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diet.py

#!/usr/bin/env python3.7

# Copyright 2021, Gurobi Optimization, LLC

# Solve the classic diet model, showing how to add constraints
# to an existing model.

import gurobipy as gp
from gurobipy import GRB

# Nutrition guidelines, based on
# USDA Dietary Guidelines for Americans, 2005
# http://www.health.gov/DietaryGuidelines/dga2005/

categories, minNutrition, maxNutrition = gp.multidict({
'calories': [1800, 2200],
'protein':  [91, GRB.INFINITY],
'fat':      [0, 65],
'sodium':   [0, 1779]})

foods, cost = gp.multidict({
'hamburger': 2.49,
'chicken':   2.89,
'hot dog':   1.50,
'fries':     1.89,
'macaroni':  2.09,
'pizza':     1.99,
'salad':     2.49,
'milk':      0.89,
'ice cream': 1.59})

# Nutrition values for the foods
nutritionValues = {
('hamburger', 'calories'): 410,
('hamburger', 'protein'):  24,
('hamburger', 'fat'):      26,
('hamburger', 'sodium'):   730,
('chicken',   'calories'): 420,
('chicken',   'protein'):  32,
('chicken',   'fat'):      10,
('chicken',   'sodium'):   1190,
('hot dog',   'calories'): 560,
('hot dog',   'protein'):  20,
('hot dog',   'fat'):      32,
('hot dog',   'sodium'):   1800,
('fries',     'calories'): 380,
('fries',     'protein'):  4,
('fries',     'fat'):      19,
('fries',     'sodium'):   270,
('macaroni',  'calories'): 320,
('macaroni',  'protein'):  12,
('macaroni',  'fat'):      10,
('macaroni',  'sodium'):   930,
('pizza',     'calories'): 320,
('pizza',     'protein'):  15,
('pizza',     'fat'):      12,
('pizza',     'sodium'):   820,
('salad',     'calories'): 320,
('salad',     'protein'):  31,
('salad',     'fat'):      12,
('salad',     'sodium'):   1230,
('milk',      'calories'): 100,
('milk',      'protein'):  8,
('milk',      'fat'):      2.5,
('milk',      'sodium'):   125,
('ice cream', 'calories'): 330,
('ice cream', 'protein'):  8,
('ice cream', 'fat'):      10,
('ice cream', 'sodium'):   180}

# Model
m = gp.Model("diet")

# Create decision variables for the foods to buy
buy = m.addVars(foods, name="buy")

# You could use Python looping constructs and m.addVar() to create
# these decision variables instead.  The following would be equivalent
#
# buy = {}
# for f in foods:
#   buy[f] = m.addVar(name=f)

# The objective is to minimize the costs
m.setObjective(buy.prod(cost), GRB.MINIMIZE)

# Using looping constructs, the preceding statement would be:
#
# m.setObjective(sum(buy[f]*cost[f] for f in foods), GRB.MINIMIZE)

# Nutrition constraints
m.addConstrs((gp.quicksum(nutritionValues[f, c] * buy[f] for f in foods)
== [minNutrition[c], maxNutrition[c]]
for c in categories), "_")

# Using looping constructs, the preceding statement would be:
#
# for c in categories:
#  m.addRange(sum(nutritionValues[f, c] * buy[f] for f in foods),
#             minNutrition[c], maxNutrition[c], c)

def printSolution():
if m.status == GRB.OPTIMAL:
print('\nCost: %g' % m.objVal)
print('\nBuy:')
for f in foods:
if buy[f].x > 0.0001:
print('%s %g' % (f, buy[f].x))
else:
print('No solution')

# Solve
m.optimize()
printSolution()

print('\nAdding constraint: at most 6 servings of dairy')
m.addConstr(buy.sum(['milk', 'ice cream']) <= 6, "limit_dairy")

# Solve
m.optimize()
printSolution()


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