Sequencing, task failures, and capacity when failures are driven by a non-homogeneous Poisson process

TL;DR

This paper investigates optimal task sequencing on machines affected by time-varying random disruptions modeled by a non-homogeneous Poisson process, identifying conditions where simple rules like SPT and LPT are optimal.

Contribution

It provides new insights into sequencing strategies under non-homogeneous Poisson disruptions, establishing when simple heuristics are optimal.

Findings

SPT and LPT rules can minimize batch completion time under certain conditions.

The disruption process's time-varying nature influences optimal sequencing.

Conditions are derived for the effectiveness of simple sequencing rules.

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.