The classical single-period inventory problem is a tool to find order quantity in a short term that maximizes the expected profit under the probabilistic demand. In this model it is assumed that discount is applied in selling only if any inventory is remained at the end of the period and the news-vendor loses some profit only if order quantity is less than the real demand. In the current survey the utilization of single-period production is considered in which the budget and warehouse space are limited and the end product and raw materials are purchased before the start of selling period and depending on the type of demand during the period the raw materials may transform into end products. The objective of this problem is to find the order quantities of both the raw materials and the end product at the start of the period such that the expected profit and service providing to customers are maximized. Total discount has also been used to purchase raw materials. Due to the complexity of the considered problem, two multi-objective meta-heuristic algorithms of Non-dominated Sorting Genetic Algorithm and Imperialist Competitive Algorithm have been applied to solve the real sized problems in reasonable computational time. Since the performance of meta-heuristic algorithms is significantly influenced by their parameters, Taguchi methodology has been applied to tune the parameters of developed algorithms. Finally the efficiency and applicability of the proposed model and solution methodologies are illustrated through designed experimental problems in various dimensions.
