A new heuristic method for solving unbalanced multi-objective assignment problem

Abstract In the era of globalization, institutions face increasing challenges in effectively managing their resources to achieve diverse and differentiated objectives. The unbalanced multi-objective assignment problem reflects these challenges, as the distribution of limited resources requires achieving a balance between objectives such as minimizing time, cost, etc. In this study, an application case in the industrial field of rolling process was investigated, where the objective of the assignment problem is to minimize total assignment. In order to tackle this problem, the multi-objective problem was addressed by converting it into a single-objective problem through the weighted sum method by assigning a weight to each objective. A new heuristic method was then applied to solve the unbalanced single-objective assignment problem where the machines were loaded with more than one job. The Hungarian method was also used to solve the problem in order to assess the proposed method, and the outcomes were then compared. The proposed method proved efficient as it reduced idle time by 28%, increased machine efficiency by 5% and reduced costs by an average of 15%.