An integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment

¹ Department of Mathematics, IIT Kharagpur, Kharagpur 721302, India
² Department of Mathematics (UG & PG), Midnapore College (Autonomous), Midnapore, India
³ Department of Mathematics, BITS Pilani, Dubai Campus, Dubai, UAE

^* Corresponding author: goswami@maths.iitkgp.ac.in

Received: 29 August 2018
Accepted: 17 September 2020

Abstract

Brand substitution is common observed phenomenon in daily life. It is the decision makers’ economic understanding and potential scheme for business-industries. Also, it provides the flexibility in management and increases the ability to control the production. This works proposes an integrated supplier–retailer inventory model for substitutable products. Two suppliers work not works with two different brand products with their corresponding demand are involved and one retailer sells each of the products. To nullify the complexities of the joint optimization problem, we first develop a deterministic model for three cases: no substitution, partial substitution and full substitution, then we go for its fuzzification. Keeping the financial constraint of each producer, we have studied over the elasticity of the cost parameters by means of triangular dense fuzzy lock set approach with its locking and unlocking property for final decision making. Finally, sensitivity analysis and graphical illustrations are made to justify the model.