Recent Advances in Computer Scienceand Communications Send Orders for Reprints to reprints@benthamscience.net Recent Advances in Computer Science and Communications, 2022, 15, 131-138 131 RESEARCH ARTICLE Optimal Inventory Policies for Price and Time Sensitive Demand Under Advertisement Nita Shah 1,* , Ekta Patel 1 and Kavita Rabari 1 1 Department of Mathematics, Gujarat University, Ahmedabad - 380009, Gujarat, India Abstract: Aims: This article analyzes an inventory system for deteriorating items. The demand is a quadratic function of time and is dependent on time, price and advertisement. Shortages are allowed and partially backlogged. Background: Demand and pricing are the two most crucial factors in inventory policy for any busi- ness to be successful. In today’s era of competitive circumstances, any product is promoted through advertisement, which plays a vital role in changing the demand pattern among the community. The marketing of an item through advertisement in media such as TV, radio, newspaper etc., and also through the trade person, attracts the customers to buy it more. However, this idea is not always true for some goods like wheat, vegetables, fruits, food grains, medicines and other perishable goods due to their deteriorating nature and this, in turn, decreases demand for such goods. Deterioration may define as decay, damage, spoilage, evaporation, obsolescence, or pilferage of an item. Hence, the deterioration effect is a major part of the inventory control theory. So in this article, the demand rate is considered to be a function of selling price and the time of the occurrence of advertisement. Objective: A solution procedure is obtained to find the optimal price change and the optimal selling price to maximize the total profit. Methods: Classical Optimization works under the necessary conditions proposed by Kuhn-Tucker method. The optimal values of the decision variables are obtained by setting partial derivatives of the objective function equal to zero. Sufficiency conditions are explored through second-order derivative of the objective function with respect to decision variables. Results: From the sensitivity analysis table, it can be seen that the optimal profit is highly sensitive to advertisement coefficient and purchase cost. With an increase in the rate of deterioration, selling price decreases. Scale demand has a reasonable effect on cycle time and selling price. When the val- ue increases, the cycle length and profit decrease. With an increase in the demand, the total profit increases significantly.. Price elasticity has a negative impact on the selling price. If the backlogging rate increases, the profit will decrease. The inventory parameters, holding cost, back-order cost and lost sale cost have a marginal effect on the total profit. Conclusion: In this article, an inventory model is proposed for deteriorating items with variable de- mand depending upon the advertisement, selling price of the item and time of the deteriorating cycle. The shortages of such items are allowed and partially backlogged, and the backlogging rate depends on the waiting time for the next replenishment. From this article, one can conclude that the parame- ters are not sensitive to optimal profit, cycle time, selling price and the rest of the parameters have a practical effect on the total profit. A R T I C L E H I S T O R Y Received: November 01, 2019 Revised: January 10, 2020 Accepted: July 14, 2020 DOI: 10.2174/2666255813999200922122754 Keywords: Deterioration, price, linearly increasing demand, advertisement, shortages, convexity, sensitivity analysis, classical optimization. 1. INTRODUCTION Demand and pricing are the two most crucial factors in inventory policy for any business to be successful. In today’s era of competitive circumstances, any product is promoted * Address correspondence to this author at the Department of Mathematics, Gujarat University, Ahmedabad - 380009, Gujarat, India; E-mail: nitahshah@gmail.com through advertisement, which plays a vital role in changing the demand pattern among the community. The advertise- ment of an item through well-known media such as TV, ra- dio, newspaper, etc. attracts more customers to buy it more. However, this idea is not always true for some goods like wheat, vegetables, fruits, food grains, medicines and other perishable goods due to their deteriorating nature and this, in turn, decreases demand for such goods. Deterioration may define as decay, damage, spoilage, evaporation, obsoles- 2666-2566/22 $65.00+.00 © 2022 Bentham Science Publishers