Solving the multi-criteria: Total completion time, total late work, and maximum earliness problem

Abstract

Within this research, The problem of scheduling jobs on a single machine is the subject of study to minimize the multi-criteria and multi-objective functions. The first problem, minimizing the multi-criteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑C_j,∑V_j,E_max ), and the second problem, minimizing the multi-objective functions ∑C_j+ ∑V_j+E_max are the problems at hand in this paper. In this study, a mathematical model is created to address the research problems, and some rules provide efficient (optimal) solutions to these problems. It has also been proven that each optimal solution for ∑C_j+ ∑V_j+E_max is an efficient solution to the problem (∑C_j,∑V_j,E_max ). Because these problems are NP-hard problems so it is difficult to determine the efficient (optimal) solution set for these problems so some special cases are shown and proven which find some efficient (optimal) solutions suitable for the discussed problem, and highlight the significance of the Dominance Rule (DR), which can be applied to this problem to enhance efficient solutions.