Exact Method with Dominance Rules for Solving Scheduling on a Single Machine Problem with Multiobjective Function

Ahmed, Manal Ghassan; Ali, Faez Hassan

doi:10.23851/mjs.v33i2.1091

Cited by 2 publications

(4 citation statements)

References 7 publications

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“…Such developments may heavily reduce the number of nodes in searching for an efficient solution. Where the DRs are also applicable to such problems [29,30].…”

Section: Dominance Rules For Single Machine Scheduling Problemmentioning

confidence: 99%

“…in Table 5, contain (7) likely sequences some /all are subject to the aforementioned DRs. The adjacency matrix 𝐴 is as followings: The sequences (1-7) provide the problem ( 𝑆𝐶𝑆𝐸𝑇 ) an effective value and the sequence (7) an optimal value for the problem (S₱ 7 ), as can be shown in Table 5.…”

Section: Rule (1)mentioning

confidence: 99%

“…When more than one objective (criteria) is needed, scheduling problems become more difficult to model and solve. It is frequently implausible that different objectives will be best served by the same set of decision variables [5][6][7][8]. As a result, there is a trade-off between the multiple objectives.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Minimizing Total Completion Time, Total Earliness Time, and Maximum Tardiness for a Single Machine scheduling problem

Kalaf,

Nagham Muosa Neamah,

Khalifa

2024

IHJPAS

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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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“…Such developments may heavily reduce the number of nodes in searching for an efficient solution. Where the DRs are also applicable to such problems [29,30].…”

Section: Dominance Rules For Single Machine Scheduling Problemmentioning

confidence: 99%

Section: Rule (1)mentioning

confidence: 99%

See 1 more Smart Citation

Minimizing Total Completion Time, Total Earliness Time, and Maximum Tardiness for a Single Machine scheduling problem

Kalaf,

Nagham Muosa Neamah,

Khalifa

2024

IHJPAS

View full text Add to dashboard Cite

show abstract

“…Jawad et al [12] provided the BAB to solve multi-criteria objective function 1// (∑𝐶 𝑗 , ∑𝐸 𝑗 ) problem in the SMSP. Ahmed and Ali [13] suggested BAB and heuristic approaches to minimize the ∑𝐶 𝑗 + 𝑅 𝐿 + 𝑇 𝑚𝑎𝑥 for single machine scheduling problem. Al-Tameemi [14] used BAB to solved the problem 1// ∑𝐶 𝑗 + ∑𝑇 𝑗 + 𝐸 𝑚𝑎𝑥 .…”

Section: Introductionmentioning

confidence: 99%

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

Neamah,

Kalaf,

Mansoor

2024

MMEP

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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 ∑𝐶 𝑗 , Total Earliness ∑𝐸 𝑗 , and Maximum Tardiness Time 𝑇 𝑚𝑎𝑥 for multicriteria and multi-objective functions (1//(∑𝐶 𝑗 , ∑𝐸 𝑗 , 𝑇 𝑚𝑎𝑥 ) and (∑𝐶 𝑗 + ∑𝐸 𝑗 + 𝑇 𝑚𝑎𝑥 )) 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.

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Exact Method with Dominance Rules for Solving Scheduling on a Single Machine Problem with Multiobjective Function

Cited by 2 publications

References 7 publications

Minimizing Total Completion Time, Total Earliness Time, and Maximum Tardiness for a Single Machine scheduling problem

Minimizing Total Completion Time, Total Earliness Time, and Maximum Tardiness for a Single Machine scheduling problem

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

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