Sequencing in operations management: FCFS, SPT, EDD and critical ratio rules compared on a worked five-job example, plus Johnson's rule for two machines with a Gantt chart, and how sequencing differs from scheduling.
Updated 12 min read
Sequencing means deciding the order in which waiting jobs, tasks or customers are processed at a work centre. When several jobs compete for the same machine or person, sequencing answers one question: which job goes first, which goes second, and so on. The order is chosen with the help of priority rules, such as first come first served or shortest processing time.
The topic matters because the same set of jobs, on the same machine, can give very different results depending on the order. A good sequence cuts waiting time, work-in-process inventory, idle time and late deliveries; a poor one wastes capacity and upsets customers, even though nothing else has changed.
The main objective is to arrange jobs so that resources are used efficiently and customer due dates are met. More specifically, a sequence may aim to:
minimise the average flow time (time a job spends in the system);
minimise the number of late jobs and average tardiness;
minimise idle time of machines and workers;
minimise the makespan, the total time to finish all jobs;
minimise work-in-process inventory;
keep the system fair and simple to operate.
No single rule is best for all of these at once, so the manager chooses the rule that fits the objective that matters most.
Sequencing as part of production planning and control#
Production planning and control (PPC) moves through planning, routing, scheduling, loading, sequencing, dispatching, follow-up and corrective action. Once jobs are loaded onto a work centre, sequencing fixes their order there, and dispatching releases them to the shop floor in that order.
Routing decides the path a job follows, that is, which machines or departments it passes through and in what order of operations. Sequencing decides the order in which different jobs are taken up at one machine or work centre. Routing is about the route of one job; sequencing is about the queue of many jobs.
Scheduling fixes the timetable, that is, the start and finish time of each job. Sequencing fixes only the order. In practice the sequence is decided first and the schedule is then built from it.
In job shops, each order is different, routings vary and many jobs compete for general-purpose machines. Sequencing is most important and most difficult here, because every day brings a new mix of jobs with different processing times and due dates.
Batches of different products share the same equipment. Sequencing decides which batch runs next, often considering changeover (set-up) times, since some orders of products need less cleaning or resetting than others.
In mass and continuous production the flow is fixed by the line, so day-to-day sequencing is limited. It still matters in mixed-model assembly lines, where the order of different models on the line must be planned.
The job with the earliest due date is done first. A tailor finishing the wedding outfit due tomorrow before one due next week is using EDD.
Advantages: focuses on customer deadlines; minimises the maximum lateness on a single machine and often reduces tardiness.
Disadvantages: ignores processing time, so average flow time may be higher than under SPT; one very long job with an early due date can delay many others.
The longest job is done first. It is sometimes used when large jobs are important or need to be started early, but it usually gives the worst average flow time.
The critical ratio compares the time left until the due date with the processing time still required:
CR=Work (processing) time remainingDue date−Today’s date
The job with the lowest CR is done first, and ratios are recalculated each time a job is completed, which makes CR a dynamic rule.
CR value
Meaning
CR greater than 1
Ahead of schedule: more time left than work needed
CR equal to 1
Exactly on schedule
CR less than 1
Behind schedule: urgent attention needed
CR zero or negative
Due now or already overdue
CR is useful because it combines both urgency (due date) and workload (processing time) in one number, and because it keeps updating as the situation changes.
At day 0: CRA=8/6=1.33, CRB=6/2=3.00, CRC=18/8=2.25, CRD=15/3=5.00, CRE=23/9=2.56. The lowest is A, so A runs first and finishes on day 6.
At day 6: CRB=(6−6)/2=0, CRC=12/8=1.50, CRD=9/3=3.00, CRE=17/9=1.89. B is lowest and finishes on day 8.
At day 8: CRC=10/8=1.25, CRD=7/3=2.33, CRE=15/9=1.67. C runs and finishes on day 16.
At day 16: CRD=(15−16)/3=−0.33, CRE=7/9=0.78. D runs and finishes on day 19; E finishes on day 28.
