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diet.py


#!/usr/bin/env python3.11

# Copyright 2024, 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(f"\nCost: {m.ObjVal:g}")
        print("\nBuy:")
        for f in foods:
            if buy[f].X > 0.0001:
                print(f"{f} {buy[f].X:g}")
    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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