Production Scheduling in Operations Management

Why pro­duc­tion sched­ul­ing is impor­tant#

Take a print­ing press that has received three orders: wed­ding cards, school note­books and busi­ness fly­ers. The man­ager must decide which order goes first, which machine prints what, when bind­ing starts, when pack­ing starts and which order must be deliv­ered first. Get­ting this right means every order leaves on time using the same machines and staff. Get­ting it wrong means rush work, over­time and unhappy cus­tomers. The whole time-based arrange­ment is pro­duc­tion sched­ul­ing.

Good sched­ul­ing:

• ensures timely deliv­ery and bet­ter cus­tomer ser­vice;
• improves machine and labour util­i­sa­tion;
• reduces idle time, wait­ing and con­ges­tion;
• low­ers work-in-progress inven­tory and over­time cost;
• gives man­agers a clear stan­dard to com­pare actual progress against.

Plan­ning, rout­ing, sequenc­ing, sched­ul­ing and dis­patch­ing#

These terms appear together in pro­duc­tion plan­ning and con­trol, and stu­dents often con­fuse them.

Plan­ning is broader and looks fur­ther ahead; sched­ul­ing con­verts the plan into a detailed time table. Sched­ul­ing pre­pares the timetable, and dis­patch­ing puts it into action by releas­ing orders, mate­ri­als and instruc­tions.

Objec­tives of pro­duc­tion sched­ul­ing#

Com­plete work on time#

Meet promised deliv­ery dates and reduce the num­ber of late jobs.

Use machines effi­ciently#

Keep costly equip­ment busy with­out over­load­ing it.

Reduce wait­ing time#

Shorten the time jobs spend queu­ing between oper­a­tions.

Reduce pro­duc­tion delays#

Coor­di­nate mate­ri­als, tools and labour so that work is not held up.

Improve cus­tomer ser­vice#

Give reli­able deliv­ery promises and respond to changes quickly.

Bal­ance the work­load#

Spread work evenly across machines, depart­ments and shifts.

Reduce pro­duc­tion cost#

Cut over­time, idle time, set-up changes and work-in-progress.

Fea­tures of a good sched­ule#

• Real­is­tic: based on actual capac­ity and stan­dard times.
• Clear: easy for super­vi­sors and work­ers to under­stand.
• Flex­i­ble: able to absorb rush orders and break­downs.
• Coor­di­nated: in step with pur­chas­ing, stores, main­te­nance and dis­patch.
• Pri­or­ity-based: urgent and impor­tant jobs are iden­ti­fied.

Types of pro­duc­tion sched­ul­ing#

Mas­ter sched­ul­ing#

The mas­ter pro­duc­tion sched­ule (MPS) states which end prod­ucts will be made, in what quan­tity and in which week. It links the aggre­gate plan with detailed shop-floor sched­ules and mate­r­ial require­ments plan­ning.

Detailed sched­ul­ing#

Detailed or oper­a­tion sched­ul­ing fixes the start and fin­ish time of each oper­a­tion on each machine, usu­ally for the next few days or shifts.

For­ward sched­ul­ing#

Work is sched­uled from today onward, plac­ing each oper­a­tion as early as pos­si­ble. It tells the man­ager the ear­li­est pos­si­ble com­ple­tion date. It is com­mon in job shops where orders must be done as soon as pos­si­ble, but it can build up inven­tory if work fin­ishes well before the due date.

Back­ward sched­ul­ing#

Work is sched­uled back­wards from the due date, plac­ing each oper­a­tion as late as pos­si­ble while still fin­ish­ing on time. It keeps inven­tory low and is used in assem­bly and MRP sys­tems, but it leaves lit­tle slack for dis­rup­tions.

Load­ing: finite and infi­nite#

Before sequenc­ing, jobs are assigned to work cen­tres, which is called load­ing. Infi­nite load­ing assigns work with­out regard to capac­ity and then shows the over­loads; finite load­ing never lets the load exceed capac­ity. Load­ing is often dis­played on a load chart, a type of Gantt chart.

