Mumbai Dabbawalas: Operational Excellence Based on Trust Chains and dharma

Most 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 'six sigma' 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 hundred years now. As background, here 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 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:
how can they sustain this? and why do they?

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'.

How do they sustain it?
We turn to Prof. P. Kanagasabapathi's gem of a book "Indian Models of Economy, Business and Management (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 real part works, read this book, and Dr. R. Vaidyanathan's equally brilliant 'India, Uninc'. Both are data-driven 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.

Let us see what Prof. PKS has to say (emphasis in bold / square bracket is mine):

"...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.

"....see how the supply chain management works. The dabba-wallas are semi-literate people, with rural backgrounds from Pune district. They belong to the warrior [clan] of Malua, which fought for [the great Indian king Shivaji] 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 only one mistake for eight million deliveries "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, 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? 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.

We start to get some answers above on the 'how'. Now we turn to find answers for how they're able to sustain this:
".. community relationships provide certain benefits and cost advantages in business. One is trust, which is very important for business. 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..."

Trust. 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:
"The ability to associate depends, in turn, on the degree to which communities share norms and values and are able to subordinate individual interests to those of larger groups. Out of such shared values comes trust, and trust, as we will see, has a large and measurable economic value." Trust results in `social capital.'"

Trust can arise out of that bi-directional relationship called mutual respect. This blog 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:
"From time immemorial, groups of people have created strong communities, based on commonly observed rules and mutual self-help. 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..."

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.

Why do they?
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)




The Dabbawalas are doing their dharma, their cosmic duty. This idea of cosmic/sanctity implies an unmanifest motive to their duty. The effect 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 seva.  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 shubh laabh, 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.

Brief look at Soccer versus Basketball Foul Models

In 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 incentive to commit cynical and tactical fouls. Consequently, you often end up with foul-a-minute matches like the Brazil-Colombia world cup clash, where the game stops every few minutes and kills the momentum.

It's just not cricket
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.

Optimizing a Kid's Birthday Party

The 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.

A distributed optimization approach could, for example, let kids do their own thing and perform two-opt book swaps until every kid achieves their user-optimal solution, or no candidate is available for swapping.

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.

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.

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.

Being Optimally Sorry: When to Apologize?

A Delayed Apology
This post examines modeling ideas related to the timing of an apology in a two-person scenario that results in a maximally effective 'sorry'. We optimize timing here not to maximize own benefits (user optimal), but on the basis of mutual respect, to express regret and maximally repair the damage in a timely manner that most helps the subject (recipient optimal). We start with the findings in Frank Partnoy's book "Wait: the Art and Science of Delay". It's one of the many useful books in the last couple of years that analyze human decision making. We introduce a mental decision support model for a timely apology that is derived from decision analytical methods employed in an industrial setting.

Objectives and Constraints
Justice delayed may be justice denied, but an apology that is optimally delayed may not be such a bad thing. The 'Wait' book recognizes the existence of a suitable time to apologize, and notes that the fastest apology in not necessarily the most effective. Given that we may have to apologize more than once, in general we have to determine an optimal trajectory of timed apologies. Thus, our goals are to:
i)   apologize at least once,
ii)  in a timely manner, and
iii) within a finite time horizon, such that
iv) a measure of the recipient's benefits is maximized

'Wait' notes:
"... Saying you are sorry is always better than not apologizing at all. But as with the first study, the students felt better about a delayed apology: “Improvement in the late apology condition was significantly greater than improvement in the early apology condition.” In fact, a statistically significant improvement in the students’ reactions occurred only in the late apology condition, when there was a chance for them to discuss what had happened and why. Overall, these studies suggest that the relationship between apologies and timing follows a “bell curve” distribution: effectiveness is low at first, then rises, peaks, and ultimately declines."

(It seems that these ideas are related to the complementary 'problem' of delivering the most time-effective 'Thank You')


We can see that the timing-effectiveness curve described in the book extract above is related to the subject's level of distress/angst (which we represent as 'entropy') that follows a similar trajectory of rise, cruise, and a gradual demise. Depending on the person, the 'cruise' and 'demise' portions can last long and result in a very fat-tailed distribution. But before we get into 'when', a quick comment from the book on the what/why/how questions:
".... effective apologies typically contain four parts: 
1. Acknowledge that you did it. 
2. Explain what happened. 
3. Express remorse. 
4. Repair the damage, as much as you can."

Searching for the Optimal Timing
'Wait' notes:
"The art of the apology centers on the management of delay. For most of us, the lesson is that the next time we do something wrong to a close friend or family member, or say something at work we wish we could take back, we should try to imagine how the victim might react to an apology tomorrow instead of today, or in a few hours instead of right now. If delay will give a friend or relative or coworker a chance to react, to voice a response and prepare themselves to hear our regret, the apology will mean more later than right away."

