MIP models and hybrid algorithm for minimizing the makespan of parallel machines scheduling problem with a single server

Mi Yi Kim, Young Hoon Lee

Research output: Contribution to journalArticle

32 Citations (Scopus)


This paper considers the identical parallel machines scheduling problem (PMSP) with a single server in charge of job setups. A job can be processed with a precedent setup by a server on one of the machines. The setup can be processed at only one machine at any time. In this paper, the problem P, S1|s j|C max with a general job set is formulated using mixed integer programming in two ways. The first one is developed by taking into account the characteristics of the single server problem, and the second one is developed by adding the concept of the server waiting time suggested by Abdekhodaee and Wirth (2002) [3]. Abdekhodaee and Wirth (2002) [3] define the equation of the server waiting time applied to only the special case with two machines and a regular job set. The general model for several machines is studied in this paper by developing the properties on the server waiting time. The hybrid heuristic algorithm is developed for the practical use, which can yield a near-optimal schedule in a reasonable computational time. The performance of algorithm is evaluated by comparing with the results of MIP models and heuristics appearing in the literature.

Original languageEnglish
Pages (from-to)2457-2468
Number of pages12
JournalComputers and Operations Research
Issue number11
Publication statusPublished - 2012 Nov 1


All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research

Cite this