Sequencing in Operations management

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.

Objec­tives of sequenc­ing

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.

Sequenc­ing ver­sus rout­ing

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.

Sequenc­ing ver­sus sched­ul­ing

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.

Sequenc­ing in dif­fer­ent pro­duc­tion sys­tems

Job pro­duc­tion and job shops

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.

Batch pro­duc­tion

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.

Mass pro­duc­tion

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.

Fac­tors affect­ing sequenc­ing deci­sions

• Pro­cess­ing time of each job
• Due dates promised to cus­tomers
• Order of arrival
• Impor­tance of the cus­tomer or the order value
• Set-up and changeover times
• Avail­abil­ity of machines, work­ers and mate­ri­als
• Num­ber of machines each job must pass through
• Man­age­ment objec­tives such as speed, fair­ness or on-time deliv­ery

Com­mon sequenc­ing (pri­or­ity) rules

First Come, First Served (FCFS)

Jobs are processed in the order they arrive. A bank queue works this way.

• Advan­tages: sim­ple, fair and easy for cus­tomers to accept.
• Dis­ad­van­tages: ignores job length and due dates, so a long job can hold up many short urgent ones; usu­ally gives poor aver­age flow time.

Short­est Pro­cess­ing Time (SPT)

The job with the short­est pro­cess­ing time is done first. A pho­to­copy shop that fin­ishes a two-page job before a 300-page job is using SPT.

• Advan­tages: min­imises aver­age flow time, aver­age num­ber of jobs in the sys­tem and work-in-process; many jobs are fin­ished quickly.
• Dis­ad­van­tages: long jobs keep get­ting pushed back and may become very late; due dates are ignored.

Ear­li­est Due Date (EDD)

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.

Longest Pro­cess­ing Time (LPT)

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.

Crit­i­cal Ratio (CR)

The crit­i­cal ratio com­pares the time left until the due date with the pro­cess­ing time still required:

$$\displaystyle CR = \frac{\text{Due date} - \text{Today's date}}{\text{Work (processing) time remaining}}$$

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 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.

Mea­sur­ing sequence per­for­mance

• Flow time of a job = its com­ple­tion time, mea­sured from when all jobs are avail­able (time zero).
• Aver­age flow time = total flow time divided by the num­ber of jobs.
• Tar­di­ness of a job = com­ple­tion time minus due date, if pos­i­tive; oth­er­wise zero.
• Aver­age num­ber of jobs in the sys­tem = total flow time divided by total pro­cess­ing time.

Worked exam­ple 1: four rules on one machine

Sup­pose a print­ing unit has five jobs wait­ing at the start of day 0, in the order they arrived. Times are in days.

Total pro­cess­ing time is $6 + 2 + 8 + 3 + 9 = 28$ days.

FCFS: sequence A, B, C, D, E

Aver­age flow time $= 77/5 = 15.4$ days; aver­age tar­di­ness $= 11/5 = 2.2$ days; 3 jobs late; aver­age jobs in sys­tem $= 77/28 = 2.75$.

SPT: sequence B, D, A, C, E

Aver­age flow time $= 65/5 = 13.0$ days; aver­age tar­di­ness $= 9/5 = 1.8$ days; 3 jobs late; aver­age jobs in sys­tem $= 65/28 = 2.32$.

EDD: sequence B, A, D, C, E

Aver­age flow time $= 68/5 = 13.6$ days; aver­age tar­di­ness $= 6/5 = 1.2$ days; only 2 jobs late; aver­age jobs in sys­tem $= 68/28 = 2.43$.

Dynamic crit­i­cal ratio

At day 0: $CR_A = 8/6 = 1.33$, $CR_B = 6/2 = 3.00$, $CR_C = 18/8 = 2.25$, $CR_D = 15/3 = 5.00$, $CR_E = 23/9 = 2.56$. The low­est is A, so A runs first and fin­ishes on day 6.

