Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources

Abstract

In this paper we analyze a parallel machine scheduling problem in which the processing of jobs on the machines requires a number of units of a scarce resource. This number depends both on the job and on the machine. The availability of resources is limited and fixed throughout the production horizon. The objective considered is the minimization of the makespan. We model this problem by means of two integer linear programming problems. One of them is based on a model previously proposed in the literature. The other one, which is based on the resemblance to strip packing problems, is an original contribution of this paper. As the models presented are incapable of solving medium-sized instances to optimality, we propose three matheuristic strategies for each of these two models. The algorithms proposed are tested over an extensive computational experience. Results show that the matheuristic strategies significantly outperform the mathematical models.

Heuristic algorithms for the unrelated parallel machine scheduling problem with one scarce additional resource

“…In this section, comprehensive computational results on a benchmark originally proposed by Fanjul-Peyro et al (2017) are given. The proposed benchmark consists of three sets of small, medium and large instances.…”

“…As a result, heuristic methods for the general problem where both processing times and resource consumption of the jobs are different according to the machine to which jobs are assigned, have not been proposed yet in the literature. A recent study, where an adaptation of the model presented in Edis and Oguz (2012) is given, together with other different MILP mathematical models and matheuristics methods for the more general problem studied in this paper, can be found in Fanjul-Peyro et al (2017). A matheuristic is a combination of a mathematical model with a heuristic, some variables of the model are fixed according to the solution provided by a heuristic method.…”

“…Some examples related to scheduling problems are Croce et al (2014) and Billaut et al (2015). Therefore, the objective of this paper is to propose efficient (in terms of CPU time) and effective (in terms of quality of the solution) heuristic methods for the general problem, so that they are able to solve much larger instances than the methods presented in Fanjul-Peyro et al (2017), where only small and medium instances are considered.…”

A meta-heuristic algorithm for integrated optimization of dynamic resource allocation planning and production scheduling in parallel machine system

“…[27][28][29][30][31][32][33] The second category focused on parallel machine scheduling under the allocation constraint of reusable and renewable resources. [34][35][36][37] Resource allocation among machines and jobs was known in advance, and thus, a schedule plan should include three decisions, that is, job assignment among machines, job sequence, and start time on machines. It is noticeable that the most works only concerned the allocation of resources among machines and jobs in a static way.…”

Simultaneous Considering of Machine Availability Constraint, Sequence Dependent Setup Time and Ready Time in a No-wait Hybrid Flow Shop Scheduling Problem to Minimize Mean Tardiness

“…Recently, solving some new problems in scheduling area have been attracted by many researchers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] The problem of how to sequence jobs in a no-wait hybrid flow shop has received vast attention in the academic literature, but the majority of literature focuses on how to minimize maximum completion time (i.e. makespan).…”