Scheduling in stochastic bicriteria single machine systems with set-up times

Abstract

This paper deals with a single machine scheduling problem where job attributes are random variables, setup times are sequence–dependent, and a scheduler utilises a cost function to evaluate two criteria associated with a sequence. The objective is to determine the optimal sequence that minimises the scheduler's expected cost. We show that problem scenarios wherein cost functions are linear, exponential, and fractional can be formulated as Quadratic Assignment Problems (QAPs). Also, special cases with sequence–independent setup times are shown to be solvable optimally in polynomial time. Our computational results on scenarios with sequence–dependent setup times demonstrate that good solutions can be approximated within reasonable amounts of time.