Re: [Help-glpk] Stigler's 1939 diet problem

[Brady Hunsaker]

Andrew Makhorin wrote:
> Another example was added to glpk examples subdirectory, which is the
> original Stigler's 1939 diet problem (please see the model below).
>
> I am wondering (if there is a dietologist on the list :) why in dietary
> problems one requires nutrients to be *not less* than recommeneded
> allowance while it would be more resonable to require them to be *equal*
> to.

I am not a dietician, but I regularly use a diet problem as a project 
for undergraduates learning linear programming.  They collect actual 
data from fast-food restaurants.  I think that you're correct that a 
good diet would have values close to the recommended values for each 
nutrient--not just greater than.

I think the reason that Stigler used greater than is that each of the 
nutrients on his list are ones for which the usual problem is not 
getting enough.  It's rare that anyone has too much vitamin A in their 
diet, for example.

For other "nutrients" like total fat or sodium, however, a less than 
constraint would generally make more sense.

When I assign the problem, I use a different set of "nutrients", and I 
let the students decide whether to use a greater than constraint, less 
than constraint, or double bounded constraint.  It's good practice for 
them to think about which makes sense in advance, but then also to react 
to the solution they get by reconsidering their choices.

The one exception is that I require that they satisfy the calorie 
constraint exactly.

Brady

--
Brady Hunsaker
Assistant Professor
Industrial Engineering
University of Pittsburgh
http://www.engr.pitt.edu/hunsaker/