This study considers a general production and delivery integration problem, commonly faced by a manufacturer that adopts make-to-order and commit-to-delivery business strategies. In the problem, the manufacturer determines acceptance or rejection of customers, produces products for accepted customers, and cooperates with third-party logistics providers who offer multiple shipping modes chosen by the manufacturer to deliver the finished products to customers. To better reflect the practical needs, this problem takes into account nonlinear production cost functions, nonlinear earliness and tardiness penalty functions, and nonlinear shipping cost functions of both shipping time and shipping quantity. The problem is to determine an integrated customer acceptance, production, and delivery plan by minimizing the total cost of production, shipping and inventory holding, and the total penalty of rejection, earliness, and tardiness. We investigate two variants of the problem where splittable delivery for the orders from customers is allowed and where splittable delivery is not allowed. For both the variants, we develop exact algorithms which achieve pseudo-polynomial running time in some practical situations, and design column generation-based heuristic algorithms to find near-optimal solutions efficiently. The computational results demonstrate that the heuristic algorithms are capable of generating near-optimal solutions for the instances generated randomly, with average optimality gap less than 4% in a reasonable running time.

中文翻译：

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用于一般生产和交付集成的新的精确和启发式算法

本研究考虑了采用按订单生产和承诺交付业务策略的制造商通常面临的一般生产和交付集成问题。在该问题中，制造商决定接受或拒绝客户，为接受的客户生产产品，并与提供制造商选择的多种运输方式的第三方物流提供商合作，将成品交付给客户。为了更好地反映实际需求，该问题考虑了非线性生产成本函数、非线性提前和迟到惩罚函数以及运输时间和运输数量的非线性运输成本函数。问题是通过最小化生产、运输和库存持有的总成本以及拒绝、提前和迟到的总惩罚来确定综合的客户验收、生产和交付计划。我们研究了该问题的两种变体，其中允许客户订单的可拆分交付和不允许可拆分交付。对于这两种变体，我们开发了在某些实际情况下实现伪多项式运行时间的精确算法，并设计基于列生成的启发式算法以有效地找到接近最优的解决方案。计算结果表明，启发式算法能够为随机生成的实例生成接近最优的解决方案，在合理的运行时间内平均最优性差距小于 4%。