LAUSR

Parallel machines scheduling problems with continuous availability of machines are NP-hardness (non-deterministic polynomial-time hardness) and have become very popular for the last decade; there is still very limited literature on this problem. The purpose of this paper is to focus on the problem of scheduling n independent jobs to be processed on m unrelated identical parallel machines with availability constraints to minimize the maximum completion time of jobs (makespan). For this NP-hard problem, a mixed-integer linear programming (MILP) model is proposed to find an optimal solution for this problem. Two metaheuristics, tabu search (TS) and simulated annealing (SA) are proposed to solve large scale problem. Moreover, the performance of the solution obtained by the proposed metaheuristics is evaluated based on a lower bound, which decreases the time required to find the optimal solution. Extensive experiments are carried out to assess the performance of all proposed metaheuristics. The computational results highlight the ability of the proposed metaheuristics to obtain optimal solutions for most of the instances compared with the solutions of the proposed MILP model and lower bounds. Moreover, SA and TS can provide good efficiency for the problem in any jobs size and any machine size, but TS provides worse CPU time as the size of jobs become large.