrium.<br />
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Veda Vyasa composed the Mahabharata in beautiful, often dense verse that Ganesha had to decipher and comprehend even as he was writing it down without lifting the piece of his tusk that he had broken off to inscribe, from the palm leaves. If Ganesha was too slow, it would potentially give Vyasa the opportunity to increase the density and frequency of incoming verses that may overload even his divine cognitive rate. If he went too fast, he would risk violating Vyasa's constraint. Similarly, if Vyasa was too slow, he would violate Ganesha's constraint. If he went too fast, his verse would lose density and risk becoming error-prone, and of course, then Ganesha would not have to think much and perhaps write it down <i>even </i>faster. Imagine if you will, a Poisson arrival of verses from Vyasa divinely balanced by the exponentially distributed comprehension times of Ganesha. Writer and composer optimally delayed each other to produce the greatest integral epic filled with wisdom ever known; written ceaselessly in spell-binding Sanskrit verse, without error, and flowing ceaselessly to this day without pause.<br />
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I can think of no better way to celebrate <a href="http://hinduism.about.com/od/festivalsholidays/a/ganeshchaturthi.htm" target="_blank">Ganesha Chathurthi</a> than to recall and apply this lesson in everyday life.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7435391049679382734.post-54779718362672620882014-07-05T10:02:00.000-04:002014-07-05T10:09:29.519-04:00Brief look at Soccer versus Basketball Foul ModelsIn Basketball, fouls are allowed up to a limit, and results in automatic penalties that turn into potential baskets and/or getting fouled out, once the limit is breached. Therefore, hoops foul-rules represent a capacitated model that comes with a marginal cost (dual value) and players have to pay a shadow price per foul and have to smartly manage this dual cost along as the game reaches its climax. In soccer, however, the foul model is uncapacitated, with little penalty unless it is a hard foul that invites a yellow or red card. In fact, soccer appears provide a net <i>incentive</i> to commit cynical and tactical fouls. Consequently, you often end up with foul-a-minute matches like the <a href="http://www.goal.com/en-sg/news/3999/world-cup-2014/2014/07/05/4937782/brazil-v-colombia-had-most-fouls-at-the-world-cup" target="_blank">Brazil-Colombia</a> world cup clash, where the game stops every few minutes and kills the momentum. <br />
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<b>It's just not cricket</b><br />
Soccer, like cricket, leaves part of the how ethically the game is played to the players. Cricket does this even more, and I personally love this decentralized approach that requires every individual to take responsibility for their actions to protect the integrity of their sport and their character (since it represents a dharma-karma like way of dealing with ethics), but off late, we see in both sports that this 'spirit of the game' has been sacrificed precisely when the stakes are the highest. Therefore, some centralized penalty approach that the American way of life prefers may be brought in to restore balance, unless the teams can reform themselves. I personally prefer a capacitated foul model in soccer.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7435391049679382734.post-46486888093314493602014-05-21T00:17:00.002-04:002014-05-21T20:29:52.375-04:00Predicting the Indian Elections - A Win for Data ScienceThe exit polls for the recently concluded Indian elections threw up a spectrum of results. Several Cable-TV networks ran their own polls, most of their numbers falling within a seemingly reasonable range, barring a public research group called 'Todays Chanakya', whose numbers were literally off the charts, predicting a massive win for Narendra Modi. People began to take averages of these polls to come up with an 'expected result', and many of these 'poll of polls' excluded TC's result as an outlier, discarding it as unbelievable.<br />
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I spent quite a bit of time looking at the meager information provided in the <a href="http://todayschanakya.com/">todayschanakya.com</a> (TC) website before the results were announced. Buzz-words aside, what caught my attention was the meticulous attention they paid toward obtaining a representative data sample in every single constituency. Their prior track record in predicting elections in India was simply stunning. In a recent state election too, their prediction was an outlier, and turned out to be accurate. This data sampling step is important, especially given the incredibly diverse nature of India's population. Translating projected vote-shares into actual seats won in India's 'first past the post' system is an incredibly daunting problem. If your sample is even slightly messed up, then your seat predictions can be way off, regardless of the sophistication of the predictive analytics you employ. <a href="http://cquotient.staging.wpengine.com/big-data-and-human-judgment/" target="_blank">Human judgment</a> and domain expertise is critical.<br />
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As <a href="http://learnandteachstatistics.wordpress.com/2012/01/26/sampling_error/" target="_blank">this</a> useful blog points out, it's not about 'sampling error', but sampling <i>bias</i>. And once we see this, it is not difficult to see why the English TV networks of India, virtually every single one a willing and well-compensated participant in the witch hunt of Narendra Modi since 2002, miserably fail in their predictions, time and again. Their reporting has rarely been fact-driven, and is usually ratings-driven. Few, if any on their payroll, are trained in the rigorous scientific method. Reporters appear to be hired based on ideology, west-accented English-speaking ability, and political connections rather than merit or technical proficiency. So, when by force of habit, you <i>look</i> for a sample that <i>you</i> like, then you will <i>only</i> get the predictions <i>you</i> want viewers to see in your TV shows, which has little to do with reality. The media <a href="http://www.manushi.in/bukfilm_detail.php?booksfilmsid=37" target="_blank">witch hunt against Modi</a>, like their exit polls, as is now known, was never fact-driven from day one. It was doomed from the start. After this election, few will take their "predictions" seriously again unless they reform.<br />
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<a href="http://todayschanakya.com/loksabha_result_2014.html" target="_blank">TC's predictions were quite accurate</a>. Modi indeed won in a landslide as they predicted, with the incumbent Nehru dynasty (aka "UPA" coalition) whose corruption almost surely qualifies as a crime against humanity, getting deservedly annihilated. On election day, at around 1-2:00 AM EST, while following the election trends, UPA was leading in about a hundred of the 543 seats up for grabs, way higher the predicted range of 61-79 seats that TC predicted they would get. However, as the day progressed, it was amazing to see UPA's leads petering out one by one, as if an invisible rope was magically pulling it back into the predicted range. Statistical destiny. Only two people appeared to be convinced about the result before May 16. TC, who adopted a <i>scientific</i> approach to gathering and analyzing data, and Narendra Modi, who created the history in the first place. Both of them dared to be different and put their reputations on the line, and were worthy winners.<br />
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This election result and Modi becoming the Prime Minister of India has taught many of us a scientific lesson. Data <i>science</i> is about being guided by facts, not emotion, or prejudiced opinion, or preferred outcome. Carefully constructed fact-driven methods are less likely to fail. Gujarat's development, both rural and urban, spearheaded by Modi for 12 years, is real, and cannot be falsified. It happened, and it is there to be seen regardless of what the New York Times tells you. <a href="http://dualnoise.blogspot.com/2012/12/the-scamster-versus-statesman.html" target="_blank">I blogged in 2012</a> that the heavy-lifting done in Gujarat may pay rich dividends in the future. The people <i>there</i> lived that development and they knew, and the thousands of migrants returned from Gujarat to other states to speak about their experience there. TC's data sample accurately reflected this reality. The media-heads sitting in Delhi, London, and New York were high on ideology-meth, low on fact. Few visited the state of Gujarat to make a factual assessment. Some of the open-minded critics who did, ended up becoming Modi's strongest supporters. Not surprisingly, his fact-driven campaign won him <i>every</i> single parliamentary seat there. The amazing number of Indians cutting across religious, class, language, age, gender, and geographical 'barriers', who voted for Modi, too cannot be brushed aside. Facts cannot be ignored until time-travel becomes practical.<br />
