A fuzzy multi objective programming techniques applied to a case study on an apparel Industry

Abstract

The textile and apparel industries have been using linear programming (LP) techniques to optimize profit and costs of production. While LP techniques are useful for decision-making, it has limitations when dealing with trade-offs between multiple objectives. Fuzzy multi-objective linear programming (FMOLP) addresses this issue by modeling uncertain parameters. In FMOLP, the developed LP models were solved separately. The objective function values were determined for each optimal solution, and a pay-off matrix was constructed using solutions of the objective functions. Finally, linear membership functions were defined for each objective to achieve the results. A case study is sourced from a study by R. Chanda, V. Pabalkar, and S. Gupta and that study is to optimize the profit and cost of an apparel company's product mix using an Excel-based LP model. According to that study, all raw materials of stocks have been used for production considering only maximizing the profit while satisfying the demand. In this study, the FMOLP model has been developed for maximizing profit while minimizing labor and material costs in the apparel industry and solving the formulated model using Excel solver to get profitable values than the above study's results with the same data. Comparison has been made as follows; the profit was reduced by 27 % but material and labor costs were reduced by 27 % and 22 %, respectively using the FMOLP model and minimizing the extra pieces manufactured according to the result given in the reference paper.