Wednesday, January 21, 2009

 

How many pats of butter per day is "optimal"?



After reading Michael Trick's Operations Research blog post, "A Sheriff Goes to Jail for Not Using Operations Research" I followed the link he provided to the Menu Optimizer he cited. I've been interested in such models for many, many years.

My first professional assignment was to help food scientists doing product development use such models. In so doing, and reading an article or two in the ORSA (now INFORMS) journal, I came to appreciate their limitations and consider alternative ways to address the question possibly better. The major limitation was, and probably still is, palatability. Another challenge, also very hard to regulate, which jam-makers and wine-makers will understand, is the variability of the attributes of the raw materials; sugar content of grapes depends on the weather, where they were grown, and when they were picked, for a simple example.

The palatability challenge comes down to something like this: if all your meals of the week (which are the same as the meals of all other weeks) are put in the blender, would you be able to swallow one day's worth each day? Astronauts said "no" to the first "blends" and provoked the follow-up research on how many different tubes of paste were necessary and what combinations they could contain (if I am not mistaken [reference needed]). The opinions of cats, dogs and other "dumb" animals is harder to obtain, but there are industries trying to provide foods these animals will eat day after day, and which will keep the animals healthy.

One approach to the "palatability" constraint was researched and the results were published over thirty years ago. The first phase of the research was to gather "how often would you like to eat..." ratings. The second phase was the linear programming optimization with the results of the first phase as constraints (salmon not more than three times a week, coffee not more than once an hour except before 9:00 a.m., etc.). The cost of "minimum decent subsistance" with the variety constraints was nearly double the cost of just plain (water torture?) "minimum subsistance" without.

Consequently, and with all the disclaimers ("your doctor may not approve") as well, not to mention price-per-serving assumptions which may not be "current" where I live, I didn't expect an "optimal menu" I would want to eat every day in every season. But I didn't expect to be told a lot of popcorn and a baked potato with a fair amount of butter, and a little egg and broccoli and a few glasses of milk, would be my sentence.

The Solution and Cost Breakdown by Food

Food Servings Cost ($)
Frozen Broccoli 0.41 0.06
Butter,Regular 5.54 0.28
Scrambled Eggs 0.65 0.07
3.3% Fat,Whole Milk 3.09 0.49
Popcorn,Air-Popped 10.00 0.40
Potatoes, Baked 0.94 0.06
Serving size and nutrient information



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