In other words, the timing has to take into account where the subject is located in their entropic life cycle: is the person likely to be getting angrier by the hour now (positive entropic gradient), or has reached the peak and is calming down (negative entropic gradient). To formulate a model based on these observations, we borrow ideas from a classical inventory management problem analyzed in retail operations research: Markdown Optimization (MDO).

An Optimization Model
MDO is employed to manage an inventory of short-life cycle (SLC) products that are manufactured pre-season, with the (sunk) costs paid up-front. Thus MDO typically focuses on total revenue earned in-season. Analogously, we already messed up in the beginning incurring an irreversible cost, and thereafter it costs relatively little to issue a sincere apology.  Retailers employ a cadence of optimally delayed price cuts to smartly boost the end-of-season demand rate so as to maximize revenue over the remaining life of the product. Like MDO, we eventually have to solve an entropic inventory depletion problem: optimally alter the entropic gradient via one or more carefully timed apologies, which will (ideally) reduce the inventory level to zero within a finite time period.

Disclaimer: The postulated model is not assumed to be the most suitable or even a "correct" one for this problem, but merely a useful starting point. Some brief comments on the modeling elements, next.

a. Life-cycle of the entropy
SLC products (like designer fashion apparel) often have little to no historic data early in the season, and retailers may borrow results for a comparable historical "like-item" to produce an initial prediction and then continually update their sales projection based on in-season demand. Here, we play the role of a 'like-item' and place ourselves in the recipient's shoes to better appreciate the degree of distress caused and the impact it will have on the recipient over time. The entropy level is an uncertain quantity that must be learned, but its 'mean value' is assumed to representable using an approximately concave function like the one shown in the figure below. Note that unlike the MDO case where inventory is always non-increasing, entropic inventory initially increases before gradually decreasing.

b. Elasticity of the entropy with respect to an apology

Elasticity ~ % change in entropy / % change in regret and effort, as perceived by the subject
 
A simple model like the inverse square law that abounds in nature (elasticity = -2) may be a good starting point. Ill-timed and empty-sounding apologies may have zero elasticity and do little to reduce entropic inventory. A careless apology can result in an entropic spike ("adding insult to injury"). On the other hand, an apology that is 'deep and sincere' and well-timed can be expected to have a calming effect.

c. Timings
Optimally timing a single apology requires impeccable timing. On the other hand, randomly distributed, and incessant apologies may not be helpful either. A premature apology (e.g. around an increasing entropic gradient) that kicks the can down the road is a greedy approach that may be counter-productive. Thus, optimally timing multiple apologies can require a degree of coordination between decisions. Today's apologize-or-delay decision will impact the timings of future decisions, so we have to holistically manage the impact on the entropic life-cycle. 

Often, despite our best efforts, the damage can never be fully repaired. Note that our objective function was setup to be indifferent to personal benefits. To paraphrase a profound Indian saying: "You have the right to optimize, but not to the fruits of your actions". Regardless of the outcome, a sincere and optimally timed apology is good Karma.

How long is a game of snakes and ladders?

The detailed answer can be found here. You can stop right now or roll the dice and play on ...

The game originated in India more than 800 years ago and is still popular there. Other board games (Chaturangam or chess, and Pachisi or Ludo) also originated here, and a future post will explore the familiar stochastic OR topic of 'a gambler's ruin' in ancient India. Here's a picture of a native SNL board. The original Indian name of the SNL game translates to 'the path to salvation' and was supposed to be morally educational as well as enjoyable for kids. It's actually pretty profound.

From an Operations Research perspective, the game can be modeled as a Markov Chain. The moral lessons for kids in the Markovian property of SNL seems to be that no matter how terrible a path you took to get to a certain point, you retain the same possibility of salvation by consistently performing good deeds. Note the absence of any non-Markovian historical baggage of original sin. Similarly, a lifetime of virtuousness can be temporarily undone by a single big act of indiscretion that can literally bring you back to square one. As kids, we always felt nervous about the long snake lurking around the 99th square waiting to yank us down.

Per the paper (linked above) published in 1993, simulations indicated that the average number of moves for a 10X10 square game of SNL was around 39. More precisely, using the Markov Chain state transition equations, the authors (Althoen, King, and Schilling) calculate the exact expected number of moves in the "Milton Bradley version of Chutes and Ladders" to be equal to this impressive but twitter-unfriendly ratio:

225837582538403273407117496273279920181931269186581786048583
5757472998140039232950575874628786131130999406013041613400

or approximately 39.2. Other interesting results based on a sensitivity analysis of this value wrt adding or dropping snakes and/or ladders include:
- a six-sided die based game of SNL with no snakes or ladders lasts around 33 moves on average. A unit snake seemingly prolongs the game more than a ladder can speed it up. I felt that pretty acutely as a kid. Yet again, in true Steve Jobsian fashion (or maybe not), it turns out that the seemingly idle SNL time in Bangalore, India was a solid foundation for a career in O.R practice.