Retailers optimal pricing and economic order quantity in stock and price sensitive demand environment

Availability of adequate stock in stores to attract more customers is a common phenomena in the industries such as fashion apparel, electronic, high-tech, automobile industry, first moving consumer goods, etc. though the product becomes outdated after a certain period or its usefulness decreases as time progresses. But the customers are not fully satisfied with only availability and freshness of products, rather they are quite aware of the price of the product in different stores and take decisions. This inspires the departmental store managers searching the ideal selling price and stock in shelf to influence demand. In this paper, a single-item inventory model is developed, to address this issue. It is assumed that the demand is stock and price sensitive before deterioration and it is only price sensitive as soon as the deterioration starts. Instead of imposing a restriction of fixed number of price changes like earlier models with price sensitive demand, it is assumed that the decision-maker has the opportunity to set the prices before as well as after the start of deterioration. A mathematical model is developed and existence of its solution is verified. A solution procedure is presented to find optimal number of price changes, optimal selling prices and optimal lot-size to maximise profit. The model is illustrated by a numerical example.