Presenting a Joint Replenishment-location Model Under all-units Quantity Discount and Solving by Genetic Algorithm and Harmony Search Algorithm

Abstract

In this paper a model is proposed for distribution centers location and joint replenishment of a distribution system that is responsible for orders and product delivery to distribution centers. This distribution centers are under limitedwarehouse space and this can determine amount of requirement product by considering proposed discount.The proposed model is develop to minimize total costs consists of location, ordering, purchaseunder All-units quantity discount condition and items maintenance by adjustment Frequency of replenishment in each distribution center. To solve this model, first we solve the model with genetic algorithm by confining the time between too replenishments then by use of the Quantity Discount RAND algorithm method the upper and lower limits of the time between two replenishments will be determined. After obtaining the optimal upper and lower limits, the model will be resolved by harmony search and genetic algorithms. The results show that the presented chromosome structure is so efficient so that the statistical experiments result indicates there isn’t much difference between solution means after finding the optimal upper and lower limits. We used response surface methodology for tune proposed algorithms parameters. Efficiency of proposed algorithms is examined by diverse examples in different dimensions. Results of these experiments are compared by using of ANOVA and TOPSIS with indexes of objective function value and algorithms runtime. In both comparisons harmony search algorithm has more efficiency than genetic algorithm.

Keywords

• joint replenishment problem
• location
• all units discount
• genetic algorithm
• harmony search