Fuzzy Optimal Inventory and Shipment Policy on Non- Coordinated Supply Chain Under Quadratic Price Dependent Demand

Abstract

Inventory management in the supply chain has been discovered to be the key to long-term success. Inventory is important in the supply chain because it balances supply characteristics and consumer demand. In this non-coordinated supply chain model, the merchant determines the appropriate order quantity based on the various expenses involved. Under quadratic price dependent demand, an extension of the lagrangian method is used to optimize fuzzy EOQ, total variable cost of the relevant retailer, and the supply chain. To support the model, a numerical case is solved.

Introduction

I. INTRODUCTION

Globalization, or globalism, refers to the world's growing economy, culture, and population over the last few decades. Globalization has accelerated dramatically since the 18th century, thanks to advances in transportation and communication technology. As a result, many current globalization research projects focus on developing a model that aligns the role and notion of supply chain in such a way that it garners a lot of attention in both the academic and industry worlds. The current model focuses on the supply chain and its various characteristics. This study on supply chain is solved and optimized using an extension of the lagrangian approach, with cost parameters taken as pentagonal fuzzy numbers. To demonstrate the model, a numerical case is framed and solved.

Huang and Gangopadhyay (2004) created a simulation model to examine the impact of information sharing in a SC and discovered that information sharing contracts benefit both distributors and wholesalers. Furthermore, as evidenced by the literature, product demand is a critical factor in inventory decision-making. Retail pricing is a key aspect in maximising the SC's revenue/cost (He et al., 2009). Under trade credit phenomenon, Zhong and Zhou (2013) established a coordinated and non-coordinated two-level SC model for optimal inventory decisions and the length of the allowable wait time. They assumed that the retailer's storage space is limited, and that he is aware of inventory-dependent demand. Under revenue sharing contracts, Cao (2014) provided mathematical models for optimal price decisions and production methods. Kumar et al. (2016a, 2016b), Nagaraju et al. (2016a, 2016b), Kuntian et al. (2017), Lu and Zhou (2016) and Nagaraju et al. (2017) have all recently reported inventory and shipping decisions under-price dependent demand changes (2018). Unlike the other articles, this one proposes an inventory model for determining the optimal total relevant cost of non-coordinated Supply chain with single retailer. Product is a key component of the suggested paradigm. The retailer's unit selling price is used to calculate demand, which is written as a quadratic function. Model costs include ordering/setup costs, carrying costs, and shipping costs are considered for model development.

II. DEFINITIONS

Conclusion

The mathematical model proposed in this research is extremely valuable for industries that produce fast-moving consumer items while making inventory decisions. With the existing approach, management may make replenishment and shipment decisions to keep optimal stock levels at the SC\'s various entities. Especially when the store is dealing with quadratic price dependent demand. A mathematical model for non-coordinated Supply chain is constructed. Numerical example is performed to show that inventory decisions are optimal.

References

[1] Dega Nagaraju, Burra Karuna Kumar and S. Narayanan (2020) “On the optimality of inventory and shipment policies in a two-level supply chain under quadratic price dependent demand” Int. J. Logistics Systems and Management, Vol. 35, No. 4, 2020 [2] Huang, Z. and Gangopadhyay, A. (2004) ‘A simulation study of supply chain management to measure the impact of information sharing’, Information Resources Management Journal, Vol. 17, No. 3, p.20. [3] He, Y., Zhao, X., Zhao, L. and He, J. (2009) ‘Coordinating a supply chain with effort and price dependent stochastic demand’, Applied Mathematical Modelling, Vol. 33, No. 6, pp.2777–2790. [4] Peng, H. and Zhou, M. (2013) ‘Quantity discount supply chain models with fashion products and uncertain yields’, Mathematical Problems in Engineering, 11pp¸ Article ID 895784, http://dx.doi.org/10.1155/2013/895784. [5] Cao, E. (2014) ‘Coordination of dual-channel supply chains under demand disruptions management decisions’, International Journal of Production Research, Vol. 52, No. 23, pp.7114–7131. [6] Kumar, B.K., Nagaraju, D. and Narayanan, S. (2016a) ‘Three-echelon supply chain with centralised and decentralised inventory decisions under linear price dependent demand’, International Journal of Logistics Systems and Management, Vol. 23, No. 2, pp.231–254. [7] Kumar, B.K., Nagaraju, D. and Narayanan, S. (2016b) ‘Optimality of cycle time and inventory decisions in a coordinated and non-coordinated three-echelon supply chain under exponential price dependent demand’, International Journal of Logistics Systems and Management, Vol. 25, No. 2, pp.199–226. [8] Lu, H. and Zhou, J. (2016) ‘The supply chain coordination for non-instantaneous deteriorating items with stock and price sensitive demand’, in Control and Decision Conference (CCDC), 2016 Chinese, IEEE, pp.4574–4581. [9] Kuntian, M., Jiangtao, M., Juanjuan, L. and Chongchong, P. (2017) ‘Coordination of supply chain with fairness concern retailer based on wholesale price and option contract’, in Proceedings of the 2017 International Conference on Management Engineering, Software Engineering and Service Sciences, ACM, January, pp.225–230.

Copyright

Copyright © 2022 Vinola Elisabeth. V, Rexlin Jeyakumari. S. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.