Retailer’s optimal pricing and replenishment policy for new product and buy back policy for used product with price and time dependent demand and shortages

Katariya, Dharmesh K.; Shukla, Kunal T

doi:10.47974/JSMS-1223

Open Access Research Article

Retailer’s optimal pricing and replenishment policy for new product and buy back policy for used product with price and time dependent demand and shortages

Dharmesh K. Katariyadrkunalshukla.maths@gmail.comDepartment of MathematicsShantilal Shah Engineering CollegeBhavnagar, Gujarat, 364060, IndiaView full profile → , ^*Kunal T ShuklaCorresponding authorkunal_niketa@yahoo.co.inDepartment of Science and HumanitiesVishwakarma Government Engineering CollegeAhmedabad, Gujarat, 382424, IndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 681–701Vol. 27Issue 3March 2024DOI: 10.47974/JSMS-1223XML

Received:: 07 Oct 2020
Published Online:: 30 Mar 2024
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1223
Pages:: 681–701

Abstract

The new age consumer, manufacturers and government is aware about the hazardous impact of manufacturing on the environment and limited assets are factors which are considered while buying a product. As an outcome, consumers have demonstrated their enthusiasm to purchase utilized or restored items. We looked at a scenario in this article where a retailer collects and resells old products to customers in addition to selling new products. Detailed formulation and discussion are given to the optimum price and ordering strategies for new products as well as the optimum buyback strategy for used products. The demand of the products is the time and price sensitive. Additionally, Shortages are permitted and there is a partial backlog. Maximizing a retailer’s total profit per time unit while determining the best selling price and quantity to place an order for new products and the best amount to buy back for used products is the objective. The numerical example demonstrates the framework and sensitivity evaluations are carried out on the significant parameters.

