Solving Tricriteria Machine Scheduling Problem using New Efficient Method

• DOI: 10.52783/anvi.v28.2088
• Publication Date: 2024-11-15T08:59:43Z
• Authors: Yasameen M.Mohammed

In this study, an MBA model which can select a single machine for production and simultaneously consider many criteria is proposed. In this paper we present the description of the machine scheduling problem (MSP), which is the set of n tasks accomplished by a single machine. The task will be to minimise a function with reference to the criteria that are enumerated below: ∑C_j – total time whereas R_L – range of lateness; T_max – maximum of tardiness. Proofs have been made to conclude that this problem is NP hard. The matter we are concerned with calls for the emergence of a number of subissues, all of which will be discussed in more detail later on. In the theoretical part of our investigation, we have shown that the SPT rule offers a viable solution to the issue that we are attempting to solve. Furthermore, we have shown that it is possible to implement certain manifestations of the dominance rule (DR). In order to solve the suggested MSP tricriteria, the Branch and Bound (BAB) algorithm is used throughout the practical portion of the evaluation process. The objective of this approach is to identify a set of solutions that are not only successful but also efficient for 1//(∑C_j,R_L,T_max) up to n=18 jobs. In addition, the BAB method is used in conjunction with DR for a maximum of n=39 tasks within a reasonable amount of time in order to uncover estimated effective solutions for the problem at hand.