Journal of Mathematics and Statistics

Policy Decisions for a Price Dependent Demand Rate Inventory Model with Progressive Payments Scheme

Mukesh Kumar and Rajat Kumar

DOI : 10.3844/jmssp.2012.157.164

Journal of Mathematics and Statistics

Volume 8, Issue 1

Pages 157-164

Abstract

Problem statement: In this proposed research, we developed an inventory model to formulate an optimal ordering policies for supplier who offers progressive permissible delay periods to the retailer to settle his/her account. We assumed that the annual demand rate as a decreasing function of price with constant rate of deterioration and time-varying holding cost. Shortages in inventory are allowed which is completely backlogged. Approach: The main objective of this study to frame an inventory model in real life situations. In this study, we introduced a new idea of trade credits, namely, the supplier charges the retailer progressive interest rates if the retailer prolongs its unpaid balance. By offering progressive interest rates to the retailers, a supplier, can secure competitive market advantage over the competitors and possibly improve market share profit. This study has two main purposes, first the mathematical model of an inventory system are establish under the above conditions and second demonstrate that the optimal solution not only exists but also feasible. We developed theoretical results to obtain the optimal replenishment interval by examine the explicit condition. An algorithm is given to find the flow of optimal ordering policy. Results: The results is illustrated with the help of numerical example using Mathematica software and the optimal solution of the problem is Z (p, T1) = 76.8586 at (p, T1) = (0.952656, 0.128844). Conclusion: We proposed an algorithm to find the optimal ordering policy. A numerical study has been performed to observe the sensitivity of the effect of demand parameter changes.