233 REVISTA INVESTIGACIÓN OPERACIONAL VOL., 33 , NO. 3, 233-244, 2012. ORDERING POLICY FOR INVENTORY MANAGEMENT WHEN DEMAND IS STOCK- DEPENDENT AND A TEMPORARY PRICE DISCOUNT IS LINKED TO ORDER QUANTITY Nita H. Shah 1 Department of Mathematics, Gujarat University Ahmedabad – 380009, Gujarat, India ABSTRACT In this article, the effect of the sales promotional scheme viz. price discount offered by the supplier on the retailer’s ord ering policy is studied when demand is stock-dependent. It is assumed that the price discount rate depends on the order quantity of the retailer. This study will help the retailer to take the decision whether to adopt a regular or special order policy. The optimum special quantity is decided by maximizing the total cost saving between the special and regular orders for the cycle time. The algorithm is proposed to take the favorable decision. The numerical examples are given to validate the derived results. The sensitivity analysis is carried out to determine the critical inventory parameters. KEYWORDS : Inventory model, stock-dependent demand, a temporary price discount, special order MSC : 90B05 RESUMEN En el presente artículo, el efecto del plan de promoción de ventas, a saber descuento sobre el precio ofrecido por el proveedor, con la política de pedidos del minorista, se estudia cuando la demanda es existencia-dependiente. Se supone que la tasa de descuento sobre el precio de la orden depende de la cantidad del pedido del minorista. Este estudio ayudará al minorista a aceptar la decisión de adoptar un período ordinario o extraordinario como política para comprar. La cantidad especial óptima es fijada maximizando el costo total del ahorro entre la orden especial y la regular para un ciclo de tiempo. El algoritmo propuesto determina la decisión favorable. Ejemplos numéricos son dados para validar los resultados. El análisis de sensibilidad se lleva a cabo para determinar los parámetros críticos óptimos del inventario. 1. INTRODUCTION The offer of price discount by the supplier boost the demand, attracts more retailers, increase the cash-flow to reduce his inventory. But then the question “Is it always advantageous to avail of discount for a special order ?” is at the retailer end. Dixit and Shah (2005) gave a review article on inventory models when a temporary price discount is offered by the supplier to the retailer to study the relationship between price discounts and order policy. The all-unit quantity discounts ordering policy is discussed by Arcelus et al. (2003), Shah et al. (2005), Bhaba and Mahmood (2006), Abad (2007), Dye et al. (2007), Shah et al. (2008), Mishra and Shah (2009). They assumed that the price discount rate is independent of the special order quantity. However, in market, it is observed that the supplier offers a quantity discount to encourage larger orders. For the larger order, the higher price discount rate is given by the supplier. As a result, the retailer has to settle the trade-off for purchase price savings against higher total holding cost. 1 nitahshah@gmail.com