# Copyright 2025 Samarth Mistry # This file is part of the `opti-extensions` package, which is released under # the Apache Licence, Version 2.0 (http://www.apache.org/licenses/LICENSE-2.0). """ Diet problem ============ Please refer to chapter 2 in the `AMPL Book `_ for a detailed description of the problem. We demonstrate how to implement this model with DOcplex, gurobipy, Xpress, and highspy along with the functionality from `opti-extensions`. Implementation reference: https://github.com/ampl/colab.ampl.com/blob/master/ampl-lecture/diet_case_study.ipynb — Copyright (c) 2022-2022, AMPL Optimization inc. (licensed under the MIT License) """ # %% # Mathematical formulation # ------------------------ # # **Index-sets**: # # - | Nutrients to consider: # | :math:`i \in NUTR` # - | Food items to consider: # | :math:`j \in FOOD` # # **Parameters**: # # - | Cost of food item :math:`j`: # | :math:`cost_{j} \in \mathbb{R}^{+} \quad \forall \; j \in FOOD` # - | Minimum purchase quantity required for food item :math:`j`: # | :math:`f\_min_{j} \in \mathbb{R}_{0}^{+} \quad \forall \; j \in FOOD` # - | Maximum purchase quantity allowed for food item :math:`j`: # | :math:`f\_max_{j} \in \mathbb{R}_{0}^{+} \quad \forall \; j \in FOOD` # - | Minimum amount required of nutrient :math:`i`: # | :math:`n\_min_{i} \in \mathbb{R}_{0}^{+} \quad \forall \; i \in NUTR` # - | Maximum amount required of nutrient :math:`i`: # | :math:`n\_max_{i} \in \mathbb{R}_{0}^{+} \quad \forall \; i \in NUTR` # - | Amount of nutrient :math:`i` in food item :math:`j`: # | :math:`amt_{i, j} \in \mathbb{R}_{0}^{+} \quad \forall \; i \in NUTR \; \& \; \forall \; j \in FOOD` # # **Variables**: # # - | Quantity of food item :math:`j` to be purchased: # | :math:`buy_{j} \in \mathbb{R}_{0}^{+} (\geq f\_min_{j}, \leq f\_max_{j}) \quad \forall \; j \in FOOD` # # **Objective**: # # - | Minimize the total cost of the diet: # | :math:`\min \; \sum_{j \in FOOD} cost_{j} \times buy_{j}` # # **Constraints**: # # - | Ensure that the nutritional limits are satisfied by the diet: # | :math:`n\_min_{i} \leq \sum_{j \in FOOD} amt_{i, j} \times buy_{j} \leq n\_max_{i}, \; \forall \; i \in NUTR` # %% # Set up problem data # ------------------- # %% # Index-sets # ^^^^^^^^^^ from opti_extensions import IndexSet1D NUTR = IndexSet1D(['A', 'B1', 'B2', 'C'], name='NUTRIENT') FOOD = IndexSet1D(['BEEF', 'CHK', 'FISH', 'HAM', 'MCH', 'MTL', 'SPG', 'TUR'], name='FOOD') # %% # Parameters # ^^^^^^^^^^ from opti_extensions import ParamDict1D, ParamDictND cost = ParamDict1D( { 'BEEF': 3.19, 'CHK': 2.59, 'FISH': 2.29, 'HAM': 2.89, 'MCH': 1.89, 'MTL': 1.99, 'SPG': 1.99, 'TUR': 2.49, }, key_name='FOOD', value_name='COST', ) f_min = ParamDict1D( { 'BEEF': 0, 'CHK': 0, 'FISH': 0, 'HAM': 0, 'MCH': 0, 'MTL': 0, 'SPG': 0, 'TUR': 0, }, key_name='FOOD', value_name='MIN-QTY', ) f_max = ParamDict1D( { 'BEEF': 100, 'CHK': 100, 'FISH': 100, 'HAM': 100, 'MCH': 100, 'MTL': 100, 'SPG': 100, 'TUR': 100, }, key_name='FOOD', value_name='MAX-QTY', ) n_min = ParamDict1D( {'A': 700, 'C': 700, 'B1': 700, 'B2': 700}, key_name='NUTRIENT', value_name='MIN-AMT', ) n_max = ParamDict1D( {'A': 10000, 'C': 10000, 'B1': 10000, 'B2': 10000}, key_name='NUTRIENT', value_name='MAX-AMT', ) amt = ParamDictND( { ('A', 'BEEF'): 60, ('C', 'BEEF'): 20, ('B1', 'BEEF'): 10, ('B2', 'BEEF'): 15, ('A', 'CHK'): 8, ('C', 'CHK'): 0, ('B1', 'CHK'): 20, ('B2', 'CHK'): 20, ('A', 'FISH'): 8, ('C', 'FISH'): 10, ('B1', 'FISH'): 15, ('B2', 'FISH'): 10, ('A', 'HAM'): 40, ('C', 'HAM'): 40, ('B1', 'HAM'): 35, ('B2', 'HAM'): 10, ('A', 'MCH'): 15, ('C', 'MCH'): 35, ('B1', 'MCH'): 15, ('B2', 'MCH'): 15, ('A', 'MTL'): 70, ('C', 'MTL'): 30, ('B1', 'MTL'): 15, ('B2', 'MTL'): 15, ('A', 'SPG'): 25, ('C', 'SPG'): 50, ('B1', 'SPG'): 25, ('B2', 'SPG'): 15, ('A', 'TUR'): 60, ('C', 