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Minimizing maximum delivery completion time for order scheduling with rejection
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2020-09-16 , DOI: 10.1007/s10878-020-00649-2
Ren-Xia Chen , Shi-Sheng Li

We study an order scheduling problem with rejection, in which each order consists of multiple product types and each product type should be manufactured on a dedicated machine. The aim is to find a solution to minimize a linear sum of the maximum delivery completion time of the accepted orders and the total penalty of the rejected orders. Even if the delivery times of all orders are zero, the problem is shown to be binary \(\mathcal{NP}\)-hard in the two-machine case and it is shown to be unary \(\mathcal{NP}\)-hard when the number of machines is arbitrary. Three approximation algorithms are proposed and their worst-case performance ratios are analyzed. For the scenario where the number of machines is fixed, a pseudo-polynomial dynamic programming algorithm and a fully polynomial time approximation scheme are devised for it.



中文翻译:

最小化最大交货完成时间以进行有拒绝的订单计划

我们研究带有拒绝的订单计划问题,其中每个订单包含多种产品类型,每种产品类型应在专用机器上制造。目的是找到一种解决方案,以最小化已接受订单的最大交货完成时间与被拒绝订单的总罚款的线性总和。即使所有订单的交货时间为零,在两机情况下,问题也显示为二进制\(\ mathcal {NP} \)-困难,并且问题显示为一元\(\ mathcal {NP} \ )-hard(当机器数量任意时)。提出了三种近似算法,并分析了它们的最坏情况下的性能比。对于机器数量固定的情况,设计了一种拟多项式动态规划算法和一个完全多项式时间逼近方案。

更新日期:2020-09-16
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