Finding an Optimal Refill Strategy
For some reason or another, I have a tendency to have to do everything in my life in the most efficient way possible. I’m not sure exactly why… it’s just my nature. It’s this tendency that makes me think of things like: “Would it be more cost effective for me to refill my tank more frequently at lower gas prices than to wait and refill the whole thing at a higher price?”
It’s no secret that gas prices have been steadily rising over the past couple years. And between my fairly fuel efficient car, my relatively short commute, and the fact that otherwise I don’t really go… anywhere else, I don’t spend as much on gas as I could. However, is it possible to save more?
Between my Computer Science education and my current job as a reports analyst, my first reaction in these types of situations is to write a simulation program. So that’s what I did.
The short answer? Yes. The long answer? No.
Let’s start with a few assumptions:
- I have a 10 gallon tank
- I run out of gas every 14 days
- Gas price is currently $2.62 a gallon
- It increases eight cents a gallon per week
- I currently have a full tank
Accepting those assumptions as true, we now need two strategies to compare. Strategy 1 will be: I refill my tank whenever it is empty at the current price. Strategy 2 will be: I will top off my tank every other day at the current price.
Running the simulation for 12 weeks, we get:
STRATEGY 1: Refill When Empty... Week 1: $ 0.00 Week 2: $ 27.80 Week 3: $ 27.80 Week 4: $ 57.20 Week 5: $ 57.20 Week 6: $ 88.20 Week 7: $ 88.20 Week 8: $120.80 Week 9: $120.80 Week 10: $155.00 Week 11: $155.00 Week 12: $190.80 STRATEGY 2: Refill Every Other Day... Week 1: $ 11.42 Week 2: $ 27.11 Week 3: $ 39.22 Week 4: $ 55.83 Week 5: $ 68.62 Week 6: $ 86.14 Week 7: $ 99.62 Week 8: $118.06 Week 9: $132.22 Week 10: $151.57 Week 11: $166.42 Week 12: $186.69 Total savings of STRATEGY 2 over STRATEGY 1: $4.11
So I saved $4.11. Over 12 weeks. 12 weeks of stopping by the gas station every other day, swiping the ol’ credit card, removing the gas cap, and topping off the tank (In the 110 degree heat). I saved $4.11, but I lost it all in the opportunity cost of the time spent refilling.
What if we play with the numbers though? You have a gas-guzzling SUV that uses 20 gallons of gas every two weeks? Congrats, you saved $8.23 (it’s proportional). A longer commute causing you to burn through your 10 gallons in a week instead of two? You only save $3.43. If gas rises a quarter a week instead of eight cents, then you’re saving $12.86, but you probably have other things to worry about at that point. Even playing with the refill frequency of Strategy 2 doesn’t move the numbers substantially in either direction.
I think that pretty much debunks that theory… oh well. However, I am interested to hear if anyone else has some alternative theories to try.
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