Mathematical programming formulations for machine scheduling: A survey

Jacek Blazewicz, Moshe Dror, Jan Weglarz

Research output: Contribution to journalArticle

103 Citations (Scopus)

Abstract

Machine scheduling was and still is a rich and promising field for research with applications in manufacturing, logistics, computer architecture, communications, etc. Combinatorial complexity theory has now classified the great majority of known machine scheduling problems as 'easy' or 'very hard'. However, in most cases, mathematical programming models have not accompanied the algorithmic developments for solving 'easy' scheduling problems, nor have they facilitates solutions for 'hard' problems. Nevertheless, the analysis of the mathematical programming models for some hard combinatorial problems together with their polyhedral properties has enabled important computational advances for such problems as the TSP. In order to assess the present status and the solution potential of mathematical programming formulations for machine scheduling, we have compiled a systematic, consistent survey of formulations. The discussion has been developed in tandem with the classification of a given problem's complexity, since 'solvability' (i.e., the status of a problem as P or NP-hard) generally cannot be easily assessed from the formulation itself. A number of excellent survey papers on machine scheduling have appeared over the years (see the reference list), but none of them has been focused on mathematical formulations. This survey is the first one that attempts to compile a large number of mathematical programming formulations for scheduling into a single paper to ease the task of model building and testing scheduling formulations. Both, a newcomer and experienced researcher can use it as a reference point. Ultimately, mathematical programming formulations for scheduling problems might be used as a stepping stone to computational advances for some hard problems.

Original languageEnglish (US)
Pages (from-to)283-300
Number of pages18
JournalEuropean Journal of Operational Research
Volume51
Issue number3
DOIs
StatePublished - Apr 15 1991

Fingerprint

Machine Scheduling
Mathematical programming
Mathematical Programming
scheduling
programming
Scheduling
Formulation
Scheduling Problem
Programming Model
Mathematical Model
Combinatorial Complexity
Computer Architecture
Complexity Theory
Reference Point
Combinatorial Problems
Computer architecture
Machine scheduling
Logistics
Solvability
NP-complete problem

Keywords

  • additional resources
  • computational complexity
  • Machine scheduling
  • mathematical programming formulations

ASJC Scopus subject areas

  • Information Systems and Management
  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Modeling and Simulation
  • Transportation

Cite this

Mathematical programming formulations for machine scheduling : A survey. / Blazewicz, Jacek; Dror, Moshe; Weglarz, Jan.

In: European Journal of Operational Research, Vol. 51, No. 3, 15.04.1991, p. 283-300.

Research output: Contribution to journalArticle

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