Sched­ul­ing in dif­fer­ent pro­duc­tion sys­tems#

Fac­tors affect­ing pro­duc­tion sched­ul­ing#

• Nature of the prod­uct – sim­ple or com­plex, stan­dard or cus­tom.
• Pro­duc­tion vol­ume – high vol­umes need rate-based sched­ules; low vol­umes need job-by-job sched­ules.
• Machine capac­ity – the avail­able hours of each work cen­tre.
• Labour avail­abil­ity – num­ber, skills, shifts and absen­teeism.
• Mate­r­ial avail­abil­ity – whether inputs will arrive in time.
• Deliv­ery dead­lines – promised dates and penal­ties for delay.
• Main­te­nance and break­downs – planned down­time and break­down risk.
• Set-up time – time needed to change a machine from one job to another.

Sequenc­ing rules#

When sev­eral jobs are wait­ing at one machine, a pri­or­ity rule decides the order. The com­monly used rules are:

• First Come, First Served (FCFS) – jobs are done in order of arrival. Sim­ple and seen as fair, but urgent or short jobs may wait behind long ones.
• Short­est Pro­cess­ing Time (SPT) – the short­est job goes first. It min­imises aver­age flow time and aver­age num­ber of jobs in the sys­tem, but long jobs may keep wait­ing.
• Ear­li­est Due Date (EDD) – the job due soon­est goes first. It tends to reduce late­ness, though short, easy jobs may be delayed.
• Longest Pro­cess­ing Time (LPT) – the longest job goes first; used occa­sion­ally when big jobs must be started early.
• Crit­i­cal Ratio (CR) – com­pares time remain­ing with work remain­ing.

The mea­sures used to com­pare rules are:

$$\displaystyle \text{Average flow time} = \frac{\text{Sum of completion times}}{\text{Number of jobs}}$$

$$\text{Tardiness of a job} = \max(0,\ \text{Completion time} - \text{Due date})$$

$$\displaystyle \text{Average jobs in system} = \frac{\text{Sum of completion times}}{\text{Total processing time}}$$

Worked exam­ple: com­par­ing FCFS, SPT and EDD#

Sup­pose a print shop has five jobs wait­ing at one machine at the start of day 0, listed in order of arrival.

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

FCFS (A, B, C, D, E): com­ple­tion times are 6, 8, 16, 19 and 28. Tar­di­ness: A is 0, B is $8 - 6 = 2$, C is 0, D is $19 - 15 = 4$, E is $28 - 23 = 5$.

• Aver­age flow time $\displaystyle = \frac{6 + 8 + 16 + 19 + 28}{5} = \frac{77}{5} = 15.4$ days
• Aver­age tar­di­ness $\displaystyle = \frac{0 + 2 + 0 + 4 + 5}{5} = \frac{11}{5} = 2.2$ days; 3 jobs late
• Aver­age jobs in sys­tem $\displaystyle = \frac{77}{28} = 2.75$

SPT (B, D, A, C, E): com­ple­tion times are 2, 5, 11, 19 and 28. Tar­di­ness: B 0, D 0, A $11 - 8 = 3$, C $19 - 18 = 1$, E $28 - 23 = 5$.

• Aver­age flow time $\displaystyle = \frac{2 + 5 + 11 + 19 + 28}{5} = \frac{65}{5} = 13.0$ days
• Aver­age tar­di­ness $\displaystyle = \frac{9}{5} = 1.8$ days; 3 jobs late
• Aver­age jobs in sys­tem $\displaystyle = \frac{65}{28} = 2.32$

EDD (B, A, D, C, E): com­ple­tion times are 2, 8, 11, 19 and 28. Tar­di­ness: B 0, A 0, D 0, C 1, E 5.

• Aver­age flow time $\displaystyle = \frac{2 + 8 + 11 + 19 + 28}{5} = \frac{68}{5} = 13.6$ days
• Aver­age tar­di­ness $\displaystyle = \frac{6}{5} = 1.2$ days; 2 jobs late
• Aver­age jobs in sys­tem $\displaystyle = \frac{68}{28} = 2.43$

SPT gives the low­est aver­age flow time, while EDD gives the low­est tar­di­ness and the fewest late jobs. FCFS is worst on both mea­sures here. The choice of rule depends on what the shop val­ues most.