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And here's another prediction, an easy one. Modi will probably become India's best, and most unifying leader since Mahatma Gandhi, if he isn't already that. If, as the Nehru dynasty says, "power is poison", India has surely found their <a href="http://en.wikipedia.org/wiki/Samudra_manthan" target="_blank">Shiva</a>.Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-7435391049679382734.post-55286487297468311222014-05-14T22:30:00.000-04:002014-05-14T22:30:03.247-04:00Indian elections 2014: Long words, short storyCan long, archaic words be used to maximize overall brevity (and levity)? Take the 2014 Indian general elections that recently concluded. Although the final results will come out on May 16 (the amazing Narendra Modi as Prime Minister), exit polls already give us this clear-enough picture:<br />
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India has understood that the phoney "Idea of India" brand of secularism is nothing but <a href="http://en.wiktionary.org/wiki/antidisestablishmentarianism">antidisestablishmentarianism</a> in disguise, and we are witness to the historical <a href="http://dictionary.reference.com/browse/floccinaucinihilipilification">floccinaucinihilipilification</a> of the Nehru-dynasty by the Indian voter.<br />
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7435391049679382734.post-24286266716881701652014-03-04T11:38:00.000-05:002014-03-04T17:07:10.607-05:00Traveling Salesman Problem in a Portrait?<span style="font-size: small;">I'd planned to stop blogging until May this year to do my small bit in helping Narendra Modi become the next Prime Minister of India in the Indian general elections to be held very soon - one that will determine the future of my family there, as well as the destiny of 1.2 Billion Indians. India has suffered from a curse of culpable silence in the last ten years, but now it seems, that is changing, thanks to inspiring examples like these that asks people to come out and 'Vote for India' (thanks to <a href="https://twitter.com/sarkar_swati" target="_blank">@sarkar_swati, </a> faculty at U-Penn, for sharing <a href="https://www.youtube.com/watch?v=I75M3Vkc7ZA" target="_blank">this video</a>). </span><br />
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By sheer coincidence, this brief blog, like the previous one, is related to Asian (Japanese) art, and one i felt 'compelled' to do. Thanks to <span class="username js-action-profile-name"><a href="https://twitter.com/SimoneCerbolini" target="_blank">@</a><b><a href="https://twitter.com/SimoneCerbolini" target="_blank">SimoneCerbolini</a> </b>for sharing this beautiful portrait on twitter. What is interesting about this art is that it was done, as Simone tweets, using "a</span> single thread wrapped around thousands of nails. Artwork "Mana" by Kumi Yamashita"<br />
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<span class="username js-action-profile-name">The artist, </span><span class="username js-action-profile-name">Kumi Yamashita, has a <a href="https://www.facebook.com/KumiYamashitaStudio" target="_blank">facebook page</a>, and here is another picture from there.</span><br />
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<a href="https://scontent-a.xx.fbcdn.net/hphotos-prn1/t1/1017084_381046728663910_213776062_n.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://scontent-a.xx.fbcdn.net/hphotos-prn1/t1/1017084_381046728663910_213776062_n.jpg" width="452" /></a></div>
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<span class="username js-action-profile-name">The
effect is stunning, and one marvels at the human 'cognitive shift' that convinces us that within this collection of thread and nails, is a lady. Here is a brilliant talk by neuroscientist V. S. Ramachandran (</span><span class="username js-action-profile-name">Director, Center for Brain and Cognition, UC, San Diego) on</span><span style="font-size: small;"><span style="font-family: inherit;"><span class="watch-title long-title yt-uix-expander-head" dir="ltr" id="eow-title" title="Aesthetic Universals and the Neurology of Hindu Art - Vilayanur S. Ramachandran"> 'Aesthetic Universals and the Neurology of Hindu Art' that explains this in depth.</span></span></span><br />
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<iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/7ZTvHqM-_jE" width="560"></iframe>
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<span class="username js-action-profile-name">From the operations research perspective, we gravitate toward the
mathematical problem hidden in this portrait: determining the least
length of thread to traverse through all these nails. A mathematical optimization model that can be used to answer this question is the celebrated 'Traveling Salesman Problem' (TSP), which is known to be difficult to solve, in theory. In practice, however, extremely large instances have been solved to provable optimality.</span><br />
<span class="username js-action-profile-name"><br /></span>
<span class="username js-action-profile-name"><b> </b></span><span class="username js-action-profile-name">Here is <a href="http://dish.andrewsullivan.com/2013/05/19/face-of-the-day-165/" target="_blank">another page</a> that displays a collection of pictures from the artist's 'constellation series'. It also includes this ultra-close up that lets us see how the threading really progresses at the micro-level.</span><br />
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Each nail is traversed multiple times, and a greater density of thread is used to create a darker shade (e.g. the eye and the brow). Additionally, there appears to be a greater density of nails in that area. Can a thread-traversal path generated by a TSP solver (e.g. <a href="http://www.math.uwaterloo.ca/tsp/concorde.html" target="_blank">concorde</a>) produce a similar effect to the eye and the brain? I'm not sure, although it may still produce 'a reasonable picture of a lady'. If the density of nails is increased in these areas, then perhaps the TSP-artwork may do a good job. Alternatively, it may be possible to modify the TSP network structure to induce such an effect.<br />
<span class="username js-action-profile-name"><b> </b></span>Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-7435391049679382734.post-16657834220208823852014-01-25T19:49:00.000-05:002014-01-28T20:53:04.991-05:00Building the Unsolvable MazeI came across a tweet via <a href="http://en.wikipedia.org/wiki/Simon_Singh" target="_blank">Simon Singh</a>, famous writer of books based on math-topics. I've read a couple of them: 'Fermat's last theorem' and 'The code book'. His tweet points to a picture of an amazing maze hand-drawn over 30 years ago in Japan. Although it is supposed to be 'unsolvable', some comments there claim that it could be solved very quickly if it was made publicly available. Among the very first papers I read after coming to the U.S to study traffic engineering (to understand the reasons for India's chaotic, maze like traffic) was about <a href="http://en.wikipedia.org/wiki/Edward_F._Moore" target="_blank">Moore</a>'s algorithm entitled "shortest path through a maze". Mathematically, the shortest path problem formulation has a couple of properties of small interest in the context of this discussion. It has no duality gap, and is totally unimodular: It is sufficient to solve the continuous 'relaxation' to recover an <a href="http://ocw.nctu.edu.tw/upload/classbfs1211090940107417.pdf" target="_blank">integral optimal solution</a> to the primal or dual formulation. Wikipedia has a <a href="http://en.wikipedia.org/wiki/Maze_solving_algorithm" target="_blank">page</a> on maze-solving algorithms. Interesting as the optimization problem of finding an 'optimal route' to 'escape' this maze is, a more interesting question to me personally was: why would someone hand-build such an intricate maze over years; and then why not claim any credit for it? I have tried to interpret this based on my understanding of the Indian way.<br />
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(source link and main article at: <a href="http://imgur.com/gallery/4kyvVVb">http://imgur.com/gallery/4kyvVVb</a>)<br />
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The intense concentration required for such a task is surely daunting: to at once elevate one's consciousness while also dissolving one's <i>aham</i> (ego) that hinders the mind from systematically growing a complex maze whose paths increase rapidly over time as more forks and merges are constructed. Paths that stop even as they begin, paths that ultimately lead nowhere, paths where you travel for a while, only to discover that you are back where you were before... and then after a lot of calm, refined, and introspective searching (<i>not</i> suffering), finding a path that leads one to <i>satya</i> (ultimate reality/truth) that transcends the <i>maya </i>of the maze that held us in its thrall. A path that dissolves the noisy duality between the world within the maze and without, uniting them harmoniously into a unified whole, even as the space enclosed within the maze maintains a provisional identity within this overall unity. And then perhaps a realization that there could be a pluralism of such (alternative optimal) transcendental paths to <i>satya</i>. A harmonious unity within multiplicity that celebrates its diversity, rather than a synthesized unity derived by optimizing the goal of orderly sameness. The latter produces an efficient monoculture, but one that invariably regards pluralism as a seed of chaos. The former, <i>integral</i> unity best represents the nature of the underlying philosophical unity of India that has continually preserved and refined its dharma civilization over several thousand years. This forms the dharmic basis for any reasonable 'idea of India'. I look forward to reading <a href="http://indrasnetbook.com/" target="_blank">Rajiv Malhotra's new book</a> on this subject.<br />
