On employing pythagorean fuzzy processing time to minimize machine rental cost

Salwa El-Morsy; Junaid Ahmad; Reny George; Salwa El-Morsy; Junaid Ahmad; Reny George

doi:10.3934/math.2023882

AIMS Mathematics

2023, Volume 8, Issue 7: 17259-17271. doi: 10.3934/math.2023882

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Research article

On employing pythagorean fuzzy processing time to minimize machine rental cost

1.
Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia
2.
Basic Science Department, Nile Higher Institute for Engineering and Technology, Mansoura, Egypt
3.
Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan
4.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Received: 22 March 2023 Revised: 23 April 2023 Accepted: 23 April 2023 Published: 18 May 2023
MSC : 03E72, 68Q01

The aim of this paper is to obtain the minimal rental cost of the three-phases flow shop scheduling problems. A novel strategy to tackle this issue using Pythagorean fuzzy processing time is introduced. It depends on converting the three stages machine into two stages when the minimum value of processing time of the first machine is greater than the maximum value of processing time of the second machine. The vague processing time does not convert to its crisp form. The jobs sequencing in machines is obtained using Johnson procedure. The zero element of the Pythagorean set is defined as, $ {\widetilde{\mathrm{O}}}^{\mathrm{p}} = \left(\mathrm{0, 1}\right) $ i.e., it has zero membership and one nonmembership values. A numerical example include Pythagorean rental cost is delivered to demonstrate the reliability of the suggested strategy. The idle time, utilization time, and the overall cost are calculated. The idle time of all machines is zero, which minimize the required time and hence, minimize the total rental cost.
- flow shop scheduling,
- pythagorean fuzzy numbers,
- fuzzy processing time,
- optimization problems,
- decision making
Citation: Salwa El-Morsy, Junaid Ahmad, Reny George. On employing pythagorean fuzzy processing time to minimize machine rental cost[J]. AIMS Mathematics, 2023, 8(7): 17259-17271. doi: 10.3934/math.2023882

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Abstract

The aim of this paper is to obtain the minimal rental cost of the three-phases flow shop scheduling problems. A novel strategy to tackle this issue using Pythagorean fuzzy processing time is introduced. It depends on converting the three stages machine into two stages when the minimum value of processing time of the first machine is greater than the maximum value of processing time of the second machine. The vague processing time does not convert to its crisp form. The jobs sequencing in machines is obtained using Johnson procedure. The zero element of the Pythagorean set is defined as, $ {\widetilde{\mathrm{O}}}^{\mathrm{p}} = \left(\mathrm{0, 1}\right) $ i.e., it has zero membership and one nonmembership values. A numerical example include Pythagorean rental cost is delivered to demonstrate the reliability of the suggested strategy. The idle time, utilization time, and the overall cost are calculated. The idle time of all machines is zero, which minimize the required time and hence, minimize the total rental cost.

References

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