diet.py
#!/usr/bin/python
# Copyright 2016, Gurobi Optimization, Inc.
# Solve the classic diet model, showing how to add constraints
# to an existing model.
from gurobipy import *
# Nutrition guidelines, based on
# USDA Dietary Guidelines for Americans, 2005
# http://www.health.gov/DietaryGuidelines/dga2005/
categories, minNutrition, maxNutrition = multidict({
'calories': [1800, 2200],
'protein': [91, GRB.INFINITY],
'fat': [0, 65],
'sodium': [0, 1779] })
foods, cost = 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 = Model("diet")
# Create decision variables for the nutrition information,
# which we limit via bounds
nutrition = m.addVars(categories, lb=minNutrition, ub=maxNutrition, name="nutrition")
# 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
# to the preceding two statements...
#
# nutrition = {}
# for c in categories:
# nutrition[c] = m.addVar(lb=minNutrition[c], ub=maxNutrition[c], name=c)
#
# 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(
(quicksum(nutritionValues[f,c] * buy[f] for f in foods) == nutrition[c]
for c in categories), "_")
# Using looping constructs, the preceding statement would be:
#
# for c in categories:
# m.addConstr(
# sum(nutritionValues[f,c] * buy[f] for f in foods) == nutrition[c], c)
def printSolution():
if m.status == GRB.Status.OPTIMAL:
print('\nCost: %g' % m.objVal)
print('\nBuy:')
buyx = m.getAttr('x', buy)
nutritionx = m.getAttr('x', nutrition)
for f in foods:
if buy[f].x > 0.0001:
print('%s %g' % (f, buyx[f]))
print('\nNutrition:')
for c in categories:
print('%s %g' % (c, nutritionx[c]))
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()
