Page 294 - DMGT206_PRODUCTION_AND_OPERATIONS_MANAGEMENT

Unit 14: Operations Scheduling

First Come First Served and Last Come Last Served Notes

These terms reflect exactly what they say. In the former, jobs are scheduled on the basis of their
arrival. In the latter, the last arrival is scheduled first and the first arrival scheduled last.

Shortest Processing Time Procedure

A schedule obtained by sequencing jobs in increasing order of processing times is called a
shortest processing time (SPT) rule.
This schedule minimizes mean flow time, F. In addition, the SPT rules also minimize mean
lateness and mean waiting time. The mean flow time is computed by simply adding the flow
time for each job and dividing by the number of jobs.
Due Date Procedure: In the due date procedure, jobs are sequenced in the order of decreasing due
dates. The job with the earliest due date will be sequenced first. The due date procedure minimizes
the maximum tardiness.
Caution: Random: Jobs are chosen randomly. There is no apparent logical method of scheduling
jobs.
Slack Time Remaining: The STR is the difference between the time remaining before the due
date and the remaining processing time.
The ‘SPT sequencing rule’ shows better performance, compared to the other scheduling rules,
when there are many jobs for a single machine. SPT minimizes the total flow time, average flow
time, and average tardiness of jobs, etc., in most cases. An example will make it easier to
visualize the impact of the different rules on scheduling. Before going to the example, let us
define some of the terms that we are going to use.
Each job in a one machine-scheduling model (n/1 scheduling) is described by two parameters,
where ‘i’ is the number of the sequence of the job.
p = Processing time for the ‘i’th job
i
d = Due date of the ‘i’ th job
i
The definition of p includes set up time for job ‘i’. If job ‘i’ is defined as a lot of several identical
i
pieces, then pi will denote the time required to process the complete batch. The due date is the
time by which a job must be completed, otherwise, the job will be deemed late.

F is the ‘flow’; it is the amount of time the ‘ith’ job spends in the system. The ‘makespan’ is the
i
cumulative time it takes the shop to complete all the jobs. Lateness, L is the amount of time by
i
which the completion time of job ‘i’ exceeds its due date. Lateness is designated as ‘L ’. As
i
lateness can be either positive or negative, a positive lateness, i.e., when the due date is not met
is called tardiness, T .
i
Thus, tardiness is a measure of the deviation of the completion time from the due date. Since
there is often a penalty associated with not meeting due dates, the tardiness measure is important.
Flow Time = F = C – r = F + pi
i i i (i-1)
Makespan = Total flow time =  
Mean flow time = Total flow time/Number of jobs =  
Lateness of Job = L = F – d .
i i i
Tardiness of Job = T = F - d if F > dn otherwise T = 0
i i i i i

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