Reliability dependent production-inventory model for redundancy allocation via fuzzy logic

¹ Department of Applied Mathematics, Vidyasagar University, Midnapore 721102, West Bengal, India
² Department of Mathematics, The University of Burdwan, Burdwan 713104, West Bengal, India

^* Corresponding author: shyamal@mail.vidyasagar.ac.in

Received: 20 February 2024
Accepted: 21 June 2024

Abstract

This study deals with a reliability dependent production-inventory model in two scenarios: a redundancy allocation with crisp structure and the other with fuzzy logic. Here, a manufacturer purchases some raw-materials/components in variable cycles and arranges them as series-parallel system to produce a single item with production cost dependent on system reliability. In this model, a retailer gets the opportunity of warranty period and credit period offered by the manufacturer. Also, the retailer’s demand is dependent on system reliability, credit period and selling price. In the crisp model, the component reliability is exponentially dependent on known failure rate and failure time. However, there is no dependent relationship between these two parameters. Actually, the real world is full of uncertainty and these two parameters may depend on each other following some uncertain nature which can be expressed as fuzzy logic. So, in the fuzzy model, failure time has been considered as dependent on failure rate following fuzzy logic and these fuzzy relations are defuzzified by using three fuzzy inference techniques: Mamdani, Sugeno and Tsukamoto. Main goal of this article is to determine the optimum number of cycles and components to maximize manufacturer’s profit and system reliability with some constraints. The model is solved by using elitist non-dominated sorting genetic algorithm (NSGA-II) and some numerical examples closed to real-world have been executed. Comparative analyses are done for different cases; different fuzzy inference techniques and for active and mixed strategies. Finally, some sensitivity analyses and managerial insights are drawn.