The aim of lot sizing problems is to determine the periods where production takes place and the quantities to be produced in order to satisfy the customer demand while minimizing the total cost. Due to its importance on the efficiency of the production and inventory systems, Lot sizing problems are one of the most challenging production planning problems and have been studied for many years with different modeling features. In this paper, we propose a fuzzy mathematical model for the single-item capacitated lot-sizing problem in closed-loop supply chain. The possibility approach is chosen to convert the fuzzy mathematical model to crisp mathematical model. The obtained crisp model is in the form of mixed integer linear programming (MILP), which can be solved by existing solver in crisp environment to find optimal solution. Due to the complexity of the problems harmony search (HS) algorithm and genetic algorithm (GA) have been used to solve the model for fifteen problem. To verify the performance of the algorithm, we computationally compared the results obtained by the algorithms with the results of the branch-and-bound method. Additionally, Taguchi method was used to calibrate the parameters of the meta-heuristic algorithms. The computational results show that, the objective values obtained by HS are better from GA results for large dimensions test problems, also CPU time obtained by HS are better than GA for Large dimensions. تفاصيل المقالة

The supply chain network design not only assists organizations production process (e.g.,plan, control and execute a product’s flow) but also ensure what is the growing need for companies in a longterm. This paper develops a three-echelon supply chain network problem including multiple plants, multiple distributors, and multiple retailers with amulti-mode demand satisfaction policy inside of production planning and maintenance. The problem is formulated as a mixed-integer linear programming model. Because of its NP-hardness, three meta-heuristic algorithms(i.e., tabu search, harmony search and genetic algorithm) are used to solve the given problem. Also, theTaguchi method is used to choose the best levels of the parameters of the proposedmeta-heuristic algorithms. The results show that HS has abetter solution quality than two other algorithms. تفاصيل المقالة