Simple approach of obtaining the optimal pricing and lot-sizing policies for an EPQ model on deteriorating items with shortages under inflation and time-discounting
In this paper, the optimal pricing and lot-sizing policies of a production lot-sizing model for deteriorating item under inflation and time discounting by considering two different decision making policies such as coordinated and decentralized decision making policies under which we derive the solution of the multivariate maximization problem are discussed. In addition, shortages are allowed and the unsatisfied demand is partially backlogged. The backlogging rate is a constant fraction of the on-hand inventory. The model is studied under inventory followed by shortages. We take demand as a function of selling price and time. The objective of this model is to maximize the total profit (TP) which includes the sales revenue, purchase cost, the set up cost, holding cost, shortage cost and opportunity cost due to lost sales. Theoretical results are given to justify the model. Finally, 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. We propose a solution procedure to find the solution and obtain some managerial results by using sensitivity analysis.