Multicriteria scheduling with controllable processing times, setup times, and learning, ageing and deterioration effects on a single machine

Abstract

This paper addresses several multicriteria single machine scheduling problems wherein a job processing time is either a convex or linear function of the amount of resource assigned to the job, learning and ageing are job-dependent and position-based, job deterioration linearly depends on the job starting time, and the job's setup time is proportional to the duration of the already processed jobs. The goal is to jointly determine the optimal resource allocations and the optimal sequence with respect to the total resource cost and a composite cost function of some criteria. We formulate the proposed multicriteria problems as constrained and unconstrained combinatorial optimisation models and introduce polynomial time algorithms to derive the optimal solutions. [Received 1 October 2015; Revised 26 November 2015; Accepted 10 February 2016]