In this study, we consider an integrated production and transportation scheduling problem faced by make-to-order manufacturers that adopt a commit-to-delivery business mode and cooperate with third-party logistics providers to deliver processed products to customers. The third-party logistics providers typically offer multiple shipping modes chosen by the manufacturers to deliver products, each shipping mode with a shipping time guarantee and a shipping cost function that is non-increasing in shipping time and sub-additive, non-decreasing in shipping quantity. The problem involves inventory holding costs which not only depend on the time that the products spend in temporary storage but also depend on customer types. The problem is to determine an integrated production and shipping schedule that satisfies the committed delivery due date limitations for the customers, such that the total cost of shipping and inventory holding is minimized. We investigate two cases with and without split delivery. For both cases, we first show that both of them are ordinarily NP-hard, prove that there exist no polynomial-time approximation algorithms with constant worst-case ratios, propose exact algorithms to solve them, and finally design column generation-based heuristic algorithms to find feasible solutions. The computational results demonstrate that the heuristic algorithms are capable of generating near-optimal solutions efficiently. We also consider two interesting practical variants of the problem.

在这项研究中，我们考虑了采用承诺交付业务模式并与第三方物流供应商合作将加工产品交付给客户的按订单制造制造商所面临的综合生产和运输调度问题。第三方物流供应商通常提供制造商选择的多种运输方式来交付产品，每种运输方式都具有运输时间保证和不增加运输时间和不增加运输时间的次加性、不减少运输的运输成本功能。数量。问题涉及库存持有成本，这不仅取决于产品在临时存储中花费的时间，还取决于客户类型。问题是确定一个集成的生产和运输计划，以满足客户承诺的交货到期日限制，从而使运输和库存持有的总成本最小化。我们调查了分批交付和不分拆交付的两个案例。对于这两种情况，我们首先证明它们通常都是 NP-hard，证明不存在具有恒定最坏情况比率的多项式时间逼近算法，提出精确算法来解决它们，最后设计基于列生成的启发式算法寻找可行的解决方案。计算结果表明启发式算法能够有效地生成接近最优的解决方案。我们还考虑了该问题的两个有趣的实际变体。从而使运输和库存持有的总成本最小化。我们调查了分批交付和不分拆交付的两个案例。对于这两种情况，我们首先证明它们通常都是 NP-hard，证明不存在具有恒定最坏情况比率的多项式时间逼近算法，提出精确算法来解决它们，最后设计基于列生成的启发式算法寻找可行的解决方案。计算结果表明启发式算法能够有效地生成接近最优的解决方案。我们还考虑了该问题的两个有趣的实际变体。从而最大限度地降低运输和库存持有的总成本。我们调查了有和没有分批交付的两个案例。对于这两种情况，我们首先证明它们通常都是 NP-hard，证明不存在具有恒定最坏情况比率的多项式时间逼近算法，提出精确算法来解决它们，最后设计基于列生成的启发式算法寻找可行的解决方案。计算结果表明启发式算法能够有效地生成接近最优的解决方案。我们还考虑了该问题的两个有趣的实际变体。证明不存在具有恒定最坏情况比率的多项式时间逼近算法，提出精确算法来解决它们，最后设计基于列生成的启发式算法以寻找可行解。计算结果表明启发式算法能够有效地生成接近最优的解决方案。我们还考虑了该问题的两个有趣的实际变体。证明不存在具有恒定最坏情况比率的多项式时间逼近算法，提出精确算法来解决它们，最后设计基于列生成的启发式算法以寻找可行解。计算结果表明启发式算法能够有效地生成接近最优的解决方案。我们还考虑了该问题的两个有趣的实际变体。