Book Example: diet¶

Description: book example autogenerated using diet.mod, diet.dat, and diet.run

Tags: ampl-only, ampl-book

Notebook author: Marcos Dominguez Velad <marcos@ampl.com>

Model author: N/A

# Install dependencies
%pip install -q amplpy

# Google Colab & Kaggle integration
from amplpy import AMPL, ampl_notebook

ampl = ampl_notebook(
    modules=["coin"],  # modules to install
    license_uuid="default",  # license to use
)  # instantiate AMPL object and register magics

Example: diet¶

Generated using diet.mod, diet.dat, and diet.run.

Consider the problem of choosing prepared foods to meet certain nutritional requirements.

Sets:

NUTR: set of nutrients to consider
FOOD: set of food to consider

Parameters:

cost {FOOD}: cost of each food
f_min {FOOD}: minimum amount of food to buy
f_max {FOOD}: maximum amount of food to buy
n_min {NUTR}: minimum amount required of each nutrient
n_max {NUTR}: maximum amount allowed of each nutrient
amt {NUTR, FOOD}: amount of each nutrient in each food

Variables:

Buy {FOOD}: amount of food to buy

Objective:

Total_Cost: total cost of the diet

Constraints:

Diet {NUTR}: ensure that the nutritional requirements are satisfied by the diet.

%%writefile diet.mod
set NUTR;
set FOOD;

param cost {FOOD} > 0;
param f_min {FOOD} >= 0;
param f_max {j in FOOD} >= f_min[j];

param n_min {NUTR} >= 0;
param n_max {i in NUTR} >= n_min[i];

param amt {NUTR,FOOD} >= 0;

var Buy {j in FOOD} >= f_min[j], <= f_max[j];

minimize Total_Cost:  sum {j in FOOD} cost[j] * Buy[j];

subject to Diet {i in NUTR}:
   n_min[i] <= sum {j in FOOD} amt[i,j] * Buy[j] <= n_max[i];

%%writefile diet.dat
data;

set NUTR := A B1 B2 C ;
set FOOD := BEEF CHK FISH HAM MCH MTL SPG TUR ;

param:   cost  f_min  f_max :=
  BEEF   3.19    0     100
  CHK    2.59    0     100
  FISH   2.29    0     100
  HAM    2.89    0     100
  MCH    1.89    0     100
  MTL    1.99    0     100
  SPG    1.99    0     100
  TUR    2.49    0     100 ;

param:   n_min  n_max :=
   A      700   10000
   C      700   10000
   B1     700   10000
   B2     700   10000 ;

param amt (tr):
           A    C   B1   B2 :=
   BEEF   60   20   10   15
   CHK     8    0   20   20
   FISH    8   10   15   10
   HAM    40   40   35   10
   MCH    15   35   15   15
   MTL    70   30   15   15
   SPG    25   50   25   15
   TUR    60   20   15   10 ;

%%ampl_eval
model diet.mod;
data diet.dat;
option solver cbc;
solve;
display Buy;

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