A model for optimizing multi-product inventory systems with multiple constraints

“How much to order” and “when to order” are the two fundamental issues managers have to resolve in an inventory system. Making these decisions in inventory systems with multiple products is a challenging task for managers because these decisions are often subject to several constraints due to limited resources such as budget, space, and the maximum weight of goods that can be stored. Most approaches in the literature for optimizing decisions in such an environment consider only a single budgetary constraint. This paper presents a mixed-integer programming model to optimize the two fundamental decisions of inventory management for ordering multiple inventory items subject to multiple resource constraints. It also determines whether a fixed cycle for all products or an independent cycle for each should be used for a lower total cost. The solution of the model does not seem to require excessive central processing unit (cpu) time as indicated by the computational experience reported in this paper; solution of the largest test problem, with 30 products and five resource constraints, required less than 20 cpu seconds on a personal computer.