Tabu Search Algorithm Based on Lower Bound and Exact Algorithm Solutions for Minimizing the Makespan in Non-Identical Parallel Machines Scheduling

Recently, several heuristics have been interested in scheduling problems, especially those that are difficult to solve via traditional methods, and these are called NP-hard problems. As a result, many methods have been proposed to solve the difficult scheduling problems; among those, effective methods are the tabu search algorithm (TS), which is characterized by its high ability to adapt to problems of the large size scale and ease of implementation and gives solution closest to the optimum, but even though those difficult problems are common in many industries, there are only a few numbers of previous studies interested in the scheduling of jobs on unrelated parallel machines. In this paper, a developed TS algorithm based on lower bound (LB) and exact algorithm (EA) solutions is proposed with the objective of minimizing the total completion time (makespan) of jobs on nonidentical parallel machines. The given solution via EA was suggested to enhance and assess the solution obtained from TS. Moreover, the LB algorithm was developed to evaluate the quality of the solution that is supposed to be obtained by the developed TS algorithm and, in addition, to reduce the period for searching for the optimal solution. Two numerical examples from previous studies from the literature have been solved using the developed TS algorithm. Findings show that the developed TS algorithm proved its superiority and speed in giving it the best solution compared to those solutions previously obtained from the literature.

Uniform Parallel Machines Scheduling with Setup Time, Learning Effect, Machine Idle Time, and Processing Set Restrictions to Minimize Earliness/Tardiness Costs

Inspired by a real industrial case, this study deals with the problem of scheduling jobs on uniform parallel machines with past-sequence-dependent setup times to minimize the total earliness and tardiness costs. The paper contributes to the existing literature of uniform parallel machines problems by the novel idea of considering position-based learning effects along with processing set restrictions. The presented problem is formulated as a Mixed Integer linear programming (MILP) model. Then, an exact method is introduced to calculate the accurate objective function in the just-in-time (JIT) environments for a given sequence of jobs. Furthermore, three meta-heuristic approaches, (1) a genetic algorithm (GA), (2) a simulated annealing algorithm (SA), and (3) a particle swarm optimization algorithm (PSO) are proposed to solve large size problems in reasonable computational time. Finally, computational results of the proposed meta-heuristic algorithms are evaluated through extensive experiments and tested using ANOVA followed by t-tests to identify the most effective meta-heuristic.

Parallel machines scheduling with time-dependent deterioration, using meta-heuristic algorithms

In this paper, we consider the identical parallel machines scheduling problem with exponential time-dependent deterioration. The meaning of time-dependent deterioration is that the processing time of a job is not a constant and depends on the scheduled activities. In other words, when a job is processed later, it needs more processing time compared to the jobs processed earlier. The main purpose is to minimize the makespan. To reach this aim, we developed a mixed integer programming formulation for the problem. We solved problem in small scale using GAMS software, while due to the fact that in larger scales the aforesaid case is a complex and intricate optimized problem which is NP-hard, it is not possible to solve it by standard calculating techniques (in logical calculating times); we applied the meta-heuristic genetic algorithm, simulating annealing and artificial immune system, and their performance has been evaluated. In the end, we showed that solving the problem in small scale, with the meta-heuristic algorithms (GA, SA, and AIS) equals the optimal solution (GAMS), And on a large scale, at a time of approximately equal solution, meta-heuristic algorithm simulating annealing, provides a more optimal solution.

Computational Experiments on Workflow Balancing of Parallel Machine Scheduling with Precedence Constraints and Sequence Independent Setup Time

The workflow balancing of parallel machines scheduling (PMS) with precedence constraints and sequence independent setup time is considered for study. The setup time consideration produces alternate schedule along with lesser relative percentage of imbalance (RPI) value for PMS problem is demonstrated with an example. The lesser RPI indicates better workflow balancing among machines. The computational experiments are conducted on large instances of randomly generated PMS problems with precedent constraints and setup time. The various combinations of heuristics are used to solve the problems. The results show that genetic algorithm (GA) performs well against the other heuristics with lesser RPI values

Workforce influence on manufacturing machines schedules

This study addresses a parallel machines scheduling problem with sequence-dependent setup times and additional resource constraints related to workforce management. In most industrial cases, the execution of jobs requires the involvement of human resources in addition to machines: this work addresses the many complications due to workforce-specific issues that arise in a real industrial application. This is achieved separating the complex yet classical parallel machines scheduling problem with sequence-dependent setup times from the additional human resources planning problem: the former is formulated and solved through constraint programming, while an ad hoc procedure is provided for the latter. An Italian specialized firm, Prosino S.r.l., provides the industrial case to both validate the adequacy of the adopted method to the actual industrial problem and test the effectiveness of the proposed approach. Computational results obtained over six months of experimentation at the partner firm are presented.