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Journeys that traverse such a path have led to amazing discoveries that enlightened the world, and will continue to do so. Perhaps it produced this captivating art that simultaneously appeals to the casual observer, the artist, the seeker, and the analyst alike; yet each of us seeing only a partial facet of its underlying truth. A work of art to which its 'creator' deliberately did not append a signature to, and claim ownership of, perhaps unwilling to disturb it's harmony. That is the way of the Yogi.<br />
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<i>Dedicated to Rajiv Malhotra on the occasion of India's 65th republic day.Thank you.</i>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7435391049679382734.post-42877503265026320802014-01-19T09:20:00.002-05:002014-01-19T09:27:20.031-05:00The King and the Vampire - 3: The Flaw of Optimizing-On-AverageThis is the third episode of the 'King Vikram and the Vetaal' series.<br />
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(link: juneesh.files.wordpress.com)<br />
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<i>Dark was the night and weird the atmosphere. It rained from time to time. Eerie laughter of ghosts rose above the moaning of jackals. Flashes of lightning revealed fearful faces. But King Vikram did not swerve. He climbed the ancient tree once again and brought the corpse down. With the corpse lying astride on his shoulder, he began crossing the desolate cremation ground. "O wise King, it seems to me that your ministers are sometimes too quick in taking policy decisions based on an average scenario, ignoring the distribution. But it is better for you to know that such decisions invariably results in complaints. Let me cite an instance. Pay your attention to my narration. That might bring you some relief as you trudge along," said the Betaal, which possessed the corpse. </i><br />
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<a href="https://wordpress.com/imgpress?fit=1000,1000&url=http%3A%2F%2Fpryas.wordpress.com%2Ffiles%2F2009%2F06%2Fvikram_betaal1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://wordpress.com/imgpress?fit=1000,1000&url=http%3A%2F%2Fpryas.wordpress.com%2Ffiles%2F2009%2F06%2Fvikram_betaal1.jpg" width="481" /> </a></div>
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(pic source link: pryas.wordpress.com)</div>
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<i>The retailing vampire went on:</i><br />
Once there lived a retailer who always optimized his scarce resource constrained planning problems based on an average planning week. It was a quick and easy heuristic, and he claimed that it worked just fine. One day, an OR practitioner challenged this assumption, quoting points from the well-known '<a href="http://www.amazon.com/The-Flaw-Averages-Underestimate-Uncertainty/dp/1118073754" target="_blank">flaw of averages</a>' book, and said that with a bit more effort, and without increasing the problem size much, one can generate true optimal merchandising decisions by including all scenarios, using CPLEX. This would also be relatively more robust in reality compared to optimizing to the average. The retailer replied that while this issue was of theoretical importance, it did not matter much in practice, unless he saw some hard evidence. The practitioner decided to make an empirical point and proceeded to evaluate a number of historical instances by evaluating the recommendations generated by these two approaches over all the scenarios. In 75% of the instances, the practitioner's method yielded relatively better metrics, while in 25% of the cases, the retailer's average method did better. The retailer took one look at the results and said that the experimental setup was erroneous, inconclusive, and remained unconvinced.<br />
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So tell me King Vikram, Why did the retailer conclude the test setup was faulty? Was he correct in this assessment? Which method is better in the retailer's context? <i>Answer me if you can. Should you keep mum though you may know the answers, your head would roll off your shoulders!"</i><br />
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<i><i>King Vikram was silent, then closed his eyes, as if going into a Yogic trance in a moment of intense meditation. He reopened his eyes soon enough along with a smile, and then spoke</i>:</i> "Vetaal, unlike the last time, this one is pretty easy, so let's take the first question first.<br />
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1. The retailer felt the experimental setup was flawed because, if the practitioner's method truly yielded optimal solutions as claimed, then it should have done just as well or better in 100% of the instances.<br />
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2. However, the retailer was wrong because his old method optimized against constraints based on an average scenario. There is no guarantee that his decisions will be feasible to the original problem, over all scenarios. Therefore, in the instances where the old method did better, the recommendations had to be infeasible, since we cannot, of course, find a feasible solution better than an optimal one.<br />
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3. So we now know that the old method generated infeasible solutions at least 25% of the time. If we ignore these cases where we know it was surely infeasible, and look at the remaining 75% of the cases where it may have been feasible, it did worse 100% of the time due to a combination of suboptimality and overly-constrained instances.<br />
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In every case, the old method was either infeasible or suboptimal. The average-based heuristic must be discarded.<br />
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<i>No sooner had King Vikram concluded his answer than the vampire, along with the corpse, gave him the slip.</i></div>
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(pic source link: omshivam.files.wordpress.com)</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7435391049679382734.post-36090634157658784092013-12-30T13:09:00.002-05:002014-01-05T22:29:51.973-05:00Indian Intellectuals and the Fighter-Pilot Syndrome<b>Update: title changed</b><br />
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Legendary formula car racer Michael Schumacher suffered a serious <a href="http://www.chicagotribune.com/sports/motorracing/chi-michael-schumacher-head-injury-20131229,0,2225915.story" target="_blank">injury</a> in a skiing fall. As millions around the world pray for his safe recovery, a troubling question was triggered by this sad news:<br />
<br />
"How
likely is it for a skiing enthusiast, who is known to have made a successful career in the superfast and dangerous
world of Formula car racing, to meet with a skiing accident?"<br />
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Does this conditional probability increase or decrease? I am not aware that Schumi claimed he was a skiing expert or thought of himself as one. This is just a sample of one and could just be a tragic coincidence. The question remains open and the focus of this post is on a related topic. <br />
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Here's a wikipedia <a href="https://en.wikipedia.org/wiki/John_Stapp#Car_safety" target="_blank">blurb</a> on a US Air Force officer John Stapp:<br />
"<i>During his work at <a href="https://en.wikipedia.org/wiki/Holloman_Air_Force_Base" title="Holloman Air Force Base">Holloman Air Force Base</a>, Stapp became interested in the implications of his work for <a class="mw-redirect" href="https://en.wikipedia.org/wiki/Car_safety" title="Car safety">car safety</a>. At the time, cars were generally not fitted with <a class="mw-redirect" href="https://en.wikipedia.org/wiki/Seatbelts" title="Seatbelts">seatbelts</a>,
but Stapp had shown that a properly restrained human could survive far
greater impacts than an unrestrained one. Many traffic-accident deaths
were therefore avoidable but for the lack of seatbelts. Stapp became a
strong advocate and publicist for this cause, frequently steering
interviews onto the subject, organizing conferences, and staging
demonstrations (including the first known use of automobile <a href="https://en.wikipedia.org/wiki/Crash_test_dummy" title="Crash test dummy">crash test dummies</a>).
