ortools-clone/examples/python/appointments.py

#!/usr/bin/env python3
# Copyright 2010-2022 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.

# [START program]
"""Appointment selection.

This module maximizes the number of appointments that can
be fulfilled by a crew of installers while staying close to ideal
ratio of appointment types.
"""

# overloaded sum() clashes with pytype.

# [START import]
from absl import app
from absl import flags
from ortools.linear_solver import pywraplp
from ortools.sat.python import cp_model

# [END import]

_LOAD_MIN = flags.DEFINE_integer("load_min", 480, "Minimum load in minutes.")
_LOAD_MAX = flags.DEFINE_integer("load_max", 540, "Maximum load in minutes.")
_COMMUTE_TIME = flags.DEFINE_integer("commute_time", 30, "Commute time in minutes.")
_NUM_WORKERS = flags.DEFINE_integer("num_workers", 98, "Maximum number of workers.")


class AllSolutionCollector(cp_model.CpSolverSolutionCallback):
    """Stores all solutions."""

    def __init__(self, variables):
        cp_model.CpSolverSolutionCallback.__init__(self)
        self.__variables = variables
        self.__collect = []

    def on_solution_callback(self) -> None:
        """Collect a new combination."""
        combination = [self.value(v) for v in self.__variables]
        self.__collect.append(combination)

    def combinations(self) -> list[list[int]]:
        """Returns all collected combinations."""
        return self.__collect


def enumerate_all_knapsacks_with_repetition(
    item_sizes: list[int], total_size_min: int, total_size_max: int
) -> list[list[int]]:
    """Enumerate all possible knapsacks with total size in the given range.

    Args:
      item_sizes: a list of integers. item_sizes[i] is the size of item #i.
      total_size_min: an integer, the minimum total size.
      total_size_max: an integer, the maximum total size.

    Returns:
      The list of all the knapsacks whose total size is in the given inclusive
      range. Each knapsack is a list [#item0, #item1, ... ], where #itemK is an
      nonnegative integer: the number of times we put item #K in the knapsack.
    """
    model = cp_model.CpModel()
    variables = [
        model.new_int_var(0, total_size_max // size, "") for size in item_sizes
    ]
    load = sum(variables[i] * size for i, size in enumerate(item_sizes))
    model.add_linear_constraint(load, total_size_min, total_size_max)

    solver = cp_model.CpSolver()
    solution_collector = AllSolutionCollector(variables)
    # Enumerate all solutions.
    solver.parameters.enumerate_all_solutions = True
    # solve
    solver.solve(model, solution_collector)
    return solution_collector.combinations()


def aggregate_item_collections_optimally(
    item_collections: list[list[int]],
    max_num_collections: int,
    ideal_item_ratios: list[float],
) -> list[int]:
    """Selects a set (with repetition) of combination of items optimally.

    Given a set of collections of N possible items (in each collection, an item
    may appear multiple times), a  given "ideal breakdown of items", and a
    maximum number of collections, this method finds the optimal way to
    aggregate the collections in order to:
    - maximize the overall number of items
    - while keeping the ratio of each item, among the overall selection, as close
      as possible to a given input ratio (which depends on the item).
    Each collection may be selected more than one time.

    Args:
      item_collections: a list of item collections. Each item collection is a list
        of integers [#item0, ..., #itemN-1], where #itemK is the number of times
        item #K appears in the collection, and N is the number of distinct items.
      max_num_collections: an integer, the maximum number of item collections that
        may be selected (counting repetitions of the same collection).
      ideal_item_ratios: A list of N float which sums to 1.0: the K-th element is
        the ideal ratio of item #K in the whole aggregated selection.

    Returns:
      A pair (objective value, list of pairs (item collection, num_selections)),
      where:
        - "objective value" is the value of the internal objective function used
          by the MIP Solver
        - Each "item collection" is an element of the input item_collections
        - and its associated "num_selections" is the number of times it was
          selected.
    """
    solver = pywraplp.Solver.CreateSolver("SCIP")
    if not solver:
        return []
    n = len(ideal_item_ratios)
    num_distinct_collections = len(item_collections)
    max_num_items_per_collection = 0
    for template in item_collections:
        max_num_items_per_collection = max(max_num_items_per_collection, sum(template))
    upper_bound = max_num_items_per_collection * max_num_collections

    # num_selections_of_collection[i] is an IntVar that represents the number
    # of times that we will use collection #i in our global selection.
    num_selections_of_collection = [
        solver.IntVar(0, max_num_collections, "s[%d]" % i)
        for i in range(num_distinct_collections)
    ]

