Parallel machine problems with equal processing times: a survey

Abstract

The basic scheduling problem we are dealing with is the following. There are n jobs, each requiring an identical execution time. All jobs have to be processed on a set of parallel machines. Preemptions can be either allowed or forbidden. The aim is to construct a feasible schedule such that a given criterion is minimized. For a couple of problems of this type, recently the complexity status has been solved and several interesting results have been presented. In this paper, we survey existing approaches for the problem class considered.

Two-Machine Job-Shop Scheduling with Equal Processing Times on Each Machine

“…Some results on parallel machine and single machine scheduling problems with unit and equal processing times of the jobs are presented in [9,10]. Single machine problems are equivalent to the special case of a two-machine job shop scheduling problem with n j = 2, p j1 = a, p j2 = b, where a is sufficiently small so that it can be disregarded.…”

Parameterized complexity of machine scheduling: 15 open problems

“…The three problems P|pmtn, r j |ΣC j , P|pmtn|ΣU j , and P|pmtn|ΣT j are all NP-hard (Du et al, 1990;Lawler, 1983;Kravchenko and Werner, 2013), yet the special cases with equal processing times are polynomial-time solvable (Baptiste et al, 2004(Baptiste et al, , 2007Kravchenko and Werner, 2011).…”

Heuristic algorithms for the unrelated parallel machine scheduling problem with one scarce additional resource

“…Some recent results can be found in Zeidi and MohammadHosseini (2015) and Chen (2015). A review of parallel machine scheduling problems can be found in Kravchenko and Werner (2011). According to Lenstra et al (1977), this problem is NPhard even for the simplest version with two identical parallel machines.…”