# Sequencing Models : Operations Research

In the previous chapter, you studied the mechanics of obtaining an optimal replacement policy for machines. This chapter concentrates on the problem of determining the sequence (order) in which a number of jobs should be performed on different machines in order to make effective use of available facilities and achieve greater output.

For example, consider a sequencing problem where n jobs are to be performed on m different machines. In such a case, our problem is to determine the sequence, which minimizes the total elapsed time. Here, the term elapsed time means the time from the start of first job upto the completion of the last job.

"Lost time is never found again." -Aughey

In this chapter, we discuss the following cases:

• Processing n jobs through two machines.
• Processing n jobs through three machines.
• Processing two jobs through m machines.

Few general assumptions in this chapter are as follows:

• The processing time on each machine is known.
• The time required to complete a job is independent of the order of the jobs in which they are to be processed.
• No machine may process more than one job simultaneously.
• The time taken by each job in changing over from one machine to another is negligible.
• Each job, once started on a machine is to be performed up to completion on that machine.
• The order of completion of job has no significance, i.e., no job is to be given priority.
• A job starts on the machine as soon as the job and the machine both are idle.

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