Inventory model under permissible delay in payments and inflation with generalised Pareto lifetime

Inventory models play a dominant role in analysing many practical situations arising at places like, food and vegetable markets, market yards, warehouses, oil exploration industries, etc. In this paper we develop and analyse an EOQ model for deteriorating items with permissible delay in payments under inflation. Here, it is assumed that the demand is a function of both time and selling price. It is further assumed that the lifetime of commodity is random and follows a generalised Pareto distribution. Using the differential equations the instantaneous state of inventory is derived. With suitable cost considerations the total cost function, net profit rate function are obtained. By maximising the net profit rate function the optimal ordering quantity and optimal selling price are derived. The sensitivity of the model with respect to the costs and parameters is studied. It is observed that this model includes several of the earlier models as particular cases for specific values of the parameters.