import gurobipy as gp from gurobipy import GRB, quicksum import numpy as np import pandas as pd # ==================== # 读取需求数据 # ==================== filePath = r"E:\\all_1.xlsx" try: data = pd.read_excel(filePath) # 读取文件 demand = data.to_numpy() print("需求数据成功读取。") except Exception as e: print(f"读取需求数据时出错: {e}") exit() # ==================== # 基本参数设置 # ==================== zone = 16 # 总客户数量（每个中转站有8个客户） timeInterval = 30 # 时间间隔数量 # ==================== # 成本和容量等参数 # ==================== RentCost = 0.1 # 中转站的单位容积租赁费用 RentSize = 800 # 中转站的租赁容积 HoardCost = 0.1 # 单位货物在中转站的囤积成本 TravelCost1 = np.array([1, 3]) # 工厂 -> 中转站 i 的单位货物运输成本 TravelCost2 = 2 * np.array([2, 2, 2, 3, 3, 2, 4, 4, 7, 3, 4, 2, 3, 4, 7, 5]) # 工厂 -> 客户 j 的单位货物运输成本（16个客户） TravelCost3 = 4 # 中转站 i -> 客户 j 的统一运输成本 TimeoutCost = 1000 # 客户j超时订单成本 DispatchCostForOneVehicle = 20 # 调度一次车辆的固定成本 # 车辆最大容量 Q = 100 # 每个中转站可用车辆总数 K = np.array([6, 6]) # 其他参数 Max1 = RentSize Max2 = 100 Max3 = Q M = 100000 # ==================== # 定义集合 # ==================== S = [1, 2] # 中转站节点编号为1和2 P1 = list(range(3, 11)) # 中转站1对应的客户编号3-10（8个客户） P2 = list(range(11, 19)) # 中转站2对应的客户编号11-18（8个客户） P = P1 + P2 # 所有客户 N = S + P # 所有节点（不包括仓库） # ==================== # DispatchCost 的处理 # ==================== DispatchCost_matrix = np.array([ [0, 11, 15, 13, 47, 2, 1, 2, 10], [14, 0, 8, 15, 37, 3, 14, 12, 9], [17, 8, 0, 23, 36, 9, 18, 16, 16], [13, 15, 22, 0, 42, 16, 11, 12, 7], [47, 36, 37, 42, 0, 39, 47, 45, 38], [12, 2, 8, 16, 38, 0, 10, 8, 9], [2, 12, 16, 11, 47, 9, 0, 2, 9], [3, 9, 14, 12, 46, 7, 2, 0, 8], [13, 10, 17, 7, 38, 11, 12, 11, 0], [0, 26, 34, 30, 14, 8, 25, 25, 32], [26, 0, 21, 8, 40, 35, 5, 7, 30], [34, 20, 0, 18, 48, 42, 15, 14, 15], [30, 8, 18, 0, 44, 38, 5, 5, 29], [14, 41, 48, 44, 0, 13, 40, 40, 43], [8, 34, 42, 38, 13, 0, 34, 33, 40], [25, 5, 16, 5, 39, 33, 0, 1, 25], [25, 7, 15, 6, 39, 33, 2, 0, 24], [31, 30, 16, 29, 43, 40, 25, 24, 0] ]) # ==================== # 创建模型 # ==================== model = gp.Model("Transportation_Optimization") # ==================== # 决策变量 # ==================== # x[i,j,t]: 是否有车辆从中转站i到客户j在时刻t运输 x = model.addVars(S, P, range(timeInterval), vtype=GRB.BINARY, name="x") # y1[i,t]: 从工厂到中转站 i 的货物量 y1 = model.addVars(S, range(timeInterval), lb=0, ub=Max1, vtype=GRB.CONTINUOUS, name="y1") # y2[j,t]: 从工厂到客户 j 的货物量 y2 = model.addVars(P, range(timeInterval), lb=0, ub=Max2, vtype=GRB.CONTINUOUS, name="y2") # y3[i,j,t]: 中转站 i -> 客户 j 的货物量，仅定义有效的 (i,j,t) y3 = model.addVars([(i, j, t) for i in S for j in (P1 if i ==1 else P2) for t in range(timeInterval)], lb=0, ub=Max3, vtype=GRB.CONTINUOUS, name="y3") # l[j,t]: 客户 j 在时刻 t 的未完成订单量 l = model.addVars(P, range(timeInterval), lb=0, vtype=GRB.CONTINUOUS, name="l") # h[i,t]: 中转站 i 在时刻 t 的实时存货量 h = model.addVars(S, range(timeInterval), lb=0, vtype=GRB.CONTINUOUS, name="h") # k[i,t]: 中转站 i 在时刻 t 的可用车辆数量 k_ub = {(i, t): K[i - 1] for i in S for t in range(timeInterval)} k = model.addVars(S, range(timeInterval), lb=0, ub=k_ub, vtype=GRB.INTEGER, name="k") # li[j,t]: 时刻 t 车辆到客户 j 时未卸货前的剩余负载 li = model.addVars(P, range(timeInterval), lb=0, ub=Q, vtype=GRB.CONTINUOUS, name="li") # z[i,j,t]: 车辆是否从客户i直接运送到客户j（表示多个客户服务） z = model.addVars(P, P, range(timeInterval), vtype=GRB.BINARY, name="z") # 