a few more thoughts on operations research and coffee: multiobjective decision analysis
Posted by Laura McLay on June 1, 2011
I recently wrote about how I used OR to decide how to get my coffee fix in the morning. Some of you suggested that I perform MODA to consider the tradeoffs between cost, taste, and convenience. I agree!
My previous post contains the cost, taste, and convenience scores for the six coffee options:
- Home coffee (made at home, brought to work in a mug)
- Department coffee (purchased from the coffee made in the department coffee maker)
- Coffee shop (bought from a local coffee shop on the way to work)
- Dunkin Donuts (my guilty pleasure, a little out of my way)
- Office coffee (made in my spare coffee maker in my office)
- Keurig coffee (made in my office)
- The preferential independence assumption was reasonable here.
- I used an additive value function, since it was reasonable in this situation.
- I used an exponential shape to assess the single dimensional value functions. I was linear in taste. I had a concave shape factor for cost (1.83) and a convex shape factor for convenience (-6.8). I really hate waiting.
- My swing weights are 0.5 for cost, 0.25 for convenience, and 0.25 for taste. My rationale here is that cost adds up over the year, and as a result, it is twice as important as convenience and taste. Convenience and taste seem about equally important to me.
Based on this, the MODA values for the six options lead to this ordering of my coffee options scaled between zero and one are:
- Home coffee (0.77)
- Office coffee (0.71)
- Department coffee (0.67)
- Keurig coffee (0.67)
- Coffee shop (0.32)
- Dunkin Donuts (0.25)
It looks like I naturally gravitated to my “optimal” decisions of making coffee at home or in my office. A sensitivity on the weight for cost leads to the following graph. It shows that buying coffee at a coffee shop or at Dunkin Donuts would be suboptimal across all weights (so would buying the department coffee). If I care a little less about cost, buying a Keurig coffee maker for my office would become the best option.
If I change the weights so that taste counts the most (with a weight of 0.5) and cost and convenience have weights of 0.25, then the MODA values for the six options lead to this ordering of my coffee options scaled between zero and one are:
- Home coffee (0.73)
- Keurig coffee (0.69)
- Dunkin Donuts (0.5)
- Office coffee (0.49)
- Coffee shop (0.49)
- Department coffee (0.46)
The sensitivity of the results based on the weight for taste are captured in the following figure. In both cases, it looks like continuing to make coffee at home is my best bet.
If you’re interested in working this example, check out my spreadsheet for this on my new “Files” page under the teaching materials heading. I’ll try to post some of my teaching materials, code, and data on this blog as I go.