Abstract

Most previous studies concerning process flexibility designs have focused on expected sales and demand uncertainty. In this paper, we examine the worst-case performance of flexibility designs in the case of demand and supply uncertainties, where the latter can be in the form of either plant or arc disruptions. We define the Plant Cover Index under Disruptions (PCID) as the minimum required plants’ capacity to supply a fixed number of products after the disruptions. By exploiting PCID, we establish that under symmetric uncertainty sets the worst-case performance can be expressed in terms of PCID, supply and demand uncertainties. Additionally, PCID enables us to make meaningful comparisons of different designs. In particular, we demonstrate that under disruptions the 2-long chain design is superior to a broad class of designs. Moreover, we identify a condition wherein both Q-short and Q-long chain designs have the same worst-case performance. We also discuss the notion of fragility that quantifies the impact of disruptions in the worst case and compare fragilities of Q-short and Q-long chain designs under different types of disruptions. Finally, by employing PCID, we develop an algorithm to generate designs that perform well under supply and demand uncertainties in both the worst case and in expectation.

摘要

以前有关过程灵活性设计的大多数研究都集中在预期的销售和需求不确定性上。在本文中，我们研究了在需求和供应不确定性的情况下灵活性设计的最坏情况性能，其中不确定性可以是工厂中断或电弧中断的形式。我们将中断下的工厂覆盖指数（PCID）定义为中断后提供固定数量产品所需的最低工厂能力。通过利用PCID，我们可以确定在对称不确定性条件下，最坏情况下的性能可以用PCID，供需不确定性表示。此外，PCID使我们能够对不同设计进行有意义的比较。特别是，我们证明了在断裂情况下2长链设计优于广泛的设计类别。此外，Q短链和Q长链设计具有相同的最坏情况性能。我们还讨论了脆弱的量化中断的最坏情况下的影响的概念，并比较脆弱Q -short和Q下不同类型的中断的-长链设计。最后，通过使用PCID，我们开发了一种算法来生成在最坏情况和预期情况下都能在供需不确定的情况下表现良好的设计。