A bi-objective aggregate production planning problem with learning effect and machine deterioration: Modeling and solution

Abstract

The learning effects of the workers and machine deterioration in an aggregate production planning (APP) problem have not been taken into account in the literature yet. These factors affect the performance of any real-world production system and require attention. In this paper, a bi-objective optimization model is developed for an APP problem with labor learning effect and machine deterioration. The first objective of this model maximizes the profit by improving learning and reducing the failure cost of the system. The second objective function minimizes the costs associated with repairs and deterioration, which depend on the failure rate of the machines in the production periods. The aim of this article is to obtain appropriate levels of production rates in regular and overtimes, inventory and shortage levels, workers' hiring and firing levels, and the quantities of the products that are subcontracted. To demonstrate the validity of the proposed mathematical formulation, the multi-objective model is converted into a single-objective model using the fuzzy goal programming method, based on which computational experiments are performed on a set of random small-sized instances solved by the LINGO software. As the problem is shown NP-hard, a subpopulation genetic algorithm (SPGA) is proposed to solve large-size problems. In addition, two other meta-heuristics called weighted sum multi-objective genetic algorithm (WMOGA) and non-dominated sorting genetic algorithm II (NSGA-II) are utilized to solve a set of benchmark problems, in order to validate the results obtained and to assess the performance of the SPGA. For tuning the parameters, the Taguchi method is proposed in order to obtain high-quality solutions. Finally, the performances of the proposed algorithms are statistically compared together. The computational results show that SPGA compared to the other algorithms has a better performance in terms of some multi-objective optimization criteria.