'TUR'): 20, ('B1', 'TUR'): 15, ('B2', 'TUR'): 10, }, key_names=('FOOD', 'NUTR'), value_name='AMT', ) # fmt: off # %% # Implement with DOcplex # ---------------------- # %% from docplex.mp.model import Model from opti_extensions.docplex import add_variables, solve # Instantiate model model = Model(name='diet') # Add variables buy = add_variables(model, indexset=FOOD, vartype='continuous', lb=f_min, ub=f_max, name='BUY-QTY') # Instead of: # buy = model.continuous_var_dict(FOOD, lb=[f_min[j] for j in FOOD], ub=[f_max[j] for j in FOOD], name='BUY-QTY') # Set objective model.minimize( cost @ buy # Instead of: # model.sum(cost[j] * buy[j] for j in FOOD) ) # Add constraints model.add_constraints_( model.sum(amt[i, j] * buy[j] for j in FOOD) >= n_min[i] for i in NUTR ) model.add_constraints_( model.sum(amt[i, j] * buy[j] for j in FOOD) <= n_max[i] for i in NUTR ) # Solve with additional logging output for problem and solution statistics sol = solve(model, log_output=True) # Instead of: # sol = model.solve(log_output=True) # %% sol.display(print_zeros=False) # %% # Implement with gurobipy # ----------------------- from gurobipy import GRB, Model, quicksum from opti_extensions.gurobipy import addVars # Instantiate model model = Model(name='diet') # Add variables buy = addVars(model, indexset=FOOD, lb=f_min, ub=f_max, vtype=GRB.CONTINUOUS, name='BUY-QTY') # Instead of: # buy = model.addVars(FOOD, lb=f_min, ub=f_max, vtype=GRB.CONTINUOUS, name='BUY-QTY') # Set objective model.setObjective( cost @ buy, # Instead of: # quicksum(cost[j] * buy[j] for j in FOOD) sense=GRB.MINIMIZE, ) # Add constraints model.addConstrs( quicksum(amt[i, j] * buy[j] for j in FOOD) >= n_min[i] for i in NUTR ) model.addConstrs( quicksum(amt[i, j] * buy[j] for j in FOOD) <= n_max[i] for i in NUTR ) # Solve model.optimize() # %% model.printAttr('X') # %% # Implement with Xpress # --------------------- import xpress as xp from opti_extensions.xpress import addVariables # Instantiate problem prob = xp.problem(name='diet') # Add variables buy = addVariables(prob, indexset=FOOD, vartype=xp.continuous, lb=f_min, ub=f_max, name='BUY-QTY') # Instead of: # buy = { # j: prob.addVariable(name=f'x({j})', ub=f_min.get(j, 0), ub=f_max.get(j, xp.infinity), vartype=xp.continuous) # for j in FOOD # } # Set objective prob.setObjective( cost @ buy, # Instead of: # xp.Sum(cost[j] * buy[j] for j in FOOD) sense=xp.minimize, ) # Add constraints prob.addConstraint( xp.Sum(amt[i, j] * buy[j] for j in FOOD) >= n_min[i] for i in NUTR ) prob.addConstraint( xp.Sum(amt[i, j] * buy[j] for j in FOOD) <= n_max[i] for i in NUTR ) # Solve prob.optimize() # %% print(f'var: {"value" :>20}') print('-' * 25) for k, v in prob.getSolution(buy).items(): if abs(v) > 1e-6: name = f'{buy.value_name}[{k}]:' print(f'{name:<15} {v :>8.4f}') # %% # Implement with highspy # ---------------------- from highspy import Highs, HighsVarType from opti_extensions.highspy import addVariables as addVariablesHighs # Instantiate model model = Highs() model.silent() # Add variables buy = addVariablesHighs( model, indexset=FOOD, lb=f_min, ub=f_max, type=HighsVarType.kContinuous, name_prefix='BUY-QTY', ) # Instead of: # buy = model.addVariables( # FOOD, lb=f_min, ub=f_max, type=HighsVarType.kContinuous, name_prefix='BUY-QTY' # ) # Set objective model.minimize( cost @ buy # Instead of: # Highs.qsum(cost[j] * buy[j] for j in FOOD) ) # Add constraints model.addConstrs( Highs.qsum(amt[i, j] * buy[j] for j in FOOD) >= n_min[i] for i in NUTR ) model.addConstrs( Highs.qsum(amt[i, j] * buy[j] for j in FOOD) <= n_max[i] for i in NUTR ) # Solve model.solve() # %% print(f'{"var:":<15} {"value":>8}') print('-' * 25) for idx, var in buy.items(): val = model.val(var) if abs(val) > 1e-6: name = f'{buy.value_name}[{idx}]:' print(f'{name:<15} {val:>8.4f}')