Distinct and Joint Price Approaches for Multi-Layer, Multi-Channel Selling Price by Manufacturer

Document Type : Research Paper

Authors

1 M. S. J. Govt. College Bharatpur

2 Maharani Shri Jaya Govt. College, Bharatpur, Rajasthan

3 Department of Mathematics, Govt. College Banmore, M. P., India

Abstract

This article analyses a pricing policy and coordination among members of a three-layer, multi-channel and multi-echelon supply chain, consisting of manufacturers, distributors and retailers. For a single item, demand is assumed to be a linearly decreasing function of time and selling price at the retailer's end. Each supply chain participant earns the largest profit function per unit of time after accounting for expenses. Because the holding cost of commodities is higher in cities than in rural areas, this article proposes a holding cost-sharing idea among wholesalers and merchants. In this article, we maximum retailer initial lot size, selling price, and replenishment time, as well as distributor and manufacturer initial lot size and wholesale pricing. This article is analysed in two frameworks first one is decentralized, and other one is centralized. The optimality conditions of each supply chain member’s profit function have been derived with respect to the decision variables and propositions. The results are shown in the data table to illustrate the model. We have also done sensitivity analysis with numerical examples.

Keywords


Ben-Daya, M., As’Ad, R., & Seliaman, M. (2013). An integrated production inventory model with raw material replenishment considerations in a three-layer supply chain. International Journal of Production Economics143(1), 53-61.
Cárdenas-Barrón, L. E., & Sana, S. S. (2015). Multi-item EOQ inventory model in a two-layer supply chain while demand varies with promotional effort. Applied Mathematical Modelling39(21), 6725-6737.
Chan, C. K., Wong, W. H., Langevin, A., & Lee, Y. C. E. (2017). An integrated production-inventory model for deteriorating items with consideration of optimal production rate and deterioration during delivery. International Journal of Production Economics189, 1-13.
Feng, B., Hu, X., & Orji, I. J. (2023). Multi-tier supply chain sustainability in the pulp and paper industry: a framework and evaluation methodology. International Journal of Production Research61(14), 4657-4683.
Giri, B. C., Majhi, J. K., Bardhan, S., & Chaudhuri, K. S. (2021). Coordinating a three-level supply chain with effort and price dependent stochastic demand under random yield. Annals of Operations Research307, 175-206.
Gunasekaran, A., & Kobu, B. (2007). Performance measures and metrics in logistics and supply chain management: a review of recent literature (1995–2004) for research     and applications. International journal of production research45(12), 2819-2840.
Hariom, Sharma, K. C., Singh, K., & Singh, D. (2024). Analysis of an inventory model for time-dependent linear demand rate three levels of production with   shortage. International Journal of Professional Business Review: Int. J. Prof. Bus.         Rev.9(4), 1.
Krapal Singh, D. K. C. S., Hariom, D. D. S., Singh, K., Sharma, K. C., & Singh, D. (2022). An integrated two-layer supply chain inventory with declining and price sensitive demand for deteriorating items. IJRAR-International Journal of Research and               Analytical Reviews (IJRAR)9(4), 496-506.
Kumar, H., Sharma, K. C., & Singh, D. (2023). Production Inventory Model of Constant Production and Linear Demand Rate. International Journal of Applied Optimization Studies3(2), 119-137.
Lau, A. H. L., & Lau, H. S. (2003). Effects of a demand-curve’s shape on the optimal solutions of a multi-echelon inventory/pricing model. European Journal of Operational Research147(3), 530-548.
Lin, F., Wu, P., Shi, J., Tao, J., & Zhuo, X. (2022). Impacts of expiration date on optimal ordering policy for deteriorating items under two-level trade credit: Quantity loss and quality loss. Journal of the Operational Research Society73(6), 1393-1410.
Mahata, P., Mahata, G. C., & Mukherjee, A. (2019). An ordering policy for deteriorating items with price-dependent iso-elastic demand under permissible delay in payments and price inflation. Mathematical and Computer Modelling of Dynamical Systems25(6), 575-601.
Modak, N. M., Panda, S., & Sana, S. S. (2016). Pricing policy and coordination for a distribution channel with manufacturer suggested retail price. International Journal of Systems Science: Operations & Logistics3(2), 92-101.
Nigwal, A., Khedlekar, U. K., Sharma, L., & Gupta, N. (2022). Trade credit policies for supplier, manufacturer, and retailer: an imperfect production-inventory system with rework. Journal of Mathematical & Fundamental Sciences54(1).
Pal, B., Sana, S. S., & Chaudhuri, K. (2014). Three stage trade credit policy in a three-layer supply chain–a production-inventory model. International Journal of Systems Science45(9), 1844-1868.
Pal, B., Sarkar, A., & Sarkar, B. (2023). Optimal decisions in a dual-channel competitive green supply chain management under promotional effort. Expert Systems with Applications211, 118315.
Panda, S., Modak, N. M., & Cárdenas-Barrón, L. E. (2017). Coordination and benefit sharing in a three-echelon distribution channel with deteriorating product. Computers & Industrial Engineering113, 630-645.
Parlar, M., & Wang, Q. (1994). Discounting decisions in a supplier-buyer relationship with a linear buyer's demand. IIE transactions26(2), 34-41.
Shah, H. M., Gardas, B. B., Narwane, V. S., & Mehta, H. S. (2023). The contemporary state of big data analytics and artificial intelligence towards intelligent supply chain risk management: a comprehensive review. Kybernetes52(5), 1643-1697.
Shaikh, A. A., Cárdenas-Barrón, L. E., Manna, A. K., Céspedes-Mota, A., & Treviño-Garza, G. (2021). Two level trade credit policy approach in inventory model with      expiration rate and stock dependent demand under nonzero inventory and partial backlogged shortages. Sustainability13(23), 13493 (1-19).
Shukla, D., & Khedlekar, U. K. (2016). Inventory model for convertible item with deterioration. Communications in Statistics-Theory and Methods45(4), 1137-1147.
Singh, D. (2019). Production inventory model of deteriorating items with holding cost, stock, and selling price with backlog. International Journal of Mathematics in Operational Research14(2), 290-305.
Singh, D., Jayswal, A., Alharbi, M. G., & Shaikh, A. A. (2021). An investigation of a supply chain model for co-ordination of finished products and raw materials in a       production system under different situations. Sustainability13(22), 12601 (1-21).
Singh, D., & Mukherjee, B. (2018, January). A deterministic inventory model for time-varying demand and holding cost with partial backlogging. In Proceedings of the Jangjeon Mathematical Society (Vol. 21, No. 4, pp. 667-678).
Singh, K., Sharma, K. C., Hariom, & Singh, D. (2023). An analysis of the supply chain model for production system under selling price demand rate, controllable deterioration rate with several market demand. Communications in Mathematics and Applications, 14(2), 845–860.
Song, Z., & He, S. (2019). Contract coordination of new fresh produce three-layer supply chain. Industrial Management & Data Systems119(1), 148-169.
Xu, X., Zhang, M., Dou, G., & Yu, Y. (2023). Coordination of a supply chain with an online platform considering green technology in the blockchain era. International Journal of Production Research61(11), 3793-3810.