python , pulpを用いて、グループ分け（最適化問題）

# データは読み込み済

import pandas as pd
import itertools
import math
import matplotlib.pyplot as plt
!pip install pulp
import pulp

# グループ数や人数を設定
num_groups = 13
group_size_options = [4, 3]

# 問題の定義
model = pulp.LpProblem("Grouping Problem", pulp.LpMinimize)

# メンバーの情報をリストに格納
members = []
for row in df.iterrows():
    member = row[1]
    members.append({
        "id": member["社員番号"],
        "name": member["名前"],
        "position": member["役職"],
        "team": member["チーム"],
        "prev_group": member["前回の班"],
        "prev_prev_group": member["前々回の班"]
    })

# メンバー数と班数
num_members = len(members)
num_group_sizes = len(group_size_options)

# グループごとの人数を定義する変数
group_size_vars = pulp.LpVariable.dicts("GroupSize", (range(num_groups), range(num_group_sizes)), cat="Binary")

# メンバーをグループに割り当てる変数
group_vars = pulp.LpVariable.dicts("Group", (range(num_groups), range(num_members)), cat="Binary")

# 目的関数：役職がリーダーのメンバーを各グループに最低1人配置する
for member in members:
    if member["position"] == "リーダー":
        model += sum(group_vars[group][index] for group in range(num_groups) for index in range(num_members) if members[index]["id"] == member["id"]) >= 1

# 目的関数：グループ内の人数のバランスを最小化する
total_group_size_deviation = pulp.LpVariable("TotalGroupSizeDeviation", lowBound=0, cat="Continuous")
model += total_group_size_deviation

for group in range(num_groups):
    for size_index, size_option in enumerate(group_size_options):
        model += group_size_vars[group][size_index] * size_option == sum(group_vars[group][index] for index in range(num_members))

        # 補助変数を導入してグループ内の人数のバランスを最小化する制約を表現
        group_size = pulp.lpSum(group_vars[group][index] for index in range(num_members))
        model += group_size - size_option <= total_group_size_deviation
        model += group_size - size_option >= -total_group_size_deviation

# 制約条件：1班の人数は4人ないし3人
for group in range(num_groups):
    model += pulp.lpSum(group_vars[group][index] for index in range(num_members)) >= 3
    model += pulp.lpSum(group_vars[group][index] for index in range(num_members)) <= 4

# 制約条件：部署はできるだけ分ける
for group in range(num_groups):
    department_count = {}
    for index in range(num_members):
        department = members[index]["team"]
        if department not in department_count:
            department_count[department] = 0
        department_count[department] += group_vars[group][index]
    for count in department_count.values():
        model += count <= 1

# 制約条件：役職はできるだけ分ける
for group in range(num_groups):
    position_count = {}
    for index in range(num_members):
        position = members[index]["position"]
        if position not in position_count:
            position_count[position] = 0
        position_count[position] += group_vars[group][index]
    for count in position_count.values():
        model += count <= 1

# ソルバーを使用して最適化
model.solve()

# 結果の表示
grouped_members = [[] for _ in range(num_groups)]
for group in range(num_groups):
    for index in range(num_members):
        if pulp.value(group_vars[group][index]) == 1:
            grouped_members[group].append(members[index]["name"])

# 班ごとに社員の名前を表示
for group in range(num_groups):
    print(f"Group {group + 1}: {', '.join(grouped_members[group])}")