### 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 language | English (US) |
---|---|

Pages (from-to) | 283-300 |

Number of pages | 18 |

Journal | European Journal of Operational Research |

Volume | 51 |

Issue number | 3 |

DOIs | |

State | Published - Apr 15 1991 |

### Fingerprint

### 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

*European Journal of Operational Research*,

*51*(3), 283-300. https://doi.org/10.1016/0377-2217(91)90304-E

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

Research output: Contribution to journal › Article

*European Journal of Operational Research*, vol. 51, no. 3, pp. 283-300. https://doi.org/10.1016/0377-2217(91)90304-E

}

TY - JOUR

T1 - Mathematical programming formulations for machine scheduling

T2 - A survey

AU - Blazewicz, Jacek

AU - Dror, Moshe

AU - Weglarz, Jan

PY - 1991/4/15

Y1 - 1991/4/15

N2 - 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.

AB - 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.

KW - additional resources

KW - computational complexity

KW - Machine scheduling

KW - mathematical programming formulations

UR - http://www.scopus.com/inward/record.url?scp=0026137217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026137217&partnerID=8YFLogxK

U2 - 10.1016/0377-2217(91)90304-E

DO - 10.1016/0377-2217(91)90304-E

M3 - Article

AN - SCOPUS:0026137217

VL - 51

SP - 283

EP - 300

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -