A New Approach Based on Matching Theory and Simulated Annealing for Parallel Machine Scheduling Problems

Abstract

As an extension of the classical Parallel Machine Scheduling Problem (PMSP), Unrelated Parallel Machine Scheduling Problem (UPMSP) is a much substantial issue in the modern manufacturing environment. It has been demonstrated to be a NP-hard problem. This research suggests a hybrid algorithm that combines Matching Theory (MT) and Simulated Annealing (SA) for solving an UPMSP with sequence-dependent setup time aimed at minimizing the total completion time. The hybrid algorithm is based on allocation of works to the best machine that can do it, and the determination of the order in which jobs have to be handled on the machines. The hybridization of MT and SA that integrates the features of these two individual parts is the main innovation aspect of the strategy. MT encourages the convergence, while SA promotes the diversity. Therefore, the designed algorithm can balance the intensification and diversification very well. Some tests were conducted using 16 tests for two problems to assess the efficiency of the suggested algorithm. Furthermore, the execution of the suggested algorithm with that of other meta-heuristic methods was contrasted. The outcome revealed that the performance dimensions of the suggested algorithm overrated those of other techniques.

Metaheuristics for optimizing unrelated parallel machines scheduling with unreliable resources to minimize makespan

“…Constraints (11 and 12) confirm that the starting time and completion time of the dummy jobs have to respect the preventive maintenance period [t Bi , t Ei ]. Finally, constraints (13)(14)(15)(16)(17) define the non-negativity and integrality of the variables.…”

“…Several studies, 5,10–18 have been proposed to solve parallel machine scheduling using different metaheuristic algorithms to minimize different objective functions such as makespan, total tardiness, the weighted sum of completion times, and the number of tardy jobs. Computational studies were carried out to determine the heuristics’ performance and execution time.…”