If a_ij is the amount of nutrient i in food j, and b_i is the desired amount of nutrients, and x_j is the amount of food to purchase, then
sum{x_j * a_ij : j in FOODS} – b_i = b_i*(rpos_i – rneg_i)
would then have rpos_i + rneg_i be the absolute value of the deviation of the fraction needed
From: Bjørnar Ness <bjornar.ness@gmail.com>
Sent: Wednesday, March 20, 2024 10:26 AM
To: Meketon, Marc <Marc.Meketon@oliverwyman.com>
Cc: Dušan Plavák <dusan.plavak@gmail.com>; help-glpk@gnu.org
Subject: Re: diet problem disregarding cost
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Thanks a lot. But do you have a small example I can continue on? It important that the values are not absolute, but fractions of the needed quantities
In general, if you have variables rpos_i and rneg_i (the ith constraint), and you have:
[linear equation i] = rpos_i – rneg_i
Then (rpos_i + rneg_i) is the absolute value
If you then have
rpos_i + rneg_i <= z
z would be the maximum absolute value, and then you just minimize z.
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Hi, feel free to send me an email. I did this ~ 9-10 years ago for our startup where we generate personalized nutrition plans for our clients using glpk.
Basically you want to build bunch of inequalities and most probably you want to have more variables not only nutrients... Depend on your exact use case.
Can anyone point me to an diet problem example that tries to minimize
max deviation in percentage for each nutrient, disregarding cost?
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Bj(/)rnar
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