In this paper, we have assumed that a retailer sells the new product to customers as well as collects and sells the used products. We adopt a price dependent quadratic demand function, and the return of used product as a price and time-dependent linear function. | Yugoslav Journal of Operations Research 28 (2018), Number 3, 345–353 DOI: RETAILER'S OPTIMAL PRICING AND REPLENISHMENT POLICY FOR NEW PRODUCT AND OPTIMAL TAKE-BACK QUANTITY OF USED PRODUCT Nita H. SHAH Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat, India nitahshah@ Chetansinh R. VAGHELA Department of Mathematics, Marwadi University, Rajkot-360005, Gujarat, India chetan vaghela07@ Received: November 2017 / Accepted: May 2018 Abstract: In the world of limited resources, recovery of used products for reselling or recycling is a critical issue from the economic and environmental point of view. In this paper, we have assumed that a retailer sells the new product to customers as well as collects and sells the used products. We adopt a price dependent quadratic demand function, and the return of used product as a price and time-dependent linear function. The proposed problem is formulated as a profit maximization problem for the retailer. The objective is to find the optimal selling price, the optimal ordering quantity for the new product, and the optimal quantity of used product simultaneously such that the retailers total profit is maximized. The model is validated by a numerical example and sensitivity analysis is performed for the key parameters. Keywords: Inventory, Replenishment quantity, Price-dependent demand, Used product. MSC: 90B05. 1. INTRODUCTION In todays world, one of the greatest challenges is to preserve our limited natural resources and reduce the waste material. Due to growing environmental concern among customers, the manufacturing sectors are also promoting environment- 346 N. H., Shah, and C. R., Vaghela / Retailer’s Pricing and Replenishment Policy friendly methods to attract new customers. Customers also prefer to buy from the companies with green image. That is why recovery of used materials and items has got more attention in past decade. Earlier, recycling
