Optimising multi-item economic production quantity model with trapezoidal fuzzy demand and backordering: two tuned meta-heuristics

In this paper, a multi-item economic production quantity model with fuzzy demand is developed in which shortages are backordered and the warehouse space is limited. While the demand is assumed to be a trapezoidal fuzzy number, the centroid defuzzification method is used to defuzzify fuzzy output functions. The Lagrangian relaxation procedure is first employed to solve the problem. Then, the model is extended to a constrained fuzzy integer nonlinear programming, in order to suit real-world situations. As the extended model cannot be solved in a reasonable time using exact methods, two meta-heuristic algorithms, named the genetic algorithm (GA) and the particle swarm optimisation (PSO) each tuned by the Taguchi method, are employed to solve it. Experimental results based on several problems of different sizes show that not only PSO is the faster algorithm, but also it performs better than GA in terms of other measures used to evaluate the performances.