Abstract
Parallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms.
Highlights
Studying parallel machines are of high importance both theoretically and practically
This research focused on the parallel machine scheduling with splitting jobs on a set of identical machines minimizing wastes and total tardiness
The nature of the problem in this industry is that two conflicting objectives, minimizing total tardiness and minimizing total wastes, should be taken into account
Summary
Studying parallel machines are of high importance both theoretically and practically. It is vitally important for the sake of common parallel resources in the real world, but very difficult to find an optimum solution for the problem. Since we cannot consistently find an absolute solution for parallel machines and for most of the criteria, especially those based on tardiness - that don’t have a linear relationship with completion time - the problem is nonpolynomial (NP). Based on the division problem, Lenstra et al [2] proved that a parallel machine problem of minimizing the total tardiness is a binary non-polynomial problem even for two machines. Koulamas [3], based on the single machine model in Du and Leung [4], indicated that the parallel machine problem is at least a binary non-polynomial. About the minimization of weighted tardiness, Lawler et al [5] proved that when jobs have different weights, the problem would be NPhard
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