Date:         Wed, 1 Jun 2005 11:24:12 -0700
Reply-To:     "Theise, Eric" <ETheise@anesthesia.ucsf.edu>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         "Theise, Eric" <ETheise@anesthesia.ucsf.edu>
Subject:      Re: Seeking for syntax help for a math array procedure
Comments: To: pgao@32BJFUNDS.COM
Content-Type: text/plain; charset=us-ascii

Dear Peter,

> The aim of this task is to make as much different
> combinations as possible
> to produce a yearly three-meal-a-day menu on a weekly basis.

You have a very interesting problem here, but not one that seems (to me)
suitable for analysis with SPSS.

It seems to me that this is a constrained optimization problem, where
your objective is to maximize the run of unduplicated meals subject to a
large number of constraints, which take relatively few forms.  The
constraints would ensure that you always have the right number of
components in your meals, that components not be repeated in the same
configuration until a certain amount of time passes, that preparation
falls in the most suitable time bucket (weekday or weekend/holiday), and
perhaps a few other things I am overlooking.  The richness of this kind
of formulation would allow you specify that certain combinations never
appear, due to, say, aesthetic considerations (these foods are all
mushy!), and to force others to appear due to, say, nutritional
considerations (FDA suggested minimum daily requirements).

Some of the earliest uses of constrained optimization and linear
programming were to solve "the diet problem", which minimzed the total
cost of a food program subject to daily requirements for vitamins,
calories, minerals, etc.  This is not the same problem and would require
the use of zero/one variables, but it is, as I said, a nice,
interesting, and probably tractable problem.

Do you have an operations researcher in your group?

--Eric