#Sequencing_Models
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Sequencing Problem N jobs on 2 Machines | Sequencing Models Operations Research | Operations Research
Job sequencing rules determine the priority for processing jobs. They address scheduling problems that generally lead to inefficient performance in assigning jobs and completing them. Of central importance is job flow time, which is the amount of time a job spends in a shop from order placement to its completion and release. The average time taken to complete jobs is one way of measuring a job shop's performance.
Numerical in Operational Research. In this problem we have multiple jobs which are to be processed on 2 machines. So this is a n-jobs 2-machines problem.
Sequencing problem arises when we have multiple machines and multiple jobs to be processed in the best and optimal way to save time and cost.
Optimal Sequence Algorithm – Johnson and Bellman
Select the minimum processing time out of all the Ai's and Bi's. If it is Ar then do the rth job first. If it is Bs then do the sth job in last.
If there is a tie in selecting minimum of all the processing times, then there are following three ways to deal with such a situation:
If the minimum of all the processing times is Ar, which is also equal to Bs.That is, Min (Ai, Bi) = Ar = BsThen do the rth job first and sth job in last.
If Min (Ai, Bi) = Ar, but Ar = Ak, i.e., there is a tie for minimum among Ai's, then select any one.
If Min (Ai, Bi) = Bs, but Bs = Bt, i.e., there is a tie for minimum among Bi's, then select any one.
Now eliminate the job which has already been assigned from further consideration, and repeat steps 1 and 2 until an optimal sequence is found.
