A novel approach to optimize the production cost of railway coaches of India using situational-based composite triangular and trapezoidal fuzzy LPP models

Rakesh Kumar,Neeraj Kumar,Amandeep Kaur,Gaurav Dhiman,Rajesh Kumar Chandrawat,Varun Joshi

doi:10.1007/s40747-021-00313-0

Abstract

This article offers a comparative study of maximizing and modelling production costs by means of composite triangular fuzzy and trapezoidal FLPP. It also outlines five different scenarios of instability and has developed realistic models to minimize production costs. Herein, the first attempt is made to examine the credibility of optimized cost via two different composite FLP models, and the results were compared with its extension, i.e., the trapezoidal FLP model. To validate the models with real-time phenomena, the Production cost data of Rail Coach Factory (RCF) Kapurthala has been taken. The lower, static, and upper bounds have been computed for each situation, and then systems of optimized FLP are constructed. The credibility of each model of composite-triangular and trapezoidal FLP concerning all situations has been obtained, and using this membership grade, the minimum and the greatest minimum costs have been illustrated. The performance of each composite-triangular FLP model was compared to trapezoidal FLP models, and the intense effects of trapezoidal on composite fuzzy LPP models are investigated.

Highlights

Optimization of the production cost has become an imperative component for every successful and robust manufacturing corporation
In the first attempt, the credibility of optimized cost via two different composite triangular Fuzzy Linear Programming (FLP) models is examined, and the results were compared with its extension, i.e., trapezoidal FLP model
The lower, least lower, static, upper, and most upper bounds have been calculated for each situation, and systems of optimized FLP were constructed

Summary

Introduction

Optimization of the production cost has become an imperative component for every successful and robust manufacturing corporation. The trapezoidal linear fuzzy system was converted into an objective interval program based on the order relationship of the TrFNs. In this study, newly constructed composite triangular and trapezoidal fuzzy LPP models have been proposed to deal with probabilistic increment pj in one direction and probabilistic decrement pi in other direction in the basic availability bi of classical optimization and analyzing the result with targeted membership grade. The values of bi according to their membership function are graphically represented in Fig. 2: in certain situations, the total availability of any constrain can be inflexible from the one requirement to the other, and again it can be intensified and declined by any probabilistic increment and decrement Such type of problems bi ( bi − pi ∼ bi≅ b∗i ∼ bi + pi) can be represented by the trapezoidal fuzzy number, given in Eq (5), presented due to an increase from above and decreases from below of the interval in the availability of constraints.

Solution methodology

Findings

Discussion of numerical results

Conclusion