Optimal pricing and replenishment policies of an EOQ model for non-instantaneous deteriorating items with shortages

This paper discusses the optimal pricing and replenishment policies of an economic order quantity model for non-instantaneous deteriorating items with partial backlogging over an infinite time horizon. The model is studied under the replenishment policy starting with no shortages. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The objective of this model is to maximize the total profit which includes the sales revenue, purchasing cost, set up cost, holding cost, shortage cost, and opportunity cost due to lost sales. Here, the selling price, replenishment quantity, replenishment cycle length, and the time duration of the positive inventory level are taken as decision variables to maximize the profit of the inventory system. The existence and the uniqueness of the solution of the proposed inventory system are examined. We suggest a solution procedure to find the optimal solution of the described model. Numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out and some useful managerial results are obtained.