Publication detail

The Assignment Problem and Its Relation to Logistics Problems

ŠEDA, M.

Original Title

The Assignment Problem and Its Relation to Logistics Problems

Type

journal article in Web of Science

Language

English

Original Abstract

The assignment problem is a problem that takes many forms in optimization and graph theory, and by changing some of the constraints or interpreting them differently and adding other constraints, it can be converted to routing, distribution and scheduling problems. Showing such correlations is one of the aims of this paper. Some of the derived problems having exponential time complexity, the question arises of their solvability for larger instances. Instead of the traditional approach based on the use of approximate or stochastic heuristic methods, we focus here on the direct use of mixed integer programming models in the GAMS environment, which is now capable of solving instances much larger than in the past and does not require complex parameter settings or statistical evaluation of the results as in the case of stochastic heuristics because the computational core of software tools, nested in GAMS, is deterministic in nature. The source codes presented may be an aid, because this tool is not yet as well known as the MATLAB Optimisation Toolbox. Benchmarks of the permutation flow shop scheduling problem with informally derived MIP model and the travelling salesman problem are used to present the limits of the software’s applicability.

Keywords

assignment problem; travelling salesman problem; vehicle routing problem; flow shop scheduling problem; GAMS, genetic algorithm

Authors

ŠEDA, M.

Released

16. 10. 2022

Publisher

MDPI

ISBN

1999-4893

Periodical

Algorithms

Year of study

15

Number

10

State

Swiss Confederation

Pages from

1

Pages to

27

Pages count

27

URL

https://www.mdpi.com/1999-4893/15/10/377

Full text in the Digital Library

http://hdl.handle.net/11012/208586

BibTex

@article{BUT179566,
  author="Miloš {Šeda}",
  title="The Assignment Problem and Its Relation to Logistics Problems",
  journal="Algorithms",
  year="2022",
  volume="15",
  number="10",
  pages="1--27",
  doi="10.3390/a15100377",
  issn="1999-4893",
  url="https://www.mdpi.com/1999-4893/15/10/377"
}