At one point, the military objected to funding work they believed was
outside their purview, but they were persuaded when Stapp gave them<b>
statistics showing that more Air Force pilots were killed in traffic
accidents than in plane crashes</b>. The culmination of his efforts came in
1966 when Stapp witnessed <a href="https://en.wikipedia.org/wiki/Lyndon_B._Johnson" title="Lyndon B. Johnson">Lyndon B. Johnson</a> sign the law making manufacture of cars with seatbelts (lapbelts at that time) compulsory..."</i><br />
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<sup class="reference" id="cite_ref-The_Fastest_Man_Alive_1-1"><a href="https://en.wikipedia.org/wiki/John_Stapp#cite_note-The_Fastest_Man_Alive-1"></a></sup><br />
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Controlling fast jets did not give those pilots additional skills that made them equally safe at driving <a href="http://www.improb.com/airchives/paperair/volume9/v9i5/murphy/murphy2.html" target="_blank">cars</a> at some speed. Is it possible that this 'fighter pilot effect' gave them a false sense of security while driving the much slower motor
cars? Similarly, safely driving ultra-fast cars shouldn't automatically make one an equally safe hi-speed skiing expert (<i>update</i>: initial reports indicate Schumacher was not going very fast). However, public belief in this 'fighter pilot
syndrome' appears to exist at some level, and this is especially
true in India. For example, if you win a Nobel Prize or for that matter, any prize in the west, then regardless of your field
of expertise and your near-total ignorance about what makes India tick, you are given special powers that turn you into an expert on every topic under the sun (especially Indian culture and politics), overnight. Unlike Marxist economist Amartya Sen or India's egoistic movie stars, who don't need a second invitation, there are others who prefer not to make a fool of themselves in public. However, the Indian media does not spare them the embarrassment by demanding their "fighter pilot" advice on unrelated topics. This 'intellectual celebrity' feedback is then used to try and influence public opinion. A good example is the recent NDTV-25 debate panel on "secularism in India" compered by 2G-scam tainted journalist Barkha Dutt that included exactly one genuine expert, <a href="http://www.youtube.com/watch?v=DGgHXE_7KqE" target="_blank">Arun Shourie</a>, who knew what he was talking about, and bunch of other "experts". <br />
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All-weather experts and their Indian media co-pilots must be asked to wear their seat-belts and slow down before they take the Indian public for a ride.<br />
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Happy New Year. Drive Safe. Get well soon, Schumi.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7435391049679382734.post-28472733280266600842013-12-09T18:59:00.000-05:002013-12-17T13:53:04.338-05:00Optimize Your In-store Holiday Shopping RouteRemember the last time you were <i>not</i> tired after holiday shopping in a busy mall, bulk shopping at a discount-club store, or weekend shopping at a crowded grocery store?<br />
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<a href="http://info.museumstoreassociation.org/Portals/97999/images/tired%20shopper.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="131" src="http://info.museumstoreassociation.org/Portals/97999/images/tired%20shopper.jpg" width="200" /></a><a href="http://binaryapi.ap.org/84b455e3f6c542e1b0e1f3fd07c7cf82/460x.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="132" src="http://binaryapi.ap.org/84b455e3f6c542e1b0e1f3fd07c7cf82/460x.jpg" width="200" /></a></div>
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(source links: <a href="http://info.museumstoreassociation.org/">http://info.museumstoreassociation.org</a>, <a href="http://binaryapi.ap.org/84b455e3f6c542e1b0e1f3fd07c7cf82/460x.jpg">http://binaryapi.ap.org</a>)<br />
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Hopefully, the simple and preliminary 'operations research (O.R)' analysis in this post can help make the experience a little less stressful and maybe even let us enjoy a bit of retail therapy that we can't get online. The shopping optimization problem addressed here is simple one, albeit with a twist. This post was triggered by an observation made after recent shopping expeditions to a nearby Costco outlet.<br />
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We have a long shopping list of L line-items (i) of various quantities N(i) that we have to pick up in a store. How should we optimally reorder our shopping list to reflect the sequence in which we pick up these items?<br />
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<iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/48cGEajWoyc" width="560"></iframe>
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<b>Version 1</b><br />
The simple version aims to minimize total shopping time. For example, we can formulate this as an instance of the so-called traveling salesman problem (<a href="http://en.wikipedia.org/wiki/Travelling_salesman_problem" target="_blank">TSP</a>) that finds the shortest sequence that starts at the entrance, visits each of the L 'cities' once, then the checkout counter, and ends at the store exit (entrance). A google search shows t<a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCwQFjAA&url=https%3A%2F%2Fmarketing.wharton.upenn.edu%2Ffiles%2F%3Fwhdmsaction%3Dpublic%3Amain.file%26fileID%3D3448&ei=pfelUsvTB67MsQTO3oKgCw&usg=AFQjCNEKDHCoUyLXVmnOVTTrp-UIiLQyQg&sig2=rYx79HbeU4NhNLK1xxDAvg&bvm=bv.57752919,d.cWc" target="_blank">his 2009 research paper </a>by researchers at UPenn, which shares the technical details and interesting results for this version.<br />
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To simplify our problem, we assume that the topology of the store is prior knowledge, and we can roughly pre-assign items in the same aisle to the same 'city'. The resultant problem is to find the order of visits to the aisles of interest to us. If the aisles are neatly arranged as node intersections in a rectangular grid, then we simply have to find the shortest rectilinear "Manhattan" distance tour in this grid. Depending on the type of the store, the store-layout itself may be optimized by the retailer based on the observed foot-traffic and 'heat-map' data. For example, it may be designed to retain the customer in the system to increase chances of purchase (exploratory tour, store selling expensive luxury/fashion products), or quickly out of the system (routine tour, obligatory products like groceries), or based on some other goal. Store space and layout problems are known to be commercially useful optimization problems in the retail industry.<br />
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Picture <a href="https://itunes.apple.com/us/app/concorde-tsp/id498366515" target="_blank">linked </a>from an <a href="http://itunes.apple.com/us/app/concorde-tsp/id498366515" target="_blank">iTunesApp</a> (Concorde) page of <a href="https://itunes.apple.com/us/app/concorde-tsp/id498366515" target="_blank">Prof. Bill Cook that solves TSPs</a> :)<br />
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<a href="http://a2.mzstatic.com/us/r30/Purple/v4/db/2a/3c/db2a3cf7-a3e0-b1d6-2da0-cb3468690be3/screen480x480.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://a2.mzstatic.com/us/r30/Purple/v4/db/2a/3c/db2a3cf7-a3e0-b1d6-2da0-cb3468690be3/screen480x480.jpeg" width="150" /></a></div>
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<b>Version 2</b><br />
Let us additionally assume that product attributes have an impact on our order. Suppose one or more items in our list is located in the frozen section at a grocery store, then we may prefer to get there at the end of our tour. Luckily, many stores appear to anticipate this (?), and locate this section towards the end of the store. Thus if 'maximum freshness' or 'minimum damage' is an additional consideration, this may alter the TSP route and the final ordering of items in our shopping list.<br />
