Three-echelon supply chain model in an imperfect production system with inspection error, learning effect, and return policy under fuzzy environment

Abstract

This article presents a three-echelon supply chain (SC) model, incorporating a single supplier, a single manufacturer, and a single wholesaler under fuzzy system. Three scenarios have been considered: (a) the learning effect (LE) of the employees on the production cost as well as the return contract (RC) between the supplier and an outside supplier and also between the manufacturer and the wholesaler, (b) without considering the LE on the manufacturing expenses and (c) without the RC between the SC players. The goal of this paper is to study the effect of the LE and the RC on total profit of the SC for centralised and decentralised cases. To adopt flexibility of the demand parameters of the entire process, we develop a fuzzy mathematical model of the proposed SC problem. To discuss the novelty of the proposed model, we insert a table of authors’ contribution and also perform numerical illustrations with the help of LINGO software and make a comparative study between the optimal results of the existing method and the proposed fuzzy approach. Sensitivity analysis and graphical illustrations have also been done for better realisation of the model followed by conclusion.

KEYWORDS:

• Supply chain
• inspection error
• learning effect
• return contract
• fuzzy environment

Acknowledgements

The authors are thankful to the honourable Editor-in-Chief, Associate Editor and anonymous reviewers for their constructive suggestions to improve the quality of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Gour Chandra Mahata

Dr. Gour Chandra Mahata is an Associate Professor & Head of the Department of Mathematics, Sidho-Kanho-Birsha University, Purulia - 723104, West Bengal, India. He received his B.Sc. and M.Sc. degree respectively, from Vidyasagar University, Midnapore, West Bengal, India. He received his Ph.D. degree in Operations Research from Indian Institute of Technology, Kharagpur, India. His research interest focuses on Supply Chain Management, Inventory Control, Game theory in fuzzy system, Leadership Theory in fuzzy system, Optimization Theory, Fuzzy decision making, Fuzzy optimization, Stochastic fuzzy, etc. He has published in journals such as Soft Computing, International Journal of Intelligent Systems, Computer and Mathematics with Applications, Mathematical and Computer Modelling, Expert Systems with Applications, Computer and Industrial Engineering, Journal of Intelligent Manufacturing, Production Planning and Control, Mathematical and Computer Modelling of Dynamical Systems, SADHANA, Journal of Industrial Management and Optimization, RAIRO Operations Research, International Journal of Systems Science: Operations & Logistics, Journal of Fuzzy Mathematics, International Journal of Operational Research, International Journal of Mathematics in Operational Research, OPSEARCH, International Journal of Industrial Engineering Computations, Journal of Mathematical Modelling and Algorithms, International Journal of Strategic Decision Sciences, International Journal of Management Science and Engineering Management, Journal of Industrial Engineering International, etc.

Sujit Kumar De

Dr. Sujit Kumar De is an Associate Professor of Mathematics at Midnapore College (Autonomous), West Bengal, India. He started his research work since 2001. He is also a visiting team member of NCTE, Govt. of India since 2015. His research interests include Uncertain System, Intelligent systems, Finance, Fuzzy Sets and Systems, fuzzy reasoning, Neutrosophic Sets and Systems, Game theory in fuzzy system, Leadership Theory in fuzzy system, Industrial Pollution and Production Management, Green Supply Chain Management etc. He is the reviewer of more than 60 international journals. He published more than 82 articles in various reputed international journals like: Int. J. of Intelligent Systems, Journal of Cleaner Production, Applied Soft Computing, Computers & Industrial Engineering, Soft Computing, Int. J. of Fuzzy Systems etc. He is an Associate Editor of the Journal of Fuzzy Logic and Modelling in Engineering and the Editorial Board Member of the Journal of Finance and Market and Int. J. of Mathematics and its Applications.

Kousik Bhattacharya

Kousik Bhattacharya currently works as a research scholar in Midnapore College (Autonomous), India. He completed his M.Sc. degree in 2015 from Midnapore College (Autonomous) under Vidyasagar University, West Bengal, India. He published 6 research articles in various international journals like Computers and Industrial Engineering, Applied Soft Computing, International Journal of Intelligent Systems etc. He is now working in the field of Supply Chain Management, Fuzzy decision making, Fuzzy approximate reasoning etc.

Suman Maity

Suman Maity is a state aided college teacher of Raja N.L.Khan Women's College (Autonomous) since 2016. He is also a research scholar of Vidyasagar University in the department of Applied Mathematics. He did his Masters from Vidyasagar University in the year 2015, West Bengal, India. His research interests are on Inventory management, Operational Research, Fuzzy sets etc. He published many articles in the journals like International Journal of Intelligent Systems, International Journal of Fuzzy System, RAIRO-Operational Research, Mathematics, Granular Computing, Finance and Market etc. He reviewed more than ten articles in several journals like Soft Computing, Computers and Industrial Engineering, Kybernetics, RAIRO-Operational Research, OPSEARCH etc.