Joint replenishment strategy for deteriorating multi-item through multi-echelon supply chain model with imperfect production under imprecise and inflationary environment

¹ Department of Mathematics, M.B.P.G. College, Haldwani, India
² Department of Mathematics, Inderprastha Engineering College, Ghaziabad, India
³ Department of Mathematics, Chaudhary Charan Singh University, Meerut, India
⁴ Department of Industrial Engineering, Yonsei University, 50 Yonsei-ro, Sinchon-dong, Seodaemun-gu, Seoul 03722, South Korea
⁵ Center for Transdisciplinary Research (CFTR), Saveetha Dental College, Saveetha Institute of Medical and Technical Sciences, Saveetha University, 162, Poonamallee High Road, Velappanchavadi, Chennai 600077, Tamil Nadu, India

^* Corresponding author: bsbiswajitsarkar@gmail.com

Received: 8 August 2021
Accepted: 10 May 2022

Abstract

As the industry environment becomes more competitive, the supply chain management for multi items has become an essential part of the industries. In this paper, a multi-echelon inventory model for deteriorating multi items with imperfect production has been developed under the environment of fuzzy and inflation. A single producer, multi-supplier, and multi-retailer are considered from the integrated point of view. Here, the producer only produces the retailer’s need to have a tremendous advantage and minimum loss. It is observed that the inflation rate is almost uncertain for deteriorating goods in every supply chain. In this paper, the inflation rate is taken as a triangular fuzzy number, and the centroid method is used to defuzzify the profit function. The shortage is not allowed in any part, an imperfect production process is considered, but it is not reworkable in this supply chain. Different inflation rates are considered for additional items because inflation has strained the most vulnerable consumers (the daily wage earners), who mainly demand goods in short and small quantities. This entire model is developed based on the retailer’s demand and due to which, the profit potential is maximized. The central premise of this study is to get maximum benefit by creating a production model for deterioration items. Finally, a numerical example and sensitivity analysis illustrate the present study. It is observed that if the number of shipments taken from the supplier increases during the production period, the total profit increases in crisp and fuzzy. If a positive change occurs in the number of shipments received through the producer to the retailer, then the fuzzy model has positive, but a slight negative change occurs in the crisp model. This paper shows the effect of a joint replenishment policy for multi-item compared with the independent approaches.