Production, Manufacturing and Logistics An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting Kuo-Lung Hou * Department of Statistics, National Defense Management College, National Defense University, Chungho, Taipei, Taiwan, ROC Received 3 March 2003; accepted 6 May 2004 Available online 3 August 2004 Abstract Thispaperderivesaninventorymodelfordeterioratingitemswithstock-dependentconsumptionrateandshortages under inflation and time discounting over a finite planning horizon. We show that the total cost function is convex. With the convexity, a simple solution algorithm is presented to determine the optimal order quantity and the optimal intervalofthetotalcostfunction.Theresultsarediscussedwithanumericalexampleandparticularcasesofthemodel arediscussedinbrief.Asensitivityanalysisoftheoptimalsolutionwithrespecttotheparametersofthesystemiscar- ried out. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Inventory; Stock-dependent consumption rate; Deteriorating; Inflation; Shortages 1. Introduction The classical inventory models consider the demand rate to be either constant or time-dependent but independent of the stock status. However, for certain types of inventory, particularly consumer goods, the consumption rate may be influenced by the stock levels, that is, the consumption rate may go up or down with the on-hand stock level. As reported by Levin et al. (1972) and Silver and Peterson (1985), sales at the retail level tend to be proportional to inventory displayed and a large piles of goods displayed in a supermarket will lead the customers to buy more. These observations have attracted many marketing 0377-2217/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2004.05.011 * Tel.: +886 2 22222137x8577; fax: +886 2 22250488. E-mail address: klhou@rs590.ndmc.edu.tw European Journal of Operational Research 168 (2006) 463–474 www.elsevier.com/locate/ejor