A preliminary proposal to include capacity constraint in the multi-product EOQ model using hybrid systems and integer linear programming

This paper proposes a model to incorporate the capacity constraint in a multi-product manufacturing environment managed according to a pull policy, in which production is regulated by minimum and maximum inventory levels on each item (i.e., a min-max inventory policy). In particular, this paper aims at developing a capacity-constrained version of the Economic Order Quantity (EOQ) model [2] exploiting the analogy between a multi-product production system with finite capacity and a hybrid system. The specific hybrid system considered as a reference is the “switched arrival system” proposed by [1]. In this framework, the pull policy of the production system is the equivalent to the control of the hybrid system. A mixed integer linear programming model is developed to identify the minimum and maximum inventory thresholds on each product that minimize the distance between the average order quantity of each item and the corresponding classical EOQ [2]. A numerical example illustrates the control model application.