Bicriteria single machine scheduling with setup times and learning effects

Abstract

We study a bicriteria single machine scheduling problem with job-dependent and past-sequence-dependent (psd) setup time and job-dependent learning effects. The goal is to find the optimal sequence that minimizes a linear combination of a pair of performance criteria consisting of the makespan, the total completion time, and the total absolute differences in completion times. We show that special cases of the resulting three problems are solvable polynomially. However, the general cases cannot be solved in polynomial time; thus, branch-and-bound (B&B) methods are proposed to derive optimal sequences. Computational results demonstrate that the B&B methods solve relatively large problem instances in reasonable amounts of time.