# Solving the Multi-Criteria Problem: Total Completion Time, Total Late Work, Total Earliness Time, Maximum Earliness, and Maximum Tardine

## Authors

• Nagham Muosa Neamah Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq / Department of Mathematics, College of Education for Pure Science Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0001-5393-4083
• Bayda Atiya Kalaf Department of Mathematics, College of Education for Pure Science Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq

## Keywords:

Maximum Earliness, Maximum Tardiness, Multi-Criteria (MC), Multi-Objective (MO), Total Completion Times, Total Earliness Times, Total Late Work

## Abstract

In this paper, we study the scheduling of jobs on a single machine. Each of the n jobs will be processed without interruption and becomes available for processing at time zero. The goal is to find a processing order for the jobs, minimizing the total completion time, total late work, total earliness time, and maximum earliness maximum tardiness. The posed problems in this paper are as follows: The first problem is to minimize the multi-criteria, which includes minimizing the total completion time, total late work, total earliness time, maximum earliness, and maximum tardiness that are denoted by , respectively. The second problem is to minimize the multi-objective functions ( ). The theoretical section will present the mathematical formula for the discussed problem. Because these problems are NP-hard problems. It is difficult to determine the efficient (optimal) solution set for these problems. Some special cases are shown and proven to find efficient (optimal) solutions to the discussed problem. The significance of the dominance rule can be applied to problems to improve and to get good solutions that will be highlighted.

2024-05-30

Mathematics

## How to Cite

Solving the Multi-Criteria Problem: Total Completion Time, Total Late Work, Total Earliness Time, Maximum Earliness, and Maximum Tardine. (2024). Iraqi Journal of Science, 65(5), 2724-2735. https://doi.org/10.24996/ijs.2024.65.5.30

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