An integrated production and procurement design for a multi-period multi-product manufacturing system with machine assignment and warehouse constraint

Abstract

Economic production and on-time ordering are among the most important topics related to production and inventory control issues. An economical production needs a comprehensive and precise planning to be implemented in all production stages. To have a controlled and comprehensive planning system, economic order quantity (EOQ) or economic production quantity (EPQ) models are usually used in various production-inventory environments to minimize costs, avoid delays in orders, and achieve high performance. To meet the demands, sometimes a multiperiod production-inventory planning that involves several products requires outsourcing. In this paper, a production-procurement plan that integrates EOQ with EPQ is proposed for a multiperiod multi-product production-inventory system with a limited warehouse capacity. The design aims to determine the optimal values of decision variables including the production quantity, the order quantity, inventory, shortages, and machine assignments to produce the products in a planning horizon. The problem is formulated as a non-linear mixed-integer programming model. As the problem becomes NP-Hard, a genetic algorithm (GA) is utilized to find a near-optimal solution. In addition, a random search (RS) algorithm is applied to validate the results obtained and to justify the efficiency of the GA. Since there is no benchmark available in the literature, some randomly generated numerical examples are solved and a sensitivity analysis is performed in order to demonstrate the effectiveness of the proposed methodology and the solution algorithm.