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<b>Version 3</b><br />
This was the problem that was of immediate interest to me today. Costco sells stuff in bulk, so the items tend to be heavy, and considerable energy is expended moving the cart through the store. At the risk of mangling undergrad physics, let us proceed with our analysis...<br />
Let <span style="background-color: white; font-family: sans-serif; font-size: 12.666666984558105px; line-height: 19.19791603088379px;">μ </span>be the (constant) coefficient of rolling friction between the wheels of the shopping cart and the store-floor. Then the work required to move mass m through distance d = force x displacement =<span style="background-color: white; font-family: sans-serif; font-size: 12.666666984558105px; line-height: 19.19791603088379px;">μ</span>m<i>g</i>d, where <i>g</i> is the (constant) acceleration due to gravity. Thus a squeaky-wheeled cart will make us work extra hard. Speed of shopping is a consideration if we want to keep track of power (force x velocity). Covering the same tour length in half the time requires twice the power, i.e. the rate at which our body expends stored energy.<br />
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<b>Carry versus Cart (reinventing the wheel)</b><br />
If we had zero rolling friction, technically the only work involved is in lifting items and putting them in our cart. We can assume that this work is independent of our order of visit and is a fixed quantity. On the other hand, if we are not working with a wheeled-cart, but carry our stuff in a market-basket or shopping bags, then we have to raise the potential energy of the items to height 'h' (m<i>g</i>h) all the way until checkout, and also overcome the sliding friction between our shoes and the floor, which would probably be higher than the rolling friction, as illustrated below.<br />
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(link source <a href="http://static8.depositphotos.com/">http://static8.depositphotos.com</a>)<br />
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<b>Why is a shopping experience increasingly stressful over time?</b><br />
As we add items to our cart, the work done per unit time (power) required increases. In the continuous case, this problem closely resembles our '<a href="http://dualnoise.blogspot.com/2013/02/optimally-shoveling-snow.html" target="_blank">optimal snow shoveling problem</a>' analyzed during a February snow storm. The accumulated objective function cost there increases as the <i>square </i>of the distance. Here, we look at the discrete situation. When we visit city 'i' to pick up N(i) items each having mass m(i), we instantaneously add mass N(i) * m(i) that we have to lug around until checkout. After picking up k-1 items, my total work done will approximately be:<br />
<span style="background-color: white; font-family: sans-serif; font-size: 12.666666984558105px; line-height: 19.19791603088379px;">μ<i>g</i></span><span style="background-color: white; font-family: sans-serif; font-size: 12.666666984558105px; line-height: 19.19791603088379px;"> * </span>sum (i = 0,... k-1) W(i) * d(i, i+1), where i = 0, represents the store entrance, m(0) represents the mass of an empty shopping cart, and<br />
W(i) = sum(j = 0, .., i) N(j) * m(j) = total mass carried from city i to i+1.<br />
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In other words, the 'cost' accrued while traversing any pair of cities also depends on the items we picked up earlier, i.e., it is no longer memory-less and varies depending on the cities visited earlier.<br />
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<b>Result: our shopping gets increasingly more tiring over time</b><br />
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If one of the items in our shopping list involve a heavy item, then our optimal solution may no longer be the shortest time tour. We now have to solve a minimum-effort TSP. Operations Researchers have also looked at methods for solving a path-dependent TSP in the past. A simple heuristic approach would be to break the trip into two tours. The earliest items stay with us the longest, so we first find the optimal sequence through the light items, followed by the shortest tour through the heavy items. We also have to organize the shopping cart carefully enough to ensure that our light items do not get squished by heavy products, and our ice-cream doesn't melt. I'm sure there are better algorithms than the one provided here.<br />
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<b>Recommendation</b><br />
If we want to burn calories while shopping then a good way to do that, based on our previous discussion is (a) carry our items, (b) pick up the heaviest items first, and (c) take the longest route to <i>maximize</i> energy expenditure (d) walk briskly. <a href="http://health.mylaunchpad.com.my/fitness-exercise/article/articleid/227645/10-tips-to-lose-weight-while-shopping" target="_blank">This health-and-fitness article provides ten tips</a> for exercising that includes these ideas. For the rest of us who are looking to minimize effort, we simply do the opposite:<br />
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We sort our shopping list items in decreasing order of expected weight (frozen stuff goes to the bottom too), while also ensuring that the aisles of adjacent items in the list are close to each other, and we are not revisiting aisles or zig-zagging much. Some swapping may be required to find improved sequences. Many of us have probably evolved into efficient shoppers over time, and naturally take these steps and more, but if there an opportunity for improvement that the 'science of better' can uncover for us to make our shopping less stressful, let's take it.<br />
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Happy Holidays!<br />
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<b>Update 1: December 17, 2013</b><br />
IBM Smarter Retail <a href="http://insights-on-business.com/retail/this-holiday-season-lets-not-forget-about-the-store/" target="_blank">article </a>says:<br />
"..... <span style="background-color: white; color: #222222; font-family: Helvetica, Arial, sans-serif; font-size: 12.731481552124023px;">Most recently, Lowe’s has offered the customer a <b>product location functionality that is integrated with their wish list</b>. According to Ronnie Damron, .....Whether customers are browsing the store for ideas or searching for a specific item in a hurry, we think the <b>Product Locator feature will simplify the shopping process</b>, creating a better experience that encourages customers to come back again and again.”</span><span style="background-color: white; color: #222222; font-family: Helvetica, Arial, sans-serif; font-size: 12.731481552124023px;"><br /></span>Unknownnoreply@blogger.com13tag:blogger.com,1999:blog-7435391049679382734.post-15349198297590523382013-11-25T18:17:00.002-05:002013-11-30T10:32:21.963-05:00Optimizing Shubh Laabh: Harmonious Profitability<div>
<span style="font-family: Times, Times New Roman, serif;"><b><u>Sustainable machine-generated, data-driven decisions</u></b></span><br />
<span style="font-family: Times, Times New Roman, serif;">The growing popularity of 'Big Data' coupled with 'machine learning' techniques coincides with an increasing use of automated, machine-computed solutions for a a variety of business problems that were once solved and optimized based (predominantly) on human inputs. Machine-generated solutions have been shown to be superior to these previous methods on the measured performance metrics in many instances, and companies all over the globe have deployed advanced analytics and business optimization models (e.g. built using Operations Research) to achieve incremental profitability, cost reductions, or improved system efficiency. However, all is not well. Some solutions are sustainable, and work well over time, while others begin to run into a seemingly endless stream of human or environmental issues, and fall by the wayside. </span><br />
