Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 198305, 18 pages
Research Article

Retailer's Optimal Pricing and Ordering Policies for Non-Instantaneous Deteriorating Items with Price-Dependent Demand and Partial Backlogging

1Department of Industrial Engineering & Management, Ching Yun University, Jung-Li, Taoyuan 320, Taiwan
2Department of Management Sciences and Decision Making, Tamkang University, Tamsui, Taipei 251, Taiwan
3Graduate Institute of Management Sciences, Tamkang University, Tamsui, Taipei 251, Taiwan

Received 27 December 2008; Revised 22 June 2009; Accepted 19 August 2009

Academic Editor: Wei-Chiang Hong

Copyright © 2009 Chih-Te Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An inventory system for non-instantaneous deteriorating items with price-dependent demand is formulated and solved. A model is developed in which shortages are allowed and partially backlogged, where the backlogging rate is variable and dependent on the waiting time for the next replenishment. The major objective is to determine the optimal selling price, the length of time in which there is no inventory shortage, and the replenishment cycle time simultaneously such that the total profit per unit time has a maximum value. An algorithm is developed to find the optimal solution, and numerical examples are provided to illustrate the theoretical results. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.