Parallel machine scheduling with precedence constraints and setup times

Abstract

This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. Limited discrepancy search methods mixed with local search principles, dominance conditions and specific lower bounds are proposed. The proposed methods are evaluated on a set of randomly generated instances and compared with previous results from the literature and those obtained with an efficient commercial solver. We conclude that our propositions are quite competitive and our results even outperform other approaches in most cases.

Weight-based Heuristics for Constraint Satisfaction and Combinatorial Optimization Problems

“…For discrepancy search and non-binary trees, two modes can be used to count discrepancies [10,27]. First, the binary way: exploring the branch associated with the best value, according to a value ordering heuristic, involves no discrepancy, while exploring the remaining branches implies a single discrepancy.…”

“…The value ordering heuristic is always minconflicts undergoing a succeed-first principle. In the last part of experiments, three variants of YIELDS are compared, depending on the way for discrepancy counting: binary, non-binary, and also mixed [10]. For mixed counting we consider non-binary counting at the top and binary counting at the bottom, denoted by YIELDS-NB-B, and the opposite, named YIELDS-B-NB.…”

A Linear Programming Approach for Parallel Cell Scheduling with Sequence-Dependent Setup Times

“…To meet the demand, Constraint (10) guarantees minimizing the cell number. To calculate production time of a product type which is assigned to a cell we defined constraint (11) and to add setup time to production time we defined constraint (12). Constraint (13) guarantees that total time of all parts assigned a cell cannot exceed the capacity of this cell.…”

“…Tahar et al suggest a heuristic algorithm for the problem of scheduling a set of jobs with sequence-dependent setup times on a set of parallel machines by using a linear programming modeling with setup times and job splitting [10]. Gacias et al proposed a branch-and-bound method and heuristics based on discrepancy-based search methods for the parallel machine scheduling problem with precedence constraints and setup times [11]. This paper can contribute both academic researches and business life.…”

Discrepancy search for the flexible job shop scheduling problem

“…We choose to adapt the first discrepancy definition to our work; this choice has been experimentally chosen (see [19] for more details). To more deeply understand the adopted discrepancy mechanism, see below and illustration in Figure 2.…”