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.

The main objective of the manufacture industry is to acquire the maximum profit by minimizing the production cost and maximization of the selling price of the different products fabricated by them. After accomplishment of the optimal value for the production cost the industry focuses on maximizing the selling price of items. However, the competitiveness and uncertainty of the market, the supplier sells their products of discrete selling prices. Therefore, their profit is fluctuated. Such situations to find the optimization of the profit is the main issue of the firm and such destruction can be mitigated with the help of fuzzy linear programming problem. In FLP coefficients of the objective function, constraint variables and the solution values are represented by fuzzy numbers. In this paper, proposed a newly constructed triangular fuzzy numbers (TFN∼τ1) which represent the various realistic circumstances for the selling prices of the various items of manufacturers and then TFN∼τ2 based on TFN∼τ1 is constructed which shows the all possible states of the profit received accordingly numerous sell prices industry might be earned. The data of “R.P.S entrepreneur Jalandhar” is taken which manufacture special types of pipe fitting items with particular sizes according to the demand in Punjab region. We constructed the general structure of the FLP to obtain all attainable bound of the optimal values using newly constructed TFNs. After that a comparative study of the optimal FLP to achieve the membership grades in all conceivable latitude.

Opening the new firm or branch with desired execution is very relevant to facility location problem. Along the lines to locate the new ambulances and firehouses, the government desires to minimize average response time for emergencies from all residents of cities. So finding the best location is biggest challenge in day to day life. These type of problems were named as facility location problems. A lot of algorithms have been developed to handle these problems. In this paper, we review five algorithms that were applied to facility location problems. The significance of clustering in facility location problems is also presented. First we compare Fuzzy c-means clustering (FCM) algorithm with alternating heuristic (AH) algorithm, then with Particle Swarm Optimization (PSO) algorithms using different type of distance function. The data was clustered with the help of FCM and then we apply median model and min-max problem model on that data. After finding optimized locations using these algorithms we find the distance from optimized location point to the demanded point with different distance techniques and compare the results. At last, we design a general example to validate the feasibility of the five algorithms for facilities location optimization, and authenticate the advantages and drawbacks of them.