An order-level lot size inventory model with inventory-level dependent demand and deterioration

Many inventory models have been developed for various deteriorating items with constant demand rate. It is a common experience that, for perishable consumer goods, the age of inventory has a negative impact on the demand due to the loss of consumer confidence on such product. Consumers tend to avoid perishable items which are closer to their expiry dates. This paper describes an inventory model in which the demand is considered as a composite function consisting of a constant component, and a variable component which is proportional to the inventory level in the periods when there is a positive inventory buildup. The rate of production is considered finite and the decay rate as exponential. The total cost function is composed of four cost components of all phases of the cycle (backorder replenishment, inventory buildup, inventory depletion and shortage). This cost function is later reduced to a two-variable function using boundary relations to determine iteratively the set of values of the variables that resulted in minimum cost per cycle. The optimum lot-size and order-level were then obtained with relations established previously. Results are demonstrated for an instance of the model.