Driving on 'E': Mad Max and OR

While doing my commute to work yesterday on the parkways of NY:

9 AM: fuel indicator hits 'E' and still some distance from the destination. After an initial surge of panic, like any good OR person i decided to build a quick inventory model of the quantity of gas (that would 'petrol' if you are Indian) held in my car. With all those NY drivers racing at breakneck speed (like those Mohawked goons from the Aussie outback in 'Mad Max'), doing real-time inventory optimization and driving safely is not easy.

9:10AM: Consciously slow down inventory depletion rate. Stay within your auto's fuel efficient range around 45-55 mph. Resist the urge to go too slow or too fast. Turn off heating - maybe that would help too.

9:12 AM: Toyota surely must have sound safety stock calculations thrown in to calibrate the fuel meter, so 'E' is more likely to be the 'replenishment point' rather than a truly empty "back order" point. Reasoning helps reduce panic. It's a new job in a new geographical area, but the car is the same old and trusted sedan.

9:15AM: Use GPS to locate nearest replenishment point. The nearest one was just 2 miles away. Good. When I get to that spot, there's just a pile of snow. Data issues with the GPS.

9:20 AM: Do I trust the GPS and search for another gas station or do I head to the office and postpone my decision to refill on return? feeling confident that there is enough in reserve, I head straight for the office staying on the highway, where cars are more fuel efficient, and make it, and park the car in the shade.

12PM: Offline analytics to plot return trip in the evening. I find this really great site. For an input car make and model, it displays the sample mean and deviation. I was not even close to riding on the edge. The distribution of gas miles after hitting 'E' shows a mean value of about 45 miles and a standard deviation of 25. Some road warriors appear to have done a hundred or more. There was one who apparently refueled his tank with 18.064 gallons and must have been running on fumes. On the other hand, the minimum value is 2.0 miles, indicating that there was a reasonable expected cost of being stranded in sub-zero conditions on a highway looking foolish and may yet be stranded in the office.

5PM: Decision optimization time. Do I bet on the analytical model and drive home to refuel at the gas station that (certainly) existed today morning next to my residence and also sells cheaper gas? or do I head for the nearest gas station from my current location? If I head home, I have roughly a 2/3 data-driven chance of making it based on the normal distribution fit to the curve on tankonempty.com. Despite this comfortable probability of success, I realize that it's relatively easier selling OR models to others. Furthermore, what happens if I'm stuck in a return-commute traffic jam? I decide to leave a little later to avoid peak traffic. However, if I can locate a gas station closest to a point on my shortest path to home, then that is an optimal route. The treacherous GPS will (hopefully) redeem itself and find a good solution to this tiny traveling salesman problem.

View Larger Map

5:45PM: The GPS is wrong. Twice in a day! I expended about 6 miles on this wild goose chase and burnt valuable daylight as well. I am no closer to home, my tank is still on 'E', my night vision is poor, and i'm freezing. I figure my odds have dropped close to coin-toss range. The GPS has been a let down as far as finding non-fictional gas stations for this highly wooded area that is still new to me. Given the darkness, I think I'm doing the sensible thing by assuming that the conditional probability of hitting a gas station given that we choose local roads (closer to residential areas), is higher. I ask Cassius to re-route me off the parkways, keeping in mind the drop in fuel efficiency on local roads, which is about 30% for my car.

6:00 PM: Despite driving at low speeds, I find a gas station within 4 miles and shell out 61$ for the 'juice'. I find that I had almost a gallon in reserve, safe and warm enough to just about take me home if I drove along the highway at optimal speeds in the first place. If only my night vision was as good as my hindsight. In the end, I was just another data blip that was pretty close to the median on the 'E' curve. Mad Max I was not. That and the fact that I don't have a spunky dog riding with me, nor a sawn-off shotgun.