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 <[email protected]>
Sent: Wednesday, March 20, 2024 10:26 AM
To: Meketon, Marc <[email protected]>
Cc: Dušan Plavák <[email protected]>; [email protected]
Subject: Re: diet problem disregarding cost
CAUTION: This email originated outside the company. Do not click links or open
attachments unless you are expecting them from the sender.
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
ons. 20. mars 2024 kl. 15:21 skrev Meketon, Marc
<[email protected]<mailto:[email protected]>>:
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.
From:
[email protected]<mailto:[email protected]>
<[email protected]<mailto:[email protected]>>
On Behalf Of Dušan Plavák
Sent: Wednesday, March 20, 2024 7:02 AM
To: Bjørnar Ness <[email protected]<mailto:[email protected]>>
Cc: [email protected]<mailto:[email protected]>
Subject: Re: diet problem disregarding cost
CAUTION: This email originated outside the company. Do not click links or open
attachments unless you are expecting them from the sender.
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.
On Wed, Mar 20, 2024 at 4:34 PM Bjørnar Ness
<[email protected]<mailto:[email protected]>> wrote:
Can anyone point me to an diet problem example that tries to minimize
max deviation in percentage for each nutrient, disregarding cost?
--
Bj(/)rnar
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S pozdravom Dušan Plavák
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