Int. J. Production Economics 55 (1998) 31—38 Demand promotion by upgradation under stock-dependent demand situation — a model T.K. Datta*, K. Paul, A.K. Pal  Department of Mathematics, Regional Engineering College, Silchar-788 010, Assam, India  Department of Mathematics, Karimganj College, Karimganj, Assam, India  Department of Mathematics, Jadavpur University, Calcutta-700 032, India Received 26 February 1997; accepted 21 January 1998 Abstract The idea of demand promotion by upgrading the existing system of the selling centre has been modelled in this article. The consumption rate is assumed to be dependent on the stock level. The problem has been reduced to a maximizing problem. The algorithmic approach for solving this maximizing problem is also provided. Objective is to maximize the net profit over a prescribed time. An increasing convex upgradation cost is considered. Exponential upgradation cost has been considered for the numerical examples.  1998 Elsevier Science B.V. All rights reserved. Keywords: Demand promotion; Model construction; Solution procedure; Stock-dependent demand situation 1. Introduction One of the challenging problems for the market- ing researchers and practitioners is to study and analyse the inventory systems in which the demand rate or the selling rate is influenced by the displayed stock level (DSL). The fact that the DSL has a pos- itive impact on the rate of consumption is now well-established. Many retail store managers are experiencing the situation where a large amount of stock generates more demand and the demand rate goes down if the stock is low. A typical psychology of the customers is responsible for such a situation. They may have the feeling of getting wide range for * Corresponding author. selection when a large amount is stored/displayed. Low stock may raise the perception that the prod- ucts are not fresh. Similar type of feeling is very common to all of us. Fashion apparels, sports clothes, greeting cards, baked items are examples where the stock-dependency nature of the demand rate can be observed. The intensity of the stock dependency of such items varies from item to item. Larson and Demarais [1] suggested that this type of analysis should be performed for items having high direct profitability and high sale value. Several models have recently been developed to study the effect of demand-dependence on the stock level. A review of these works is presented in the next section. Besides large stock, there is another factor which can motivate the customers. This factor is the facili- ties given to the customers. If some added facilities 0925-5273/98/$19.00 Copyright  1998 Elsevier Science B.V. All rights reserved PII S0925-5273(98)00033-4