Journal of Operational Research and Its Applications ( Applied Mathematics ) - Lahijan Azad University

Among the important and effective responsibilities in industrial units is planning and inventory control. In this case, determining the optimal balance between inventory levels, ordering, holding, and purchasing costs plays a significant role in preventing capital waste and dealing with inventory shortages. In this regard, this paper designs an economic production quantity (EPQ) model in single and multi-product cases with considering production capacity constraints, general discount on purchase orders for items and price dependence on the order quantity. This model is applicable when the production rate of products is lower than their demand rate and the production system faces production capacity constraints. Also, it is assumed that the cost function of purchasing each unit of goods follows an exponential distribution and depends on the quantity of purchase orders. The presented model cannot be solved in polynomial time, and as the number of products increases, the problem solving time increases with an exponential distribution. So, in order to solve the model in the single-product case, the GAMS software was used, and for multi-product cases, the Genetic Algorithm (GA) and Imperialist competitive Algorithm (ICA) were used. In order to improve the performance of the solution algorithms, response surface methodology (RSM) has been used to determine the optimal values of their parameters. Finally, in order to evaluate the performance of the proposed model, random problems were designed and the results were evaluated by the indicators of solution quality and run time, which indicate the superiority of the GA.