At day 6: $CR_B = (6-6)/2 = 0$, $CR_C = 12/8 = 1.50$, $CR_D = 9/3 = 3.00$, $CR_E = 17/9 = 1.89$. B is low­est and fin­ishes on day 8.

At day 8: $CR_C = 10/8 = 1.25$, $CR_D = 7/3 = 2.33$, $CR_E = 15/9 = 1.67$. C runs and fin­ishes on day 16.

At day 16: $CR_D = (15-16)/3 = -0.33$, $CR_E = 7/9 = 0.78$. 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.

Com­par­i­son

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.

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.

1. List the pro­cess­ing time of every job on both machines.
2. Find the small­est time in the whole list.
3. 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.
4. Remove that job from the list.
5. Repeat until all jobs are placed. Ties may be bro­ken arbi­trar­ily.

Worked exam­ple 2: John­son's rule

Sup­pose a work­shop must cut (M1) and then pol­ish (M2) five jobs. Times are in hours.

Step 1: Small­est time is 1 (J2 on M1), so J2 goes first: J2 _ _ _ _.

Step 2: Next small­est is 2 (J1 on M2), so J1 goes last: J2 _ _ _ J1.

Step 3: Next small­est is 3 (J4 on M1), so J4 goes in the ear­li­est free slot: J2 J4 _ _ J1.

Step 4: Next small­est is 4 (J5 on M2), so J5 goes in the lat­est free slot: J2 J4 _ J5 J1.

Step 5: J3 fills the remain­ing slot. Opti­mal sequence: J2, J4, J3, J5, J1.

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).

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.

Sequenc­ing, idle time, wait­ing time and due dates

Idle time

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.

Wait­ing time

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.

Due dates

EDD and CR focus on meet­ing promises to cus­tomers. Miss­ing due dates can mean penal­ties, lost good­will and lost future orders.

Advan­tages of proper sequenc­ing and prob­lems of poor sequenc­ing

Sequenc­ing in ser­vices

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.

Sequenc­ing and man­age­r­ial judge­ment

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.

Key terms

Sequenc­ing

Decid­ing the order in which wait­ing jobs are processed at a work cen­tre.

Pri­or­ity rule

A rule, such as FCFS, SPT or EDD, used to choose the next job.

Flow time

The time a job spends in the sys­tem from avail­abil­ity to com­ple­tion.

Tar­di­ness

The amount by which a job's com­ple­tion is later than its due date; zero if on time.

Makespan

The total time needed to com­plete all jobs in a set.

Crit­i­cal ratio

Time remain­ing until the due date divided by work time remain­ing; low­est goes first.

John­son's rule

A method that min­imises makespan for jobs pass­ing through two machines in the same order.

Rout­ing

Decid­ing the path and order of oper­a­tions a job fol­lows.

Gantt chart

A bar chart show­ing jobs against time on each machine.

Com­mon ques­tions

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.

When can John­son's rule be used?

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.

Ref­er­ences

1. John­son, S. M. (1954) "Opti­mal two- and three-stage pro­duc­tion sched­ules with setup times included". Naval Research Logis­tics Quar­terly, 1(1), 61–68.
2. Steven­son, W. J. Oper­a­tions Man­age­ment. McGraw-Hill Edu­ca­tion.
3. Heizer, J., Ren­der, B. and Mun­son, C. Oper­a­tions Man­age­ment: Sus­tain­abil­ity and Sup­ply Chain Man­age­ment. Pear­son.
4. Pan­neer­sel­vam, R. Pro­duc­tion and Oper­a­tions Man­age­ment. PHI Learn­ing.
5. Chary, S. N. Pro­duc­tion and Oper­a­tions Man­age­ment. McGraw-Hill Edu­ca­tion (India).

Related read­ing

• Main­te­nance Man­age­ment in Oper­a­tions man­age­ment
• Make or Buy Deci­sion in Oper­a­tions man­age­ment
• What is Oper­a­tions Man­age­ment