The problem of integrated production and transportation scheduling, commonly faced by make-to-order manufacturers under a commit-to-delivery business mode, is known to be strongly NP-hard. In this study, we propose two new exact algorithms to solve the problem with order acceptance decisions also taken into account. These algorithms can achieve polynomial or pseudo-polynomial running times in several practical situations. We also develop the first pseudo-polynomial time approximation scheme for this problem. It not only guarantees a worst-case performance ratio of $(1+ϵ)$ for any fixed $ϵ>0$, but also achieves good computational performance.

中文翻译：

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用于集成生产和运输调度的新精确和近似算法，具有承诺的交货到期日和订单接受

众所周知，在承诺交付业务模式下，按订单生产的制造商通常面临的集成生产和运输调度问题具有很强的 NP 难性。在这项研究中，我们提出了两种新的精确算法来解决同时考虑订单接受决策的问题。这些算法可以在几种实际情况下实现多项式或伪多项式运行时间。我们还为这个问题开发了第一个伪多项式时间近似方案。它不仅保证了最坏情况下的性能比$(\mathrm{1个}+\epsilon )$对于任何固定$\epsilon >0$，而且还实现了良好的计算性能。