A Model for Product Mix Planning Using Multi-objective Optimization Approach with Sensitivity Analysis

Abstract

The paper proposes a model for allocation problems in business organizations considering multiple objectives. It concerns the distribution of resources among options in order to achieve the best value for the goals of the business. Thus, the paper develops a model for a product mix plan using the multi-objective optimization (MOO) approach. The objectives set by the paper are to minimize production costs and waste. The inclusion of the production wastes was motivated by United Nations Sustainable Development Goal number 13, which states, “Take immediate action to combat climate change and its impacts.” The developed model was then tested in a manufacturing company and resulted in Pareto-optimal solutions. Such solutions determine the quantity of products to be produced in several production facilities at a particular period of time and will be set as the product mix plan of the case study company. A sensitivity analysis was also performed by varying the weights of the objective functions, which resulted in different decisions about the best product mix plan. It was found that solution 2 is more stable than solution 1. Moreover, the paper also analyzed the permissible ranges for the coefficients of the decision variables and the coefficients for the constraints, where the optimal solutions remain unchanged. The proposed mathematical model thus demonstrates its viability and usefulness in achieving the company's aims.