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<p style='text-indent:20px;'>In today's competitive world, scheduling problems are one of the most important and vital issues. In this study, a bi-objective unrelated parallel machine scheduling problem with worker allocation, sequence dependent setup times, precedence constraints, and machine eligibility is presented. The objective functions are to minimize the costs of tardiness and hiring workers. In order to formulate the proposed problem, a mixed-integer quadratic programming model is presented. A strategy called repair is also proposed to implement the precedence constraints. Because the problem is NP-hard, two metaheuristic algorithms, a multi-objective tabu search (MOTS) and a multi-objective simulated annealing (MOSA), are presented to tackle the problem. Furthermore, a hybrid metaheuristic algorithm is also developed. Finally, computational experiments are carried out to evaluate different test problems, and analysis of variance is done to compare the performance of the proposed algorithms. The results show that MOTS is doing better in terms of objective values and mean ideal distance (MID) metric, while the proposed hybrid algorithm outperforms in most cases, considering other employed comparison metrics.</p>

Multi-machine scheduling has been one of the best-known and practical problems in the last decade and its applications are constantly increasing. This study addresses an unrelated parallel machine scheduling problem with family setups and soft time windows, in which machine eligibility and precedence constraints are considered. The objective is to minimize the total of weighted early and tardy costs. The problem is investigated for different sizes of jobs, families and machines. Two different metaheuristic algorithms, a simulated annealing (SA) and an artificial immune system (AIS) are presented. Two strategies called repair and penalty are proposed to implement predecessor constraints. Some computational experiments are performed and one-way analysis of variance (ANOVA) is conducted to compare the performance of the proposed metaheuristics and evaluate the designed combinations in terms of objective values and computational (CPU) times. Results demonstrate that SA with repair strategy generally outperforms other proposed methods.