PowerPoint Presentation

[Audio] Welcome everyone! Today, we will examine how a Fuzzy Linear Programming Problem can be used to maximize profit and reduce costs for businesses manufacturing Polo T-Shirts, Singlets, Round Neck T-Shirts, and V Neck T-Shirts. We will investigate how our research from the University of Peradeniya can provide solutions to these issues..

[Audio] This presentation looks into maximizing profit and minimizing cost through a Fuzzy Linear Programming Problem. We will start with examining the objectives of this research and then delve into the tools and techniques used to collect data and analyze outcomes. After that, we will go over the results of this research and the sources used to come to our conclusions..

[Audio] Linear programming is an effective tool for maximising profit and minimising cost. This slide will look at the different ways of solving problems with linear programming, such as Excel Solver, LINGO, Python, and manual methods. Understanding these methods will help us to determine the most suitable one for the task. The goal is to make the most efficient use of our resources while still meeting our objectives..

[Audio] Multi-Objective Linear Programming is a method utilized to optimize two or more objectives in order to maximize profit and minimize risk. Fuzzy Linear Programming is a special form of this approach, allowing for varying levels of objectives to be included in the matrix to evaluate a problem. This model offers a more realistic solution for businesses than traditional linear programming. Furthermore, Goal Programming, in which weights are assigned to goals, and Other Methods such as non-linear programming can be employed to further maximize profit and minimize cost..

[Audio] A Fuzzy Linear Programming Model is outlined in this slide, designed to maximise profits while also minimising labour and material costs. Through the use of Excel Solver, an optimisation software, this model seeks to generate the most desirable solutions for organisations, offering cost savings in the process while still achieving greater profits..

Materials and Methods. [image]. 6.

Linear Membership Function Linear membership functions for the minimization and maximization linear programming problems are defined as follows:.

[Audio] "The goal of this research is to develop a linear programming problem with multiple objectives. Fuzzy linear programming can help us to solve such problems with less time and effort. Specifically, this research uses Fuzzy Multi-Objective Linear Programming (FMLP) to maximize profit and minimize cost. Fuzzy linear programming simplifies the optimization process by providing solutions to trade-off between different objectives. It also allows us to create more efficient solutions that are optimized for both profit and cost. " "This research demonstrates the benefits of using Fuzzy Multi-Objective Linear Programming (FMLP). By using FMLP, companies can create more efficient solutions that optimize for both profit and cost objectives. This research provides a cost-effective and efficient way to maximize profit and minimize cost, which can lead to improved business outcomes..

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[Audio] We have conducted research related to Polo T-Shirts, Round Neck T-Shirts and Basic T-Shirts. Data gathered between April 2020 and March 2021 shows potential for improved profitability when considering the market conditions. It is suggested that a Fuzzy Linear Programming Problem should be employed to optimize profit and minimize costs..

[Audio] Our research into the Fuzzy Linear Programming Problem has resulted in the presentation of data regarding the demand and profit, labor cost and material cost per unit of product. Additionally, the maximum held values of each of the resources in stock have been calculated in order to help make decisions with regard to maximizing profit and minimizing costs..

Famulated maximization model for profit is as follows:.

Solved maximization model for profit using Excel Solver is as follows:.

Famulated minimization model for labor cost is as follows:.

Solved minimization model for labor cost using Excel Solver is as follows:.

Famulated minimization model for material cost is as follows:.

Solved maximization model for material cost using Excel Solver is as follows:.

Results and Discussion. 18.

Solved final model after applying FMOLP using Excel Solver is as follows:.

[Audio] This slide compares the profitability before and after optimization with a fuzzy linear programming problem. Our research reveals a 27 percent reduction in profit, 22 percent reduction in labor cost, and 27 percent reduction in material cost. We have successfully attained higher profits and cut costs at the same time. This approach proves to be an effective way to maximize profits with minimal labor and material costs..

[Audio] Efficiency is an essential factor for any business to succeed. Our research has revealed that Fuzzy Linear Programming can help to decrease fabric usage by 9%, as seen in the table on this slide. By leveraging optimized production processes, businesses can save resources, reap higher profits and decrease costs..

[Audio] An analysis of the results of the fuzzy linear programming problem have revealed a 25% reduction in threads. This demonstrates the efficacy of problem-solving approaches in cutting down expenditure while at the same time amplifying profitability in a production process. It is crucial to comprehend the capabilities of fuzzy linear programming and the advantages it can bring to the whole organization..

[Audio] Our results from the table demonstrate that the Fuzzy Linear Programming Problem has resulted in a 27% reduction in cutting, sewing and finishing hours. This renders more efficiency throughout the production process, thus leading to higher profits..

[Audio] Our research has shown that fuzzy linear programming can be utilized to maximize profit and minimize costs for the textile and apparel industry. We have investigated the factors affecting exports in Sri Lanka and how linear programming can be applied to a product mix for better optimization. Moreover, we have explored how statistical methods can be utilized to solve fuzzy multi-objective linear programming problems, as well as how to handle uncertainties in the supply chain. Through this research, we provide a mathematical programming model and prove how a supplier selection and order allocation problem can be solved with fuzzy objectives..

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