PowerPoint Presentation

[Audio] Fuzzy Linear Programming Problem on Profit Maximization and Cost Minimization Research Student H. H. Malshani Department of Mathematics University of Peradeniya Research Supervisor Dr. Niluka Rodrigo Head of the Department Department of Mathematics University of Peradeniya.

[Audio] Outline of the Presentation Introduction Objective Materials and Methods Results and Discussion References.

[Audio] Introduction Linear Programming Linear Programming Maximization Model Excel Solver LINGO Python Minimization Model Manual Methods.

[Audio] Multi-Objective Linear Programming Multi-Objective Linear Programming Goal Programming Fuzzy Linear Programming Other Methods.

[Audio] Objective To Develop a Fuzzy Linear Programming Model for Profit Maximization while Minimizing the Labor and Material Costs and to Solve the Model using the Excel Solver.

undefined. undefined. Materials and Methods. [image].

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

undefined. undefined. Fuzzy Multi-Objective Linear Programming.

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undefined. undefined. Case Study [3]. Collecting data from April 2020 to March 2021.

[Audio] Table 1: Resources needed per unit of product. Products Fabric (g) Threads (m) Cutting (h) Sewing (h) Finishing (h) Polo T-shirt 315 215 0.03 0.35 0.03 Basic T-shirts 200 105 0.02 0.15 0.02 Round neck T-shirt 195 142 0.03 0.16 0.03 Singlets 180 105 0.02 0.09 0.02 V neck T-shirts 50 190 0.04 0.31 0.04 Table 2: Demand and profit, labor cost and material cost per unit of product. Polo T-shirt Basic T-shirts Round neck T-shirt Singlets V neck T-shirts Demand 15000 24000 12000 26000 11000 Profit 4.5 3.8 3.5 3.0 6.5 Labor Cost 11.0 5.0 6.0 4.5 7.0 Material Cost 31.0 19.0 20.0 15.5 37.0 Table 3: Maximum held values of resources in stock Recourses Fabric (g) Threads (m) Cutting (h) Sewing (h) Finishing (h) Labor Cost Material Cost Values 37125000 25621830 5775 44500 6200 1001000 5000000.

undefined. undefined. Famulated maximization model for profit is as follows:.

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

undefined. undefined. Famulated minimization model for labor cost is as follows:.

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

undefined. undefined. Famulated minimization model for material cost is as follows:.

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

[Audio] Results and Discussion. Results and Discussion.

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

[Audio] Comparison among their results of pre LP, post LP and our results after applying FMOLP of three objectives Their Results Our Results Percentage of decreases Pre LP Post LP Profit (INR) 350200.00 768056.30 559129.50 27% Labor cost (INR) 551000.00 1001000.00 776001.00 22% Material cost (INR) 197100.00 4349564.00 3160291.00 27%.

[Audio] Comparison among their results of pre LP, post LP and our results after applying FMOLP of fabric usage Their Results Our Results Percentage of decreases Pre LP Post LP Fabric (g) 13855000.00 17069315.00 15462150.00 9%.

[Audio] Comparison among their results of pre LP, post LP and our results after applying FMOLP of threads usage Their Results Our Results Percentage of decreases Pre LP Post LP Threads (m) 12269000.00 24483255.00 18376170.00 25%.

[Audio] Comparison among their results of pre LP, post LP and our results after applying FMOLP of time management Their Results Our Results Percentage of decreases Pre LP Post LP Cutting (h) 2183.33 4821.42 3535.72 27% Sewing (h) 16520.00 36448.50 26484.33 27% Finishing (h) 2183.33 4821.42 3535.72 27%.

[Audio] References H. M. S. D. Wijekoon, H. V. P. K. G. Pathirana, H. K. K. Fernando, and N. V. Chandrasekara, “The Study of Factors Affecting Textile and Apparel Exports in Sri Lanka.” Rochester, NY, Nov. 11, 2021. doi: 10.2139/ssrn.4117056. G. W. Woubante, “The Optimization Problem of Product Mix and Linear Programming Applications: Case Study in the Apparel Industry,” Open Science Journal, vol. 2, no. 2, Art. no. 2, Jun. 2017, doi: 10.23954/osj.v2i2.853. V. Pabalkar, S. Gupta, and R. Chanda, “A Study on Application of Linear Programming on Product Mix for Profit Maximization and Cost Optimization,” Indian Journal of Science and Technology, vol. 15, pp. 1067–1074, Jun. 2022, doi: 10.17485/IJST/v15i22.164. S. Nahar, M. Akter, and M. Alim, “Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method,” American Journal of Operations Research, 2022, doi: 10.4236/ajor.2022.126016. M. Dash and S. G. Nalam, “Managing Uncertainties in Textile Supply Chains.” Rochester, NY, Feb. 05, 2009. doi: 10.2139/ssrn.1338174. N. Kazemi, E. Ehsani, C. Glock, and K. Schwindl-Braun, “A mathematical programming model for a multi-objective supplier selection and order allocation problem with fuzzy objectives,” International Journal of Services and Operations Management, vol. 21, p. 435, Jan. 2015, doi: 10.1504/IJSOM.2015.070251..

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