Two parameter-tuned meta-heuristics for a discounted inventory control problem in a fuzzy environment

In this paper, a nearly real-world multi-product, multi-period inventory control problem under budget constraint is investigated, where shortages in combination with backorders and lost sales are considered for each product. The ordered quantities of products are delivered in batch sizes with a known number of boxes, each containing a pre-specified number of products. Some products are purchased under an all unit discount policy, and others are purchased under an incremental quantity discount with fuzzy discount rates. The goal is to find the optimal ordered quantities of products such that not only the total inventory cost but also the required storage space (considered as a fuzzy number) to store the products is minimized. The weighted linear sum of objectives is applied to generate a single-objective model for the bi-objective problem at hand and a harmony search algorithm is developed to solve the complex inventory problem. As no benchmarks are available to validate the obtained results, a particle-swarm optimization algorithm is employed to solve the problem in addition to validate the results given by the harmony search method. The parameters of both algorithms are tuned using both Taguchi and response surface methodology (RSM). Finally, to assess the performance of the proposed algorithms some numerical examples are generated, and the results are compared statistically.