The CR sequence is A, B, C, D, E, which here happens to match the arrival order, so its results equal FCFS: average flow time 15.4 days and average tardiness 2.2 days.
SPT gives the lowest average flow time, and EDD gives the lowest tardiness and fewest late jobs, which matches the general textbook findings. If on-time delivery is the priority, this printing unit should use EDD.
Results of the four priority rules in worked example 1: SPT wins on flow time, EDD on tardiness.
Sequencing n jobs through two machines: Johnson's rule#
When every job must pass through the same two machines in the same order (first M1, then M2), Johnson's rule (S. M. Johnson, 1954) gives the sequence that minimises total completion time (makespan) and hence idle time.
List the processing time of every job on both machines.
Find the smallest time in the whole list.
If it is on Machine 1, place that job as early as possible in the sequence. If it is on Machine 2, place it as late as possible.
Remove that job from the list.
Repeat until all jobs are placed. Ties may be broken arbitrarily.
Step 6: Build the time table. A job starts on M2 at the later of (its finish on M1) and (the finish of the previous job on M2).
Job
M1 in
M1 out
M2 in
M2 out
M2 idle before job
J2
0
1
1
7
1
J4
1
4
7
15
0
J3
4
13
15
22
0
J5
13
23
23
27
1
J1
23
28
28
30
1
Step 7: Results. Makespan = 30 hours. Machine 2 idle time = 1+1+1=3 hours, which checks with 30−(2+6+7+8+4)=30−27=3. Machine 1 finishes at 28 hours and is idle for the last 2 hours.
Gantt chart for Johnson's rule example: makespan 30 hours with 3 hours of idle time on Machine 2.
Sequencing, idle time, waiting time and due dates#
Poor sequencing leaves machines waiting for work that is stuck elsewhere. Johnson's rule shows how the right order can reduce idle time when jobs pass through several machines.
Every job that waits in a queue adds to work-in-process inventory and lead time. SPT reduces average waiting because many short jobs leave the system quickly.
Services face the same problem with customers instead of jobs. Banks and ticket counters use FCFS. Hospital emergency departments use triage, a priority rule based on how serious each case is. Repair shops often do quick jobs first (SPT). Courier firms sort deliveries by promised time (EDD). Restaurants may give priority to reservations.
Priority rules are guides, not laws. A manager may override a rule for a key customer, a job with scarce material, a large penalty clause or a job that would otherwise block a bottleneck. Good sequencing combines a clear rule with sensible judgement and keeps customers informed when priorities change.
Which sequencing rule minimises average flow time?#
Shortest Processing Time (SPT) always minimises average flow time and average number of jobs in the system on a single machine, as the worked example shows (13.0 days against 15.4 for FCFS).
What does a critical ratio of less than 1 mean?#
It means the time remaining until the due date is less than the work still needed, so the job is behind schedule and should be given priority.
What is the difference between sequencing and scheduling?#
Sequencing fixes the order of jobs; scheduling assigns actual start and finish times to them. The sequence is usually decided first and then converted into a schedule.
It applies when all jobs pass through the same two machines in the same order, processing times are known and fixed, and jobs cannot overtake each other between the machines.
Why might a manager not use SPT even though it gives the lowest flow time?#
SPT ignores due dates and keeps pushing long jobs back, so important long orders can become very late. If on-time delivery matters most, EDD or CR is usually preferred.
Johnson, S. M. (1954) "Optimal two- and three-stage production schedules with setup times included". Naval Research Logistics Quarterly, 1(1), 61–68.
Stevenson, W. J. Operations Management. McGraw-Hill Education.
Heizer, J., Render, B. and Munson, C. Operations Management: Sustainability and Supply Chain Management. Pearson.
Panneerselvam, R. Production and Operations Management. PHI Learning.
Chary, S. N. Production and Operations Management. McGraw-Hill Education (India).
