Parallel Cooperative Approaches for the Labor ConstrainedScheduling

In this paper we consider the labor constrained scheduling problem (LCSP), in which a set of jobs to be processed is subject to precedence and labor requirement constraints. Each job has a speciied processing time and a labor requirements proole, which typically varies as the job is processed. Given the amount of labor available at each period, the problem consists in determining starting times so as to minimize the overall makespan, subject to the precedence and labor constraints. We propose two parallel cooperative algorithms for LCSP: an asynchronous team and a parallel tabu search strategy. Both algorithms make use of cooperative processes that asynchronously exchange information gathered along their execution. Computational experiments on benchmark instances show that these parallel algorithms produce signiicantly better solutions than all sequential algorithms previously proposed in the literature. 1 Problem deenition In broad terms, the labor constrained scheduling problem (LCSP) involves sequencing a set of jobs on multiple machines, subject to precedence constraints given in terms of a direct (acyclic) graph. Each job has a speciied processing time and a labor requirements proole, which typically varies as the job is processed. Given the amount of labor available at each time period, the problem consists in nding a job sequence within each machine, so as to minimize the completion time of the last job to be nished (i.e., the makespan), subject to the precedence and labor constraints. The particular version of LCSP motivating this study is a simpliication of an industrial problem from BASF A.G. This problem is NP-hard and was rst discussed in 20]. Since then, some methods have been proposed for its solution: constraint programming 21], linear programming-based heuristics 27, 28], sequential tabu search 4], and integer programming 29]. The last three approaches are discussed in 5].