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

## Authors

• Manal Ghassan Ahmed Al-Mutansiriyah University
• Faez Hassan Ali Department of Mathematics, College of Science, Mustansiriyah University.

## Keywords:

Multiobjective Problem (MOP), Branch and Bound (BAB) method. Upper Bound (UB), Lower bound (LB), Dominance Rules.

## Abstract

The present article proposes an exact algorithm for the single-machine scheduling problem to minimize the sum of total completion times, range of lateness and maximum tardiness on a single machine (1/ /(∑ C_(σ_j + R_L + T_max)), where machine idle time is prohibited. In this paper, one of the multiobjective function problem for single criteria on just one machine is being studied. To obtain the optimal solution for the suggested problem, we propose to use Branch and Bound method (BAB) depending upon some dominance rules. This exact method used new technique to obtain three upper bounds (UB) and single lower bound (LB). The proposed BAB method proved its sufficiency by the practical results for n ≤ 15 in a reasonable time. Lastly, we proved a theorem as special case for our problem.

## Author Biography

• Manal Ghassan Ahmed, Al-Mutansiriyah University

Department of Mathematics

Master Degree

Lecturer

## References

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26-06-2022

Original Article

## How to Cite

[1]
M. G. Ahmed and F. H. . Ali, “Exact Method with Dominance Rules for Solving Scheduling on a Single Machine Problem with Multiobjective Function”, Al-Mustansiriyah J. Sci., vol. 33, no. 2, pp. 56–63, Jun. 2022, doi: 10.23851/mjs.v33i2.1091.

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