Solving the Multi-Criteria, Total Completion Time, Total Earliness Time, and Maximum Tardiness Problem

Authors

Bayda Atiya kalaf Department of Mathematics, College of Education for Pure Sciences, Ibn Al – Haitham, University of Baghdad Iraq
Nagham Muosa Neamah Department of Mathematics, College of Education for Pure Science Ibn AL-Haitham, University of Baghdad, Baghdad, Iraq.
Hamiden Abd El-Wahed Khalifa Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951,Saudi Arabia.

DOI:

https://doi.org/10.30526/37.1.3094

Keywords:

Single Machine Scheduling Problem, Total Completion Times, Total Earliness Time, Maximum Tardiness, Multi-Objective

Abstract

Machine scheduling problems (MSP) are considered as one of the most important classes of combinatorial optimization problems. In this paper, the problem of job scheduling on a single machine is studied to minimize the multiobjective and multiobjective objective function. This objective function is: total completion time, total lead time and maximum tardiness time, respectively, which are formulated as are formulated. In this study, a mathematical model is created to solve the research problem. This problem can be divided into several sub-problems and simple algorithms have been found to find the solutions to these sub-problems and compare them with efficient solutions. For this problem, some rules that provide efficient solutions have been proved and some special cases have been introduced and proved since the problem is an NP-hard problem to find some efficient solutions that are efficient for the discussed problem 1// and good or optimal solutions for the multi-objective functions 1// ,, and emphasize the importance of the dominance rule (DR), which can be applied to this problem to improve efficient solutions.

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