Mathematical Models to Determine Optimum Inventory Level in a Supply Chain System

The importance of inventory management for organization’s effectiveness and profitability cannot be over-emphasized considering the fact that keeping a large quantity of idle goods increases the holding cost of paying for storage facilities and risk of spoilage and theft. On the other hand, ordering for too little quantities sometimes lead to frequent reordering and thereby increasing charges on processing and receiving the items. In this research, we examine a new approach to inventory management by formulating a dynamic programming model in a linear programming form. Many research inventory models have dealt with either the correlation between the management of inventory and profitability or the impact of inventory management on retailers’ and producers’ profit. In this research we present a new approach which examines the initial and maximum capacities of a warehouse where inventory products are stocked before selling them to prospective customers. The proposed model is a dynamic programming model in a linear programming form which includes both the quantities supplied and demanded in its formulation. Thus, our proposed dynamic model in linear programming form is more applicable to practical situations than what can be found in other models. The incorporation of supply and demand factors distinguish the model from recent inventory models found in literature which are based only on supply factor and profitability. The proposed model has been applied to a warehouse of cement manufacturing industry in Nigeria. From the results obtained in the numerical example, it is observed that periodic supply and demand quantities to produce optimum inventory cost can be determined through the proposed model’s algorithm. We also observed that the optimum values of the dual objective function and that of the primal objective function are equal.