Approximation results for flow shop scheduling problems with machine availability constraints

Abstract

This paper considers two-machine flow shop scheduling problems with machine availability constraints. When the processing of a job is interrupted by an unavailability period of a machine, we consider both the resumable scenario in which the processing can be resumed when the machine next becomes available, and the semi-resumable scenarios in which some proportion of the processing is repeated but the job is otherwise resumable. For the resumable scenario, problems with non-availability intervals on one of the machines are shown to admit fully polynomial-time approximation schemes that are based on an extended dynamic programming algorithm. For the problem with several non-availability intervals on the first machine, we present a fast 3/2-approximation algorithm. For the problem with one non-availability interval under the semi-resumable scenario, polynomial-time approximation schemes are developed.

Fifty years of scheduling: a survey of milestones

“…Under the resumable scenario, the two-machine flow shop problem to minimize the makespan may admit a constant ratio approximation algorithm only if there are several MNAIs on the first machine or a single MNAI on the second machine. The problem with a single MNAI under the resumable scenario admits an FPTAS, such as the one designed by Ng and Kovalyov (2004), while under the semi-resumable scenario it can be solved by a PTAS developed by Kubzin et al (2009).…”

An improved algorithm for the two machine flow shop problem with several availability constraints

“…In this context, Kubzin et al (2009) propose a ( 3 2 )-approximation algorithm for the F2|h(q, 0), r |C max problem which is the only configuration of the two-machine flow shop problem with several holes that may admit a fixed factor approximation algorithm.…”

“…Besides, all jobs are supposed to be resumable. Following Kubzin et al (2009), we will denote the problem F2|h(q, 0), r |C max .…”

“…For the nonresumable scenario, Hadda et al (2009) develop a ( 3 2 )-approximation algorithm for the F2|h(1, 0), nr|C max problem. Finally, it has been shown that the the two-machine flow shop with a single hole admits a PTAS under the semiresumable scenario (Kubzin et al 2009) and a FPTAS under the resumable scenario (Ng and Kovalyov 2004).…”

Integrating the sequence dependent setup time open shop problem and preventive maintenance policies

“…In this paper, they provided a novel variable neighborhood search (VNS) as well as the adaptations of some existing high performing meta-heuristics in the literature. Kubzin et al (2009) considered the two-machine flow shop scheduling problem where the machines are unavailability during a period. They considered both the resumable scenario and the semi-resumable scenario and provided approximation algorithm for them.…”