This paper considers a joint order acceptance and scheduling problem under a general scenario. A manufacturer receives multiple orders with a given revenue, processing time, release date, due date, deadline, and earliness and tardiness penalties. The manufacturer can be seen as a single-machine system. Due to limited capacity, the manufacturer cannot process every order and needs to determine the optimal set of accepted orders and corresponding production schedule such that the total profit is maximized. The manufacturer can extend its capacity with overtime by paying an additional cost. A time-indexed formulation is presented to model the problem. Two exact algorithms are proposed. The first algorithm, denoted by DPIA-GR, is a dynamic programming (DP)-based algorithm that starts by solving a relaxed version of the original model and successively recovers the relaxed constraint until an optimal solution to the original problem is achieved. The second algorithm, denoted by DPIA-LRGR, improves DPIA-GR by incorporating Lagrangian relaxation (LR). The subgradient method is employed to find the optimal Lagrangian multipliers. The relaxed model in DPIA-GR and the LR model in DPIA-LRGR can be represented using a weighted di-graph. Both algorithms are equivalent to finding the longest path in the graph and applying a graph reduction strategy to prevent unnecessary computational time and memory usage. A genetic algorithm (GA) is also proposed to solve large-scale versions of the problem. Numerical experiments show that both DPIA-GR and DPIA-LRGR solve the problem efficiently and outperform CPLEX and GA, but DPIA-LRGR offers better performance.

中文翻译：

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考虑加班的具有提前和迟到惩罚的联合订单接受和调度问题

本文考虑了一般场景下的联合订单接受和调度问题。制造商收到多个订单，具有给定的收入、处理时间、发布日期、到期日、截止日期以及提前和迟到罚款。制造商可以看作是一个单机系统。由于产能有限，制造商无法处理每一个订单，需要确定可接受的订单的最佳集合和相应的生产计划，以使总利润最大化。制造商可以通过支付额外费用来延长其产能。提出了一个时间索引公式来对问题进行建模。提出了两种精确算法。第一种算法，由 DPIA-GR 表示，是一种基于动态规划 (DP) 的算法，它首先求解原始模型的松弛版本，然后连续恢复松弛约束，直到获得原始问题的最佳解决方案。由 DPIA-LRGR 表示的第二种算法通过结合拉格朗日松弛 (LR) 改进了 DPIA-GR。次梯度方法用于寻找最优拉格朗日乘数。DPIA-GR 中的松弛模型和 DPIA-LRGR 中的 LR 模型可以使用加权有向图表示。这两种算法都相当于在图中找到最长路径并应用图缩减策略来防止不必要的计算时间和内存使用。还提出了一种遗传算法 (GA) 来解决该问题的大规模版本。