如何解决CPLEX的多商品问题？

from docplex.mp.model import Model

# 创建模型
mdl = Model(name='multi_commodity_flow')

# 定义决策变量
num_nodes = 5
num_commodities = 3
num_edges = 8
flow_vars = mdl.continuous_var_dict([(i, j, k) for i in range(num_nodes) for j in range(num_nodes) for k in range(num_commodities)], name='flow')

# 定义目标函数
total_cost = mdl.sum(flow_vars[i, j, k] * cost[i, j] for i in range(num_nodes) for j in range(num_nodes) for k in range(num_commodities))
mdl.minimize(total_cost)

# 定义约束条件
for k in range(num_commodities):
    for i in range(num_nodes):
        mdl.add_constraint(mdl.sum(flow_vars[i, j, k] for j in range(num_nodes)) - mdl.sum(flow_vars[j, i, k] for j in range(num_nodes)) == supply_demand[i][k], ctname=f'flow_balance_{i}_{k}')

for (i, j) in edges:
    mdl.add_constraint(mdl.sum(flow_vars[i, j, k] for k in range(num_commodities)) <= capacity[i, j], ctname=f'capacity_{i}_{j}')

# 求解模型
mdl.solve()

# 输出结果
for i in range(num_nodes):
    for j in range(num_nodes):
        for k in range(num_commodities):
            print(f'Flow from {i} to {j} for commodity {k}: {flow_vars[i, j, k].solution_value}')