Minimizing weighted earliness–tardiness on a single machine with a common due date using quadratic models

  1. Ramon Alvarez-Valdes 1
  2. Enric Crespo 1
  3. Jose Manuel Tamarit 1
  4. Fulgencia Villa 2
  1. 1 Universitat de València, España
  2. 2 Universitat Politècnica de València, España
Journal:
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ISSN: 1863-8279,  1134-5764

Year of publication: 2012

Volume: 20

Issue: 3

Pages: 754-767

Type: Article

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Abstract

In this paper we study the problem of minimizing weighted earliness and tardiness on a single machine when all the jobs share the same due date. We propose two quadratic integer programming models for solving both cases of unrestricted and restricted due dates, an auxiliary model based on unconstrained quadratic integer programming and an algorithmic scheme for solving each instance, according to its size and characteristics, in the most efficient way. The scheme is tested on a set of well-known test problems. By combining the solutions of the three models we prove the optimality of the solutions obtained for most of the problems. For large instances, although optimality cannot be proved, we actually obtain optimal solutions for all the tested instances.

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Funding information

This study has been partially supported by the Spanish Ministry of Science and Technology, DPI2008-02700, cofinanced by FEDER funds, and by Project PCI08-0048-8577, Consejeria de Ciencia y Tecnolo-gia, Junta de Comunidades de Castilla-La Mancha, and Generalitat Valenciana ACOMP/2009/264.

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