    # num_overall_item[i] is an IntVar that represents the total count of item #i,
    # aggregated over all selected collections. This is enforced with dedicated
    # constraints that bind them with the num_selections_of_collection vars.
    num_overall_item = [
        solver.IntVar(0, upper_bound, "num_overall_item[%d]" % i) for i in range(n)
    ]
    for i in range(n):
        ct = solver.Constraint(0.0, 0.0)
        ct.SetCoefficient(num_overall_item[i], -1)
        for j in range(num_distinct_collections):
            ct.SetCoefficient(num_selections_of_collection[j], item_collections[j][i])

    # Maintain the num_all_item variable as the sum of all num_overall_item
    # variables.
    num_all_items = solver.IntVar(0, upper_bound, "num_all_items")
    solver.Add(solver.Sum(num_overall_item) == num_all_items)

    # Sets the total number of workers.
    solver.Add(solver.Sum(num_selections_of_collection) == max_num_collections)

    # Objective variables.
    deviation_vars = [
        solver.NumVar(0, upper_bound, "deviation_vars[%d]" % i) for i in range(n)
    ]
    for i in range(n):
        deviation = deviation_vars[i]
        solver.Add(
            deviation >= num_overall_item[i] - ideal_item_ratios[i] * num_all_items
        )
        solver.Add(
            deviation >= ideal_item_ratios[i] * num_all_items - num_overall_item[i]
        )

    solver.Maximize(num_all_items - solver.Sum(deviation_vars))

    result_status = solver.Solve()

    if result_status == pywraplp.Solver.OPTIMAL:
        # The problem has an optimal solution.
        return [int(v.solution_value()) for v in num_selections_of_collection]
    return []


def get_optimal_schedule(
    demand: list[tuple[float, str, int]]
) -> list[tuple[int, list[tuple[int, str]]]]:
    """Computes the optimal schedule for the installation input.

    Args:
      demand: a list of "appointment types". Each "appointment type" is a triple
        (ideal_ratio_pct, name, duration_minutes), where ideal_ratio_pct is the
        ideal percentage (in [0..100.0]) of that type of appointment among all
        appointments scheduled.

    Returns:
      The same output type as EnumerateAllKnapsacksWithRepetition.
    """
    combinations = enumerate_all_knapsacks_with_repetition(
        [a[2] + _COMMUTE_TIME.value for a in demand],
        _LOAD_MIN.value,
        _LOAD_MAX.value,
    )
    print(
        (
            "Found %d possible day schedules " % len(combinations)
            + "(i.e. combination of appointments filling up one worker's day)"
        )
    )

    selection = aggregate_item_collections_optimally(
        combinations, _NUM_WORKERS.value, [a[0] / 100.0 for a in demand]
    )
    output = []
    for i, s in enumerate(selection):
        if s != 0:
            output.append(
                (
                    s,
                    [
                        (combinations[i][t], d[1])
                        for t, d in enumerate(demand)
                        if combinations[i][t] != 0
                    ],
                )
            )

    return output


def main(_):
    demand = [(45.0, "Type1", 90), (30.0, "Type2", 120), (25.0, "Type3", 180)]
    print("*** input problem ***")
    print("Appointments: ")
    for a in demand:
        print("   %.2f%% of %s : %d min" % (a[0], a[1], a[2]))
    print("Commute time = %d" % _COMMUTE_TIME.value)
    print(
        "Acceptable duration of a work day = [%d..%d]"
        % (_LOAD_MIN.value, _LOAD_MAX.value)
    )
    print("%d workers" % _NUM_WORKERS.value)
    selection = get_optimal_schedule(demand)
    print()
    installed = 0
    installed_per_type = {}
    for a in demand:
        installed_per_type[a[1]] = 0

    # [START print_solution]
    print("*** output solution ***")
    for template in selection:
        num_instances = template[0]
        print("%d schedules with " % num_instances)
        for t in template[1]:
            mult = t[0]
            print("   %d installation of type %s" % (mult, t[1]))
            installed += num_instances * mult
            installed_per_type[t[1]] += num_instances * mult

    print()
    print("%d installations planned" % installed)
    for a in demand:
        name = a[1]
        per_type = installed_per_type[name]
        if installed != 0:
            print(
                f"   {per_type} ({per_type * 100.0 / installed}%) installations of"
                f" type {name} planned"
            )
        else:
            print(f"   {per_type} installations of type {name} planned")
    # [END print_solution]


if __name__ == "__main__":
    app.run(main)
# [END program]