Single machine scheduling with simple linear deterioration to minimize total absolute deviation of completion times

Abstract

We consider a single machine scheduling problem with simple linear deterioration. Job processing times are assumed to be a simple linear function of a job-dependent growth rate and the job's starting time. We seek an optimal schedule, so as to minimize the total absolute deviation of completion times ( TADC). We prove several interesting properties of an optimal schedule, and introduce two efficient heuristics which are tested against a lower bound. Scope and purpose In most scheduling problems jobs are assumed to have time-independent processing times. In many real life applications, jobs deteriorate at a certain rate while waiting to be processed. We study the effect of job deterioration when addressing a scheduling problem with the non-regular objective function of minimizing the total deviation of completion times. This objective can be regarded as a measure of “fairness” towards customers of the production system.