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<span style="font-family: Times, Times New Roman, serif;">What differentiates sustainable machine-generated optimizations from the unsustainable ones? The answer is not straightforward, and this post explores one aspect. For an example of what kinds of issues can crop up, s</span><span style="font-family: Times, Times New Roman, serif;">ee <a href="http://www.bbc.co.uk/news/business-25034598" target="_blank">this</a> BBC news article: "<span style="background-color: white; color: #505050; letter-spacing: -1px; line-height: 34px;">Amazon workers face increased risk of mental illness", as well as <a href="http://nautil.us/issue/3/in-transit/unhappy-truckers-and-other-algorithmic-problems" target="_blank">this </a>older article on 'unhappy truckers'</span>. </span><span style="font-family: Times, 'Times New Roman', serif;">A portion of the BBC article highlighted below is color-coded to show where sustainable decision optimization could be potentially applied to improve upon the status-quo):</span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="background-color: white; color: #505050; letter-spacing: -1px; line-height: 34px;"> </span><span style="background-color: white; color: #505050; letter-spacing: -1px; line-height: 34px;">".<i>.... </i></span><span style="background-color: white; color: #333333; line-height: 18px;"><i>Amazon said the safety of its workers was its "number one priority."</i></span></span></div>
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<i><span style="font-family: Times, Times New Roman, serif;">Undercover reporter Adam Littler, 23, got an agency job at Amazon's Swansea warehouse. He took a hidden camera inside for BBC Panorama to record what happened on his shifts.</span></i></div>
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<i><span style="font-family: Times, Times New Roman, serif;">He was employed as a "picker", collecting orders from 800,000 sq ft of storage.</span></i></div>
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<i><span style="font-family: Times, Times New Roman, serif;">A handset told him what to collect and put on his trolley. It allotted him a set number of seconds to find each product and counted down. If he made a mistake the scanner beeped.</span></i></div>
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<i><span style="font-family: Times, Times New Roman, serif;">"We are machines, we are robots, we plug our scanner in, we're holding it, but we might as well be plugging it into ourselves", he said.</span></i></div>
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<span style="font-family: Times, Times New Roman, serif;"><i>"We don't think for ourselves, maybe they don't trust us to think for ourselves as human beings, I don't know</i>.</span></div>
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<span style="font-family: Times, Times New Roman, serif;">.<i>....</i><i> </i><i>Prof Marmot, one of Britain's leading experts on stress at work, said the working conditions at the warehouse are "all the bad stuff at once".</i></span></div>
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<span style="font-family: Times, Times New Roman, serif;"><i>He said: "The characteristics of this type of job, the evidence shows increased risk of mental illness and physical illness.</i>"</span></div>
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<span style="font-family: Times, Times New Roman, serif;"><i><span style="background-color: white; color: #333333;">"</span><b><span style="background-color: white; color: blue;">There are always going to be menial jobs, but we can make them </span><u style="background-color: white;"><span style="color: #741b47;">better</span></u><span style="color: blue;"><span style="background-color: white;"> or worse. And it seems to me the demands of efficiency at the cost of </span>individual's<span style="background-color: white;"> health and </span>wellbeing<span style="background-color: white;"> - it's got to be </span></span><u style="background-color: white;"><span style="color: #660000;">balanced</span></u></b><span style="background-color: white; color: #333333;">.</span></i><span style="background-color: white; color: #333333;"><i>" </i>"</span></span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="color: #333333;"><span style="line-height: 18px;">I spent the early-mid 2000s redesigning, and improving airline crew scheduling optimization systems. This period also happened to be the industry's most </span></span><span style="color: #333333; line-height: 18px;">tumultuous:</span><span style="color: #333333; line-height: 18px;"> 9-11, out-of-control fuel and labor costs exacerbated by the invasion of Iraq, repeated strikes by various worker unions followed by contentious negotiations that lead to multiple CBAs (collective bargaining agreements) being ripped up and rewritten, and companies lining up to file for Chapter-11 bankruptcy protection, etc. Endless problems. The office atmosphere got quite intense when the R&D team somehow managed to find itself in the middle of these events, and facing heat from all sides (management, unions, soaring passenger complaints) on the kinds of solutions that were generated by our decision support systems (The US airline industry pioneered the use of such techniques). The analytical lessons empirically learnt from such episodes are hard to replicate in classrooms. One such lesson was "pay a lot of attention to the impact of your model on the people and environment". The application of this lesson has been explored in this space in a variety of contexts earlier: <a href="http://dualnoise.blogspot.com/2013/10/gandhi-and-operations-research.html" target="_blank">here</a> (Gandhi's methods), <a href="http://dualnoise.blogspot.com/2013/10/operations-research-for-smartgrid-1.html" target="_blank">here</a> (Smart-Grid), <a href="http://dualnoise.blogspot.com/2013/07/industrial-optimization-qwl.html" target="_blank">here</a> (Airline Crew scheduling), and <a href="http://dualnoise.blogspot.com/2013/03/conflict-resolution-3-contextual.html" target="_blank">here </a>(Conflict resolution). The issue is revisited here by borrowing an idea from traditional Indian business philosophy to see if new insight can be generated toward answering our question on sustainable business optimization.</span></span><br />
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<a href="http://www.indiabazaar.co.uk/images/product_image/Adhesive_Sticker_-_Red_Shubh_&_Laabh.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="161" src="http://www.indiabazaar.co.uk/images/product_image/Adhesive_Sticker_-_Red_Shubh_&_Laabh.jpg" width="320" /></a></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="color: #333333; line-height: 18px;">(pic link source: </span></span><a href="http://www.indiabazaar.co.uk/">http://www.indiabazaar.co.uk</a>)<br />
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<b>(Updated: November 30, 2013 Finally found the link to article that inspired this post)</b><br />
<span style="font-family: Times, Times New Roman, serif;"><span style="color: #333333; line-height: 18px;">It is interesting to note that for centuries, traditional business communities in </span><span style="color: #333333; line-height: 18px;">India had adopted the policy of </span><i style="color: #333333; line-height: 18px;">Shubh Laabh </i><span style="color: #333333; line-height: 18px;">(written in Hindi in the picture)</span><span style="color: #333333; line-height: 18px;">, which roughly translates into '<a href="http://centreright.in/2013/11/more-than-a-festival-deepavali/" target="_blank">auspicious/harmonious profit</a>' (Aravindan Neelakandan, co-author of 'Breaking India' in the linked article notes: "</span></span><span style="color: #333333; font-family: Times, Times New Roman, serif;"><span style="line-height: 18px;"><i>Lakshmi symbolizes the wealth that is holistic: it is wealth that puts welfare (Shub) before profit (Laabh)</i>." </span></span><span style="color: #333333; font-family: Times, 'Times New Roman', serif; line-height: 18px;">The pursuit of wealth and profitability was never frowned upon in Hindu society, while unconstrained profit maximization was recognized as a socially destabilizing and ecologically unsustainable objective. 'Shubh Laabh' recognizes and respects the presence of long-lasting and latent side-effects that arise from business decisions (that can bring you 'bad luck') and attempts to balance them equitably with the more immediate goal of profitability (Laabh). These traditional businesses employed some </span><span style="color: #333333; font-family: Times, 'Times New Roman', serif; line-height: 18px;">operational form of Ahimsa (the principle of minimal harm) to optimize Shubh Laabh</span><span style="color: #333333; font-family: Times, 'Times New Roman', serif; line-height: 18px;">:</span></div>
