bin_packing_mip.py

#!/usr/bin/env python3
# Copyright 2010-2024 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""Solve a simple bin packing problem using a MIP solver."""
# [START program]
# [START import]
from ortools.linear_solver import pywraplp
# [END import]


# [START program_part1]
# [START data_model]
def create_data_model():
    """Create the data for the example."""
    data = {}
    weights = [48, 30, 19, 36, 36, 27, 42, 42, 36, 24, 30]
    data["weights"] = weights
    data["items"] = list(range(len(weights)))
    data["bins"] = data["items"]
    data["bin_capacity"] = 100
    return data

# [END data_model]


def main():
    # [START data]
    data = create_data_model()
    # [END data]
    # [END program_part1]

    # [START solver]
    # Create the mip solver with the SCIP backend.
    solver = pywraplp.Solver.CreateSolver("SCIP")

    if not solver:
        return
    # [END solver]

    # [START program_part2]
    # [START variables]
    # Variables
    # x[i, j] = 1 if item i is packed in bin j.
    x = {}
    for i in data["items"]:
        for j in data["bins"]:
            x[(i, j)] = solver.IntVar(0, 1, "x_%i_%i" % (i, j))

    # y[j] = 1 if bin j is used.
    y = {}
    for j in data["bins"]:
        y[j] = solver.IntVar(0, 1, "y[%i]" % j)
    # [END variables]

    # [START constraints]
    # Constraints
    # Each item must be in exactly one bin.
    for i in data["items"]:
        solver.Add(sum(x[i, j] for j in data["bins"]) == 1)

    # The amount packed in each bin cannot exceed its capacity.
    for j in data["bins"]:
        solver.Add(
            sum(x[(i, j)] * data["weights"][i] for i in data["items"])
            <= y[j] * data["bin_capacity"]
        )
    # [END constraints]

    # [START objective]
    # Objective: minimize the number of bins used.
    solver.Minimize(solver.Sum([y[j] for j in data["bins"]]))
    # [END objective]

    # [START solve]
    print(f"Solving with {solver.SolverVersion()}")
    status = solver.Solve()
    # [END solve]

    # [START print_solution]
    if status == pywraplp.Solver.OPTIMAL:
        num_bins = 0
        for j in data["bins"]:
            if y[j].solution_value() == 1:
                bin_items = []
                bin_weight = 0
                for i in data["items"]:
                    if x[i, j].solution_value() > 0:
                        bin_items.append(i)
                        bin_weight += data["weights"][i]
                if bin_items:
                    num_bins += 1
                    print("Bin number", j)
                    print("  Items packed:", bin_items)
                    print("  Total weight:", bin_weight)
                    print()
        print()
        print("Number of bins used:", num_bins)
        print("Time = ", solver.WallTime(), " milliseconds")
    else:
        print("The problem does not have an optimal solution.")
    # [END print_solution]


if __name__ == "__main__":
    main()
# [END program_part2]
# [END program]