97 REVISTA INVESTIGACIO ´ N OPERACIONAL VOL 42, NO. 1, 97-103, 2021 OPTIMAL INVENTORY DECISIONS WITH ADVANCED SALES FOR DETERIORATING ITEMS Nita H. Shah* 1 ,Pratik H. Shah*,**, Kavita D. Rabari* * Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat ** Department of Mathematics, C.U.Shah Government Polytechnic, Surendranagar-363035 Gujarat, India ABSTRACT This paper studies retailer’s optimal policies which include optimal replenishment, pricing and promotional cost for a two-phase inventory system with a constant rate of deterioration. The first phase is advance booking period in which the product is offered at a discounted price and delivery of the product is given as soon as the replenishment arrives. The second phase is spot sales period in which the product is sold at a normal price. Products are considered to be deteriorated at a constant rate. Demand of the product is influenced by promotion of the product as well as by the selling price of the product. The objective is to maximize the total profit of the retailer with respect to cycle time, selling price and promotional cost through advertisement. KEYWORDS: Inventory model; Marketing; Advance booking; Deterioration; Selling price MSC: 90B05 RESUMEN Este documento estudia las políticas óptimas del minorista que incluyen reposición óptima, precios y costos promocionales para un sistema de inventario de dos fases con una tasa constante de deterioro. La primera fase es el período de reserva anticipada en el que el producto se ofrece a un precio con descuento y la entrega del producto se otorga tan pronto como llega la reposición. La segunda fase es el período de ventas al contado en el que el producto se vende a un precio normal. Los productos se consideran deteriorados a una tasa constante. La demanda del producto está influenciada por la promoción del producto, así como por el precio de venta del producto. El objetivo es maximizar el beneficio total del minorista con respecto al tiempo de ciclo, el precio de venta y el costo promocional a través de la publicidad. PALABRAS CLAVE: Modelos de Inventario; Marketing; Registro avanzdo ; Deterioro ; precio de venta 1. INTRODUCTION In present time, advertisements and promotional efforts play a major role to introduce the product to a large volume of customers very effectively and attract them to buy it. Further by booking the product at a discounted rate for some specific period of time, gives a boost to sales. Also the selling price of product is a key factor in generating revenue and increasing the demand. Table 1: Literature Survey Authors Advertisement Price dependant demand Deterioration Advance booking Abad et al.,2003 ×  × × Adekoya et al.,2011  × × × Chen & D.Simchi Levi,2004 ×  × × Chen & D.Simchi Levi,2004 ×  × × Dye & Hsieh,2013 ×    Li , Wang & Yan,2013   × × Seyedesfahani et al.,2011   × × Shah & Naik,2018 ×   × Shah, Patel & Shah,2014 × ×  × Shah, Patel & Shah,2014 ×   × Shah & Naik,2018 ×   × Szmerekovsky & Zhang,2009   × × Tsao et al.,2009 × × ×  Xie & Wei,2009   × × You et al.,2006 ×  ×  You & Wu.,2007 ×  ×  1 Corresponding author: 1 Nita H. Shah Email: 1 nitahshah@gmail.com , 2 pratik1130@gmail.com , 3 kavitagalchar1994@gmail.com