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<span style="color: #333333;"><span style="font-family: Times, Times New Roman, serif; line-height: 18px;">Rule a) limit harm (hard-constraint version)</span></span></div>
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<span style="color: #333333;"><span style="font-family: Times, Times New Roman, serif; line-height: 18px;">Rule b) minimize harm (soft-constraint version)</span></span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="color: #333333; line-height: 18px;">Let us see how this idea can be incorporated within modern decision optimization systems. </span></span><span style="color: #333333; font-family: Times, 'Times New Roman', serif; line-height: 18px;">Amazon appears to have satisfied all legal requirements via (a) by making safety a top priority. It has probably ensured that the statistical rate of accidents is below some stringent threshold. In the airline world, (a) is achieved by ensuring total compliance with respect to all FAA- and CBA-mandated safety rules. However, this represents a necessary condition that tolerates a certain level of error as 'legally acceptable collateral damage'. The resultant formulation is: maximize profitability subject to safety regulations. However, this in itself is an insufficient specification if we want our algorithms to <i>minimize </i>harmful side-effects. </span><span style="color: #333333; font-family: Times, 'Times New Roman', serif; line-height: 18px;">A</span><span style="color: #333333; font-family: Times, 'Times New Roman', serif; line-height: 18px;">n Ahimsa-based model would additionally consider (b) and eschew profit achieved at the cost of a reduced employee quality-of-work-life (QWL) or environmental degradation, as unsustainable and counterproductive in the long run. </span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="color: #333333; line-height: 18px;">For large-scale systems such as a retail supply-chain or airline crew schedules, a reasonably skilled analytics professional should be able to incorporate requirements (a)-(b) within their decision support algorithm which, among alternative near-optimal solutions (and there are often many of these), selects one that </span><u style="color: #333333; line-height: 18px;">also</u><span style="color: #333333; line-height: 18px;"> maximizes worker QWL, and/or minimizes harm (e.g. reduces carbon footprint). This requires the human-and-environment-variables in the system be treated <i>positively</i> as an active and equal partner based on mutual </span><span style="color: #333333; line-height: 18px;">respect</span><span style="color: #333333;"><span style="line-height: 18px;">, by explicitly including their requirements as part of the primary goal (objective function), going beyond a legalistic/adversarial approach of treating these variables as a 'loss-making noise that has to be managed' by specifying a minimum </span></span><span style="color: #333333; line-height: 18px;"><span style="text-decoration: underline;">tolerance constraint</span>.</span></span></div>
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<span style="color: #333333; font-family: Times, Times New Roman, serif; line-height: 18px;"><br /></span><span style="color: #333333; font-family: Times, Times New Roman, serif; line-height: 18px;"><b><u>To summarize</u></b></span><br />
<span style="color: #333333; font-family: Times, Times New Roman, serif; line-height: 18px;">It is possible to achieve sustainable profitable solutions via automated decision support systems that are also harmonious and sustainable, by paying due respect to <i>all </i>the stakeholders (including Ms. Nature), right from the design phase.</span><br />
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<span style="color: #333333; font-family: Times, Times New Roman, serif;"><span style="line-height: 18px;">An old blog discussed </span>Rajiv Malhotra's<span style="line-height: 18px;"> use of '</span><a href="http://dualnoise.blogspot.com/2012/01/working-multicultural-model-necessary.html" style="line-height: 18px;" target="_blank">mutual respect</a><span style="line-height: 18px;">' (as opposed to mere tolerance) as a simple but powerful basis for two heterogeneous groups of people, or people subscribing to conflicting thought systems, to achieve a fair and sustainable equilibrium in their interactions. It appears that such a mutual respect:</span></span><br />
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<span style="color: #333333; font-family: Times, Times New Roman, serif;"><span style="line-height: 18px;">a) is implicitly present in the idea of Shubh Laabh, which in turn</span></span><br />
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<span style="color: #333333; font-family: Times, Times New Roman, serif;"><span style="line-height: 18px;">b) can be employed as a key guiding principle of 'sustainable design' when building decision support algorithms for managing complex business problems, where multiple, and potentially conflicting, goals have to be delicately balanced.</span></span></div>
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<i><span style="font-family: Times, Times New Roman, serif;">The opinions expressed in this article are personal.</span></i></div>
Unknownnoreply@blogger.com21tag:blogger.com,1999:blog-7435391049679382734.post-29321936541135126512013-11-20T19:01:00.001-05:002013-11-20T19:01:23.677-05:00Optimizing a Kid's Birthday PartyThe previous post was about virtual books. This brief post is about children's books, and the nice idea of requesting kids to bring their used books to a birthday party. Suppose there are N kids, with kid(i) bringing book-set B(i). The optimization problem is fairly simple to state. Get the kids to exchange their books in such way that total satisfaction is maximized after the exchange.<br />
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A distributed optimization approach could, for example, let kids do their own thing and perform <i>two-opt</i> book swaps until every kid achieves their user-optimal solution, or no candidate is available for swapping.<br />
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A centralized optimization scheme may require a parent to create a library of sum(i)|B(i)| books, acquire book-attribute preferences from kids, the attribute vector for each book, and using this information to (informally) solve a partitioning problem that assigns |B(i)| books to kid(i) such that it maximizes the preference sum.<br />
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A Karmic optimization approach, which I personally prefer, could let the kids enjoy the cake and ice-cream, while a parent mixes the books up and organizes a fun lottery where the books pick the kids.<br />
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Regardless of how the books are assigned, if we do this over a sufficient number of birthday parties, the kids would eventually get to read a variety of books at no extra cost.<br />
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<br />Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-7435391049679382734.post-683058410206720962013-11-08T13:25:00.001-05:002013-11-09T12:42:19.882-05:00Optimizing Kindle Book Rentals<b>When to buy at Amazon</b><br />
