Minimizing the weighted sum of maximum earliness and maximum tardiness costs on a single machine with periodic preventive maintenance

Rachid Benmansour (1) , Hamid Allaoui (2) , Abdelhakim Artiba (1) , Said Hanafi (1)

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201
2 UA - Université d'Artois

We consider the problem of scheduling a set of jobs on a single machine against a common and restrictive due date. In particular, we are interested in the problem of minimizing the weighted sum of maximum earliness and maximum tardiness costs. This kind of objective function is related to the just-in-time environment where penalties, such as storage cost and additional charges for late delivery, should be avoided. First we present a mixed integer linear model for the problem without availability constraints and we prove that this model can be reduced to a polynomial-time model. Secondly, we suppose that the machine undergoes a periodic preventive maintenance. We present then a second mixed integer linear model to solve the problem to optimality. Although the latter problem can be solved to optimality for small instances, we show that the problem reduces to the one-dimensional bin packing problem. Computational results show that the proposed algorithm best fit decreasing performs well.

Mots clés: Scheduling; Earliness; Tardiness; Maintenance; Due date

Domaines: Informatique [cs]

Rachid Benmansour, Hamid Allaoui, Abdelhakim Artiba, Said Hanafi. Minimizing the weighted sum of maximum earliness and maximum tardiness costs on a single machine with periodic preventive maintenance. Computers and Operations Research, 2014, 47, pp.106-113. ⟨10.1016/j.cor.2014.02.004⟩. ⟨hal-03578398⟩