取 DispatchCost1 和 DispatchCost2 的第一列作为调度成本 DispatchCost1 = DispatchCost_matrix[0:8, 0] # 中转站1对应P1的调度成本 DispatchCost2 = DispatchCost_matrix[8:16, 0] # 中转站2对应P2的调度成本 # # 目标函数 # total_cost = ( # quicksum(HoardCost * h[i, t] for i in S for t in range(timeInterval)) + # 存货成本 # quicksum(TravelCost1[i - 1] * y1[i, t] for i in S for t in range(timeInterval)) + # 工厂到中转站运输成本 # quicksum(TravelCost2[j - 3] * y2[j, t] for j in P for t in range(timeInterval)) + # 工厂到客户运输成本 # quicksum(TravelCost3 * y3[i, j, t] for (i, j, t) in y3.keys()) + # 中转站到客户运输成本 # quicksum(DispatchCost1[j - 3] * x[1, j, t] for j in P1 for t in range(timeInterval)) + # 中转站1到客户调度成本 # quicksum(DispatchCost2[j - 11] * x[2, j, t] for j in P2 for t in range(timeInterval)) + # 中转站2到客户调度成本 # quicksum(TimeoutCost * l[j, t] for j in P for t in range(timeInterval)) # 客户需求超时成本 # ) # model.setObjective(total_cost, GRB.MINIMIZE) # dispatch_cost = quicksum( # DispatchCost_matrix[i - 1, j - 3] * x[i, j, t] # 从中转站到客户的调度成本 # for i in S for j in P for t in range(timeInterval) # if 3 <= j <= 10 # 客户3到客户10，确保索引不超出 # ) + quicksum( # DispatchCost_matrix[i - 1, j - 11] * x[i, j, t] # 中转站到客户的调度成本 # for i in S for j in P for t in range(timeInterval) # if 11 <= j <= 18 # 客户11到客户18，确保索引不超出 # ) # # 将dispatch_cost添加到目标函数中 # model.setObjective( # -(RentCost + HoardCost + TravelCost1 + TravelCost2 + TimeoutCost + dispatch_cost), # GRB.MAXIMIZE # ) # 目标函数 total_cost = ( quicksum(RentCost * RentSize for i in S for t in range(timeInterval)) + # 中转站租赁成本（标量乘以租赁容量） quicksum(HoardCost * k[i, t] for i in S for t in range(timeInterval)) + # 中转站存货成本 quicksum(TravelCost1[i - 1] * y1[i, t] for i in S for t in range(timeInterval)) + # 工厂到中转站运输成本 quicksum(TravelCost2[j - 3] * y2[j, t] for j in P for t in range(timeInterval)) + # 工厂到客户运输成本 quicksum(TravelCost3 * y3[i, j, t] for (i, j, t) in y3.keys()) + # 中转站到客户运输成本 quicksum(DispatchCost1[j - 3] * x[1, j, t] for j in P1 for t in range(timeInterval)) + # 中转站1到客户调度成本 quicksum(DispatchCost2[j - 11] * x[2, j, t] for j in P2 for t in range(timeInterval)) + # 中转站2到客户调度成本 quicksum(TimeoutCost * l[j, t] for j in P for t in range(timeInterval)) # 客户需求超时成本 ) # 设置目标函数为最小化总成本 model.setObjective(total_cost, GRB.MINIMIZE) # 车辆调度成本 dispatch_cost = quicksum( DispatchCost_matrix[i - 1, j - 3] * x[i, j, t] # 从中转站到客户的调度成本 for i in S for j in P for t in range(timeInterval) if 3 <= j <= 10 # 客户3到客户10，确保索引不超出 ) + quicksum( DispatchCost_matrix[i - 1, j - 11] * x[i, j, t] # 中转站到客户的调度成本 for i in S for j in P for t in range(timeInterval) if 11 <= j <= 18 # 客户11到客户18，确保索引不超出 ) # 将dispatch_cost添加到目标函数中 model.setObjective( -(total_cost + dispatch_cost), GRB.MAXIMIZE ) # ==================== # 约束条件 # ==================== # 1. 每个客户在每个时刻的需求必须被满足（包括未完成订单） for j in P: for t in range(timeInterval): if t == 0: model.addConstr( y2[j, t] + quicksum(y3[i, j, t] for i in S if j in (P1 if i ==1 else P2)) + l[j, t] == demand[t, j - 3], name=f"Demand_Fulfill_{j}_{t}" ) else: model.addConstr( y2[j, t] + quicksum(y3[i, j, t] for i in S if j in (P1 if i ==1 else P2)) + l[j, t] == l[j, t - 1] + demand[t, j - 3], name=f"Load_Balance_{j}_{t}" ) # 2. 