Sequencing, Task Failures, and Capacity When Failures Are Driven by a Non‐Homogeneous Poisson Process

ABSTRACT We study the optimal sequencing of a batch of tasks on a machine subject to random disruptions driven by a non‐homogeneous Poisson process (NHPP), such that every disruption requires the interrupted task to be re‐processed from scratch, and partially completed work on a disrupted task is wasted. The NHPP models random disruptions whose frequency varies systematically with time. In general, the time taken to process a given batch of tasks depends on the order in which the tasks are processed. We find conditions under which the simplest possible sequencing rules—shortest processing time first (SPT) and longest processing time first (LPT)—suffice to minimize the completion time of a batch of tasks.