Amazon just raised their 'free shipping' threshold to 35$, a few weeks before the holiday shopping season. This simple '<a href="http://dualnoise.blogspot.com/2012/12/entropic-decision-optimization-using.html" target="_blank">entropic optimization</a>' approach, which utilizes Amazon's wish list to time-prioritize purchases remains valid, but requires an increased level of procrastination. What also caught my attention is Amazon's Kindle rental models. Beyond the initial sunk costs, virtual products are high margin, with negligible holding cost, besides an infinite, instantaneously replenish-able inventory. They are also scratch/damage proof. The only long-term downside to providing a renting option appears to be faulty pricing. If we price too low, we may turn many potential buyers into renters, and a high price may discourage potential renters. Let's look at a couple of (real) Kindle rentals for which I laboriously pulled data while watching Sachin Tendulkar's 199th cricket test match.<br />
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<b>Kindle Book 1 (Undergrad Math textbook)</b><br />
The minimum rental period is 60 days (50$), and the maximum (apparently) is around 360 days (140$), with the marginal price held approximately constant. We pay 30 cents for every extra rental day beyond the minimum period.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-7KBPFgUwvGA/Unz4zg1lJlI/AAAAAAAABLg/vrrD4ZLwJyw/s1600/rentalbook1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="313" src="http://1.bp.blogspot.com/-7KBPFgUwvGA/Unz4zg1lJlI/AAAAAAAABLg/vrrD4ZLwJyw/s640/rentalbook1.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Kindle Book 1: Price Versus Rental Days</td></tr>
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The cost (snapshot at the point of observation) of purchasing a permanent copy was 200$. If we plot the percentage price discount versus the rental period expressed as percentage of a year, we can see that the discount varies between 25% and 70% of the full cost. Approximately linear model employed for this book. Here, we can rent the book for an entire year without paying the full price.<br />
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<tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-5tZYj_Q_xVw/Unz4zilMC1I/AAAAAAAABLc/KAS-RYkCUeU/s1600/kindle_rental2b.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="270" src="http://2.bp.blogspot.com/-5tZYj_Q_xVw/Unz4zilMC1I/AAAAAAAABLc/KAS-RYkCUeU/s400/kindle_rental2b.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Price Discount Percentage versus Rental Percentage-of-Year<br />
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<b>Kindle book 2 (Advanced forecast-modeling textbook)</b><br />
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The second example is a bit more interesting. The content is technically far more sophisticated compared to Book 1, but the target market is different, and the number of (paper) pages is far lower, and so is the price. In both instances, the cheapest rental can be purchased at less than half the full price. There are roughly three different marginal prices employed within a rental period that varies between a minimum of 30 days (~$15) and a maximum of 365 days (~$35, also the full Kindle price). The corresponding breakpoints occur (roughly) near the 90-day, and 180-day rentals, respectively. If we restrict our attention to this rental time period, the price is concave, with the marginal prices decreasing as the rental period increases. It is preferable to simply buy the book rather than rent it for close to a year.</div>
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<tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-1fzxH22-kbM/Unz8QSjZNII/AAAAAAAABL0/xZ0sifVP8v0/s1600/kindle_book2a.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="540" src="http://2.bp.blogspot.com/-1fzxH22-kbM/Unz8QSjZNII/AAAAAAAABL0/xZ0sifVP8v0/s640/kindle_book2a.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Kindle Book 2: Piece-wise linear rental pricing</td></tr>
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A percentage based plot is show below, along with an empirical power-law pricing model (using Open Office) that looks like a near-perfect fit for this particular book rental. A log(x) model also works well in this instance.<br />
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<a href="http://1.bp.blogspot.com/-lGfl4xatcw0/Unz_5VzUc5I/AAAAAAAABME/v_GE1VOsFD8/s1600/kindleboo2c.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="464" src="http://1.bp.blogspot.com/-lGfl4xatcw0/Unz_5VzUc5I/AAAAAAAABME/v_GE1VOsFD8/s640/kindleboo2c.png" width="640" /></a></div>
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<b>Optimization Models</b></div>
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<b>Seller</b>: How would optimization scientists go about determining these marginal rental prices? Suggestions welcome. Perhaps ideas from analytical rental models for other products (cars, houses, equipment ...) can be used as a starting point to figure out this "information rental" model. Perhaps the pricing model can be initialized using historical rental data gathered for similar books. This being an online retail sales model, we can dynamically and frequently update these models or their parameters to maximize performance metrics. </div>
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<b>Buyer: </b>From a user-perspective, if we can assign a value for owning a permanent copy, and have an informal mental model of the temporal utility of a rental as T(x), then (for example), we could solve some variation of this single-decision problem in 'x':</div>
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Maximize Value V = T(x)/f(x) (<span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 16.203702926635742px; line-height: 23.998119354248047px;">⇒</span> Maximize log T - log f, optionally)</div>
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<span style="background-color: white;">l <span style="font-family: Verdana, Tahoma, Arial, sans-serif; font-size: 12.731481552124023px; line-height: 16.999420166015625px; text-align: -webkit-center;">≤</span> x <span style="font-family: Verdana, Tahoma, Arial, sans-serif; font-size: 12.731481552124023px; line-height: 16.999420166015625px; text-align: -webkit-center;">≤</span> u</span><br />
to determine an optimal 'rent versus buy versus walk-away' decision based on our willingness-to-pay. Assuming a 1:1 mapping between 'f' and 'x', so we could transform any price range limit into an equivalent (l, u) bound on 'x'.<br />
A simple way to solve this problem is to enumerate the values of V for all rental days using a spreadsheet.<br />
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<b>Renting digital textbooks over a semester</b><br />
Like thousands of Indian immigrants in the U.S, I came on an assistantship, carrying a couple of hundred bucks in my pocket that represented a big chunk of my parent's savings. I actually felt rich when I discovered that the take-home monthly income from my research assistant-ship after tuition fees turned out to be more than what my engineer dad was earning after decades of dedicated service in Nehruvian India. Until I saw the prescribed textbook prices, that is. Buying overpriced books was simply out of the question when the few copies in the library were already taken. There was no Amazon then, and it would've been amazing to have a rental option like this, especially when continued funding is dependent on maintaining good grades.<br />
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For example, if we only cared about a textbook for portions of a semester (our total planning horizon), and our total price budget is 'pmax', then we can informally solve a multiple-period version of the above optimization model to come up with a best <i>waiting strategy</i> and rent for one or more time periods ("quiz time") which maximizes our total T(x) and also keeps us within our "knapsack" like price budget for the semester. This policy of "rent as needed" may work well with book rentals having a constant marginal price. On the other hand it may be worthwhile renting fewer times for an optimally longer duration if the price is concave in the length of the rental, as it is in our second instance. </div>
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