中转站库存容量限制 for i in S: for t in range(timeInterval): model.addConstr( h[i, t] <= RentSize, name=f"Storage_Limit_{i}_{t}" ) # 3. y3 与 x 的车辆容量挂钩 for (i, j, t) in y3.keys(): model.addConstr( y3[i, j, t] <= Q * x[i, j, t], name=f"Vehicle_Capacity_{i}_{j}_{t}" ) # 4. 动态库存平衡 for i in S: for t in range(timeInterval): if t == 0: model.addConstr( h[i, t] == y1[i, t] - quicksum(y3[i, j, t] for j in (P1 if i == 1 else P2)), name=f"Initial_Inventory_{i}_{t}" ) else: model.addConstr( h[i, t] == h[i, t - 1] + y1[i, t] - quicksum(y3[i, j, t] for j in (P1 if i == 1 else P2)), name=f"Inventory_Balance_{i}_{t}" ) # 5. 未完成订单 l[j,t] 动态更新 for j in P: for t in range(timeInterval): if t == 0: model.addConstr( l[j, t] == demand[t, j - 3] - y2[j, t] - quicksum(y3[i, j, t] for i in S if j in (P1 if i == 1 else P2)), name=f"Initial_Load_{j}_{t}" ) else: model.addConstr( l[j, t] == l[j, t - 1] + demand[t, j - 3] - y2[j, t] - quicksum(y3[i, j, t] for i in S if j in (P1 if i == 1 else P2)), name=f"Load_Balance_{j}_{t}" ) # 6. 客户服务约束：每个客户在每个时刻只能由一辆车服务 for j in P: for t in range(timeInterval): model.addConstr( quicksum(x[i, j, t] for i in S if j in (P1 if i == 1 else P2)) <= 1, name=f"One_Vehicle_Per_Customer_{j}_{t}" ) # 7. 车辆数量限制：中转站 i 每个时刻调度车辆 <= K[i - 1] for i in S: for t in range(timeInterval): model.addConstr( quicksum(x[i, j, t] for j in (P1 if i == 1 else P2)) <= K[i - 1], name=f"Vehicle_Limit_{i}_{t}" ) # 8. 车辆可用性约束：k[i,t] 动态追踪可用车辆 for i in S: for t in range(timeInterval): if t == 0: model.addConstr( k[i, t] == K[i - 1] - quicksum(x[i, j, t] for j in (P1 if i == 1 else P2)), name=f"Initial_Vehicle_Availability_{i}_{t}" ) else: model.addConstr( k[i, t] == k[i, t - 1] + quicksum(x[i, j, t - 1] for j in (P1 if i == 1 else P2)) - \ quicksum(x[i, j, t] for j in (P1 if i == 1 else P2)), name=f"Vehicle_Availability_{i}_{t}" ) # 9. 剩余负载约束 for j in P: for t in range(timeInterval): model.addConstr( li[j, t] >= quicksum(y3[i, j, t] for i in S if j in (P1 if i == 1 else P2)) - Q, name=f"Remaining_Load_{j}_{t}" ) model.addConstr( li[j, t] >= 0, name=f"Nonnegative_Remaining_Load_{j}_{t}" ) # 10. 客户间运输路径约束（从一个客户到另一个客户） for i in P: for j in P: if i != j: # 如果i与j不同，才能建立路径 for t in range(timeInterval): model.addConstr(z[i, j, t] <= quicksum(x[i, j, t] for i in S), name=f"Path_Condition_{i}_{j}_{t}") # ==================== # 求解模型 # ==================== model.setParam('OutputFlag', 1) # 启用详细日志以便调试 model.optimize() # ==================== # 输出结果 # ==================== if model.status == GRB.OPTIMAL: print(f"最优解找到。目标值（成本）: {model.objVal}") # 输出决策变量的值 # y1: 从仓库到中转站的运输量 print("\n从仓库到中转站的运输量 y1:") for i in S: for t in range(timeInterval): if y1[i, t].X > 0: print(f"中转站 {i}, 时间 {t}: {y1[i, t].X}") # y2: 从仓库到客户的运输量 print("\n从仓库到客户的运输量 y2:") for i in P: for t in range(timeInterval): if y2[i, t].X > 0: print(f"客户 {i}, 时间 {t}: {y2[i, t].X}") # y3: 从中转站到客户的运输量 print("\n从中转站到客户的运输量 y3:") for i in S: # 对每个中转站 for j in (P1 if i == 1 else P2): # 对每个客户 for t in range(timeInterval): # 对每个时间段 if (i, j, t) in y3 and y3[i, j, t].X > 0: # 检查变量是否存在且大于0 print(f"中转站 {i} 到客户 {j}, 时间 {t}: {y3[i, j, t].X}") # 输出 x (车辆路径) print("\n车辆路径 x:") for i in S: # 对每个中转站 for j in P: # 对每个客户 for t in range(timeInterval): # 对每个时间段 if (i != j) and (i, j, t) in x and x[i, j, t].X > 0.5: # 检查是否有车辆路径且不为自环 print(f"时间 {t}: 从中转站 {i} 到客户 {j} 有车辆") else: print("未找到最优解。")