منصة إيفاد العلمية

نغم موسى نعمه

إرسال رسالة

التخصص: رياضيات

الجامعة: بغداد

النقاط:

12.5

معامل الإنتاج البحثي

الخبرات العلمية

دكتوراه في الرياضيات - بحوث العمليات - جدولة مكائن

الأبحاث المنشورة

Solving tri-criteria: total completion time, total late work, and maximum earliness by using exact, and heuristic methods on single machine scheduling problem

المجلة: Iraqi Journal for Computer Science and Mathematics

سنة النشر: 2024

تاريخ النشر: 2024-06-24

The presented study investigated the scheduling regarding 𝑛 jobs on a single machine. Each 𝑛 job will be processed with no interruptions and becomes available for the processing at time 0. The aim is finding a processing order with regard to jobs, minimizing total completion time ∑𝐶𝑗 , total late work ∑𝑉𝑗 , and maximal tardiness 𝐸𝑚𝑎𝑥 which is an NP-hard problem. In the theoretical part of the present work, the mathematical formula for the examined problem will be presented, and a sub-problem of the original problem of minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is introduced. Also, then the importance regarding the dominance rule (DR) that could be applied to the problem to improve good solutions will be shown. While in the practical part, two exact methods are important; a Branch and Bound algorithm (BAB) and a complete enumeration (CEM) method are applied to solve the three proposed MSP criteria by finding a set of efficient solutions. The experimental results showed that CEM can solve problems for up to n = 11 jobs. Two approaches of the BAB method were applied: the first approach was BAB without dominance rule (DR), and the BAB method used dominance rules to reduce the number of sequences that need to be considered. Also, this method can solve problems for up to 𝑛 = 20, and the second approach BAB with dominance rule (DR), can solve problems for up to 𝑛 = 60 jobs in a reasonable time to find efficient solutions to this problem. In addition, to find good approximate solutions, two heuristic methods for solving the problem are proposed, the first heuristic method can solve up to 𝑛 = 5000 jobs, while the second heuristic method can solve up to 𝑛 = 4000 jobs. Practical experiments prove the good performance regarding the two suggested approaches for the original problem. While for a sub-problem the experimental results showed that CEM can solve problems for up to 𝑛 = 10 jobs, the BAB without dominance rule (DR) can solve problems for up to 𝑛 = 15, and the second approach BAB with dominance rule (DR), can solve problems for up to 𝑛 = 30 jobs in a reasonable time to find efficient solutions to this problem. Finally, the heuristic method can solve up to 𝑛 = 4000 jobs. Arithmetic results are calculated by coding (programming) algorithms using (MATLAB 2019a)

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

المجلة: Periodicals of Engineering and Natural Sciences

سنة النشر: 2023

تاريخ النشر: 2023-05-03

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 multicriteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑𝐶𝑗 , ∑𝑉𝑗 , 𝐸𝑚𝑎𝑥), and the second problem, minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 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 ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is an efficient solution to the problem (∑𝐶𝑗 , ∑𝑉𝑗 , 𝐸𝑚𝑎𝑥). 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.

Solving Tri-criteria: Total Completion Time, Total Earliness, and Maximum Tardiness Using Exact and Heuristic Methods on Single-Machine Scheduling Problems

المجلة: Mathematical Modelling of Engineering Problems

سنة النشر: 2024

تاريخ النشر: 2024-04-15

Machine scheduling problems have become increasingly complex and dynamic. In industrial contexts, managers often evaluate several objectives simultaneously and attempt to identify the optimal solution that satisfies all concerns. This study proposes two heuristic methods based on SPT and dominated rules (DR) to minimize Total Completion ∑𝐶𝑗 , Total Earliness ∑𝐸𝑗 , and Maximum Tardiness Time 𝑇𝑚𝑎𝑥 for multicriteria and multi-objective functions (1//(∑𝐶𝑗 , ∑𝐸𝑗 , 𝑇𝑚𝑎𝑥) and (∑𝐶𝑗 + ∑𝐸𝑗 + 𝑇𝑚𝑎𝑥)) based on single machine scheduling problems. in addition, two exact methods Branch and Bound (BAB with and without DR) and a complete enumeration method are applied to solve the multi- criteria and multi-objective functions. According to the calculation results, the CEM is able to solve problems up to 𝑛 = 11 jobs, while BAB without DR and BAB with DR able to resolve problems from 𝑛 = 19 to 𝑛 = 50 jobs, respectively, within a reasonable time. However, heuristic methods can solve up to 𝑛 = 5000 jobs. in addition, the experimental results for a subproblem show that the heuristic methods can solve up to 𝑛 = 4000 jobs. Practical experiments demonstrate the proposed heuristic methods are the most effective of all approaches. All methods used in this work were coded with MATLAB 2019a.

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

المجلة: Ibn Al-Haitham Journal for Pure and Applied Sciences

سنة النشر: 2024

تاريخ النشر: 2024-01-20

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 multi objective and multi objective function. This objective function is: total completion time, total lead time and maximum tardiness time, respectively, which are formulated as (∑ 𝑪𝒋 , ∑ 𝑬𝒋 , 𝑻𝒎𝒂𝒙) are formulated. In this study, a mathematical model is created to solve the research problem. This problem can be divided into several subproblems 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// 𝐹(∑ 𝑪𝒋 , ∑ 𝑬𝒋 , 𝑻𝒎𝒂𝒙), and good or optimal solutions for the multiobjective functions 1// ∑ 𝐶𝑗 + ∑ 𝐸𝑗 + 𝑇𝑚𝑎𝑥,, and emphasize the importance of the dominance rule (DR), which can be applied to this problem to improve efficient solutions.

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

المجلة: Iraqi Journal of Science

سنة النشر: 2024

تاريخ النشر: 2024-05-30

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 NPhard 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.