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Solving Tri-criteria: Total Completion Time, Total Earliness, and Maximum Tardiness Using Exact and Heuristic Methods on Single-Machine Scheduling Problems
Journal article   Open access   Peer reviewed

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

Nagham M. Neamah, Bayda A. Kalaf and Wafaa Mansoor
Mathematical modelling of engineering problems, Vol.11(4), pp.987-995
2023
DOI: https://doi.org/10.18280/mmep.110415
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CC BY V4.0,  Open Access

Abstract

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,ΣEj,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.

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