Two machine scheduling under disruptions with transportation considerations

Effective logistics scheduling requires synchronization of manufacturing and delivery to optimize customer service at minimum total cost. In this paper, we study a new scheduling problem that arises in a disruption environment. Such a problem occurs when a disruption unexpectedly happens, and consequently, some machines become unavailable for certain periods. Jobs that are assigned to the disrupted machines and have not yet been processed can either be moved to other available machines for processing, which may involve additional transportation time and cost, or can be processed by the same machine after the disruption. Our goal is to reschedule jobs so that an objective function, including the original cost function, and possibly transportation costs and disruption cost caused by deviating from the originally planned completion times, is minimized. In this paper, we focus on the two-machine case to demonstrate some major properties, and hope that these properties can provide insights for solving other general problems, such as multiple (more than two) machine scheduling and machine scheduling in other configurations (job shop or flow shop) under disruption. We study problems with different related costs. In each problem, we either provide a polynomial algorithm to solve the problem optimally, or show its NP-hardness. If the problem is NP-hard in the ordinary sense, we also present a pseudo-polynomial algorithm to solve the problem optimally.