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diet.py
#!/usr/bin/python # Copyright 2018, Gurobi Optimization, LLC # 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 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( (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.Status.OPTIMAL: print('\nCost: %g' % m.objVal) print('\nBuy:') buyx = m.getAttr('x', buy) for f in foods: if buy[f].x > 0.0001: print('%s %g' % (f, buyx[f])) 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()