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2024 年高教社杯全国大学生数学建模竞赛B题第二问详细解题思路（终版）

news 2025/7/5 12:19:57

示例代码：

import numpy as np
import pandas as pd# 参数设定
params = {'p1': 0.10, 'p2': 0.10, 'c1': 4, 'c2': 2, 'd1': 2, 'd2': 3,'pf': 0.10, 'a': 6, 'df': 3, 's': 56, 'l': 6, 'r': 5
}# 决策变量
decisions = [0, 1]# 利润计算函数
def calculate_profit(D1, D2, C, R, params):cost_parts = (params['c1'] + params['d1'] * D1) + (params['c2'] + params['d2'] * D2)cost_assembly = params['a'] + params['df'] * Crevenue = params['s'] * (1 - params['pf']) * (1 - C * params['df'])cost_rework = params['r'] * R * params['pf'] * Closs_replacement = params['l'] * params['pf']profit = revenue - cost_parts - cost_assembly - cost_rework - loss_replacementreturn profit# 遍历所有可能的决策组合
best_profit = -np.inf
best_decision = None
for D1 in decisions:for D2 in decisions:for C in decisions:for R in decisions:profit = calculate_profit(D1, D2, C, R, params)if profit > best_profit:best_profit = profitbest_decision = (D1, D2, C, R)print(f"Best Decision: {best_decision}, Maximum Profit: {best_profit}")

可视化代码：

import numpy as np
import matplotlib.pyplot as plt
import itertools# 参数设定
params = {'p1': 0.10, 'p2': 0.10, 'c1': 4, 'c2': 2, 'd1': 2, 'd2': 3,'pf': 0.10, 'a': 6, 'df': 3, 's': 56, 'l': 6, 'r': 5
}# 决策变量
decisions = [0, 1]# 利润计算函数
def calculate_profit(D1, D2, C, R, params):cost_parts = (params['c1'] + params['d1'] * D1) + (params['c2'] + params['d2'] * D2)cost_assembly = params['a'] + params['df'] * Crevenue = params['s'] * (1 - params['pf']) * (1 - C * params['df'])cost_rework = params['r'] * R * params['pf'] * Closs_replacement = params['l'] * params['pf']profit = revenue - cost_parts - cost_assembly - cost_rework - loss_replacementreturn profit# 遍历所有可能的决策组合
profits = []
decision_combinations = list(itertools.product(decisions, repeat=4))
for combo in decision_combinations:profit = calculate_profit(*combo, params)profits.append(profit)# 转换为DataFrame以便可视化
df = pd.DataFrame(decision_combinations, columns=['D1', 'D2', 'C', 'R'])
df['Profit'] = profits# 绘制成本与收益分析图
plt.figure(figsize=(10, 6))
plt.bar(df.index, df['Profit'], color='skyblue')
plt.xlabel('Decision Combination Index')
plt.ylabel('Profit')
plt.title('Profit for Different Decision Combinations')
plt.xticks(rotation=90)
plt.show()# 决策影响图
for i, decision in enumerate(['D1', 'D2', 'C', 'R']):plt.figure(figsize=(10, 6))plt.bar(df.index, df['Profit'] * (df[decision] == 1).astype(int), label=f'{decision} = 1')plt.bar(df.index, df['Profit'] * (df[decision] == 0).astype(int), bottom=df['Profit'] * (df[decision] == 1).astype(int), label=f'{decision} = 0')plt.xlabel('Decision Combination Index')plt.ylabel('Profit')plt.title(f'Impact of {decision} on Profit')plt.legend()plt.xticks(rotation=90)plt.show()# 敏感性分析图
sensitivity_params = ['c1', 'c2', 's', 'l', 'r']
for param in sensitivity_params:values = np.linspace(0.5, 1.5, 10) * params[param]profits_sensitivity = [calculate_profit(1, 1, 1, 1, {**params, param: value}) for value in values]plt.figure(figsize=(10, 6))plt.plot(values, profits_sensitivity, marker='o', label=f'Sensitivity to {param}')plt.xlabel(f'{param} Value')plt.ylabel('Profit')plt.title(f'Sensitivity Analysis for {param}')plt.legend()plt.grid(True)plt.show()