Keywords

Inventory Price and time dependent demand Buyback product Partial backlogging

Subject Classifications

90B05

References

[1] Abad, P. L., Optimal price and order size for a reseller under partial backordering. Computers & Operations Research , 28 (1), 53-65 (2001).
[2] Cárdenas-Barrón L.E., Sana, S.S., Multi-item EOQ inventory model in a two-layer supply chain while demand varies with a promotional effort. Appl. Math Model, 39(21), 6725–6737 (2015).
[3] Chen, C.K., Weng, T.C., & Lo, C.C., Optimal replenishment quantity for new products and return rate of used products for a retailer. Applied Mathematical Modelling, 40(23-24), 9754–9766 (2016).
[4] Chung, K.J., Liao, J.J., Lin, S.D., Chuang, S.T., & Srivastava, H. M.nMathematical analytic techniques and the complete squares method for solving an inventory modelling problem with a mixture of backorders and lost sales. Revista de La Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 114(28), 1-10 (2019).
[5] Daniel, S. E., Pappis, C. P., & Voutsinas, T. G., Applying life cycle inventory to reverse supply chains: A case study of lead recovery from batteries Resources. Conservation and Recycling, 37(4), 251–281 (2003).
[6] Dey, B. K., Sarkar, B., Sarkar, M., & Pareek, S., An integrated inventory model involving discrete setup cost reduction, variable safety factor, selling price dependent demand, and investment. RAIRO - Operations Research, 53(1), 39–57 (2019).
[7] González-Torre, P. L., & Adenso-Díaz, B., Reverse logistics practices in the glass sector in Spain and Belgium. International Business Review, 15(5), 527–546 (2006).
[8] Govindan, K., Soleimani, H., & Kannan, D., Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future. European Journal of Operational Research, 240(3), 603–626 (2015).
[9] Giri, B.C., & Masanta, M., Developing a closed-loop supply chain model with price and quality dependent demand and learning in production in a stochastic environment, International Journal of Systems Science: Operations & Logistics, 7(2), 147-163 (2020).
[10] Jaggi, C. K., Tiwari, S., & Goel, S. K., Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities. Annals of Operations Research, 248(1-2), 253–280 (2016).
[11] Jawla, P., & Singh, S., Multi-item economic production quantity model for imperfect items with multiple production setups and rework under the effect of preservation technology and learning environment. International Journal of Industrial Engineering Computations, 7(4), 703-716 (2016).
[12] Koh, S.G., Hwang, H., Sohn, K.I., & Ko, C.S., An optimal ordering and recovery policy for reusable items. Computers & Industrial Engineering, 43(1-2), 59–73 (2002).
[13] Kannan, G., Sasikumar, P., & Devika, K., A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling. Applied Mathematical Modelling, 34(3), 655–670 (2010).
[14] Khurana, D., & Chaudhary, R., Optimal pricing and ordering policy for deteriorating items with price and stock dependent demand and partial backlogging. Uncertain Supply Chain Management, 4(4), 307-318 (2016).
[15] Mabini, M. C., Pintelon, L. M., & Gelders, L. F., EOQ type formulations for controlling repairable inventories. International Journal of Production Economics, 28(1), 21–33 (1992).
[16] Mondal, B., Bhunia, A. K., & Maiti, M., An inventory system of ameliorating items for price dependent demand rate. Computers & Industrial Engineering, 45(3), 443–456 (2003).
[17] Mukhopadhyay, S., Mukherjee, R. N., & Chaudhuri, K. S., Joint pricing and ordering policy for a deteriorating inventory. Computers & Industrial Engineering, 47(4), 339–349 (2004).
[18] Nagurney, A., & Toyasaki, F., Reverse supply chain management and electronic waste recycling: a multi-tiered network equilibrium framework for e-cycling. Transportation Research Part E: Logistics and Transportation Review, 41(1), 1–28 (2005).
[19] Pati, R., Vrat, P., & Kumar, P., A goal programming model for paper recycling system. Omega, 36(3), 405–417 (2008).
[20] Richter, K., & Dobos, I., Production-Inventory Control in an EOQ-Type Reverse Logistics System. Supply Chain Management and Reverse Logistics, 139–160 (2004).
[21] Sundararajan, R., Palanivel M., & Uthayakumar R., An EOQ model of non-instantaneous deteriorating items with price, time-dependent demand and backlogging, Journal of Control and Decision, 1-30 (2019). DOI: 10.1080/23307706.2019.1656560.
[22] Schrady, D. A., A deterministic inventory model for reparable items. Naval Research Logistics Quarterly, 14(3), 391–398 (1967).
[23] Shah, N. H., & Shukla, K. T., Deteriorating inventory model for waiting time partial backlogging, Applied Mathematical Science, 3(9), 421-428 (2009).
[24] Soni, H.N., Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment. Int. J.Production Economics. 146, 259–268 (2013).
[25] Shukla, K. T., & Suthar, M.S., A frame work for inventory model for deteriorating items with expiration under trapezoidal type demand and partial backlogging. Logforum, 12(2), 269-281 (2016).
[26] Shah, N. H., & Vaghela, C. R., Retailer’s replenishment and pricing decisions for non-instantaneous deterioration and price-dependent demand. International Journal of Industrial Engineering & Production Research, 28 (2), 101-111 (2017).
[27] Shah, N.H., & Vaghela, C.R., Retailer’s optimal pricing and replenishment policy for new product and optimal take-back quantity of used product. Yugoslav Journal of Operations Research, 28(3), 345-353 (2018).
[28] Shah, N., & Naik, M., Optimal replenishment and pricing policies for deteriorating items with quadratic demand under trade credit, quantity discounts and cash discounts. Uncertain Supply Chain Management, 7(3), 439-456 (2019).
[29] Suthar, M.S., & Shukla, K.T., Pricing and ordering policy for deteriorating inventory system with price sensitive ramp type demand, pre and post deterioration discounts. Ravista Investigacion Operacional, 40(2), 267-274 (2019).
[30] Shaikh, A.A., & Cárdenas-Barrón, L.E., An EOQ model for non instantaneous deteriorating product s with advertisement and price sensitive demand under order quantity dependent trade credit, Ravista Investigacion Operacional, 41(2), 168-187 (2020).
[31] Singh, T., Muduly, M. M., Asmita, N., Mallick, C., & Pattanayak, H., A note on an economic order quantity model with time-dependent demand, three-parameter Weibull distribution deterioration and permissible delay in payment. Journal of Statistics and Management Systems, 23(3), 643-662 (2020).
[32] Whitin, T. M., Inventory Control and Price Theory. Management Science, 2(1), 61–68 (1955).

Views: 197Downloads: 75Citations: 0