The Optimization Problem of Product Mix and Linear Programming Applications: Case Study in the Apparel Industry

Industrial development strategy is characterized by the efficient use of resources at every production stage. The analysis and efficient utilization of resources are made sustainable by effective management decision making techniques employed in the industry. A quantitative decision making tool called linear programming can be used for the optimization problem of product mix. Understanding the concept behind the optimization problem of product mix is essential to the success of the industry for meeting customer needs, determining its image, focusing on its core business, and inventory management. Apparel manufacturing firms profit mainly depends on the proper allocation and usage of available production time, material, and labor resources. This paper considers an apparel industrial unit in Ethiopia as a case study. The monthly held resources, product volume, and amount of resources used to produce each unit of product and profit per unit for each product have been collected from the company. The data gathered was used to estimate the parameters of the linear programming model. The model was solved using LINGO 16.0 software. The findings of the study show that the profit of the company can be improved by 59.84%, that is, the total profit of Birr 465,456 per month can be increased to Birr 777,877.3 per month by applying linear programming models if customer orders have to be satisfied. The profit of the company can be improved by 7.22% if the linear programming formulation does not need to consider customer orders