Worked exam­ple: crit­i­cal ratio#

The crit­i­cal ratio is:

$$\displaystyle CR = \frac{\text{Due date} - \text{Today's date}}{\text{Work days remaining}}$$

A CR below 1 means the job is behind sched­ule, equal to 1 means on sched­ule and above 1 means ahead. Sup­pose today is day 12 and three jobs remain:

Job Y is already behind sched­ule, so it is done first, then Z, then X.

John­son's rule for two machines#

When every job must pass through two machines in the same order, John­son's rule gives the sequence that min­imises makespan, the total time to fin­ish all jobs. The steps are:

1. List the time of each job on both machines.
2. Find the short­est time remain­ing in the list.
3. If it is on Machine 1, place that job as early as pos­si­ble; if it is on Machine 2, place it as late as pos­si­ble.
4. Remove the job and repeat until all jobs are placed. Break ties arbi­trar­ily.

Worked exam­ple: print­ing and bind­ing#

Sup­pose five print orders must be printed (Machine 1) and then bound (Machine 2). Times are in hours.

1. Short­est time is 1 (J2 on M1): J2 goes first. Sequence: J2, _, _, _, _.
2. Next short­est is 2 (J1 on M2): J1 goes last. Sequence: J2, _, _, _, J1.
3. Next is 3 (J4 on M1): J4 goes sec­ond. Sequence: J2, J4, _, _, J1.
4. Next is 4 (J5 on M2): J5 goes in the last free slot from the end. Sequence: J2, J4, _, J5, J1.
5. J3 fills the remain­ing slot. Final sequence: J2, J4, J3, J5, J1.

Now com­pute start and fin­ish times. A job starts on M2 only when it has left M1 and M2 is free.

The makespan is 30 hours. Machine 2 works $6 + 8 + 7 + 4 + 2 = 27$ hours, so its idle time is $30 - 27 = 3$ hours.

Gantt charts in sched­ul­ing#

A Gantt chart is a bar chart with time on the hor­i­zon­tal axis and machines, work­ers or jobs on the ver­ti­cal axis. Each bar shows when an activ­ity starts and fin­ishes. It is easy to under­stand, shows progress clearly, helps com­pare planned with actual work and is widely used for machine and labour sched­ul­ing. Two com­mon forms are the load chart, which shows how busy each work cen­tre is, and the sched­ule chart, which tracks each job against time.

Sched­ul­ing in ser­vice organ­i­sa­tions#

Sched­ul­ing is not lim­ited to fac­to­ries:

• Hos­pi­tal – doc­tor tim­ings, oper­a­tion the­atre use and patient appoint­ments.
• Col­lege – class timetable, fac­ulty sched­ule and exam­i­na­tion sched­ule.
• Bank – staff shifts and cus­tomer ser­vice coun­ters.
• Restau­rant – chef duty tim­ings, table reser­va­tions and order flow.

Ser­vices can­not store their out­put, so they sched­ule staff to match demand and use appoint­ments and reser­va­tions to shape the demand itself.

Sched­ul­ing and pro­duc­tiv­ity#

Sched­ul­ing raises pro­duc­tiv­ity by reduc­ing idle time, improv­ing machine use, reduc­ing wait­ing and avoid­ing con­ges­tion. When jobs start and fin­ish at the right time, out­put rises with­out adding resources.

Prob­lems in pro­duc­tion sched­ul­ing#

A poor sched­ule leads to missed dead­lines, idle machines along­side over­loaded ones, high work-in-progress, over­time and frus­trated staff. Even a good sched­ule can be upset by rush orders, machine break­downs, power fail­ures, worker absence, mate­r­ial short­ages, qual­ity rejec­tions and trans­port delays. Sched­ules must there­fore be flex­i­ble and reviewed often; a rigid sched­ule fails when con­di­tions change.

Qual­i­ties of a good sched­uler#

• Under­stands the pro­duc­tion process and machine capac­i­ties.
• Knows job pri­or­i­ties and cus­tomer com­mit­ments.
• Com­mu­ni­cates clearly and responds quickly to changes.
• Coor­di­nates with pro­duc­tion, stores, main­te­nance and dis­patch.

Key terms#

Pro­duc­tion sched­ul­ing

Fix­ing the start and fin­ish time and order of pro­duc­tion activ­i­ties.

Sequenc­ing

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

Dis­patch­ing

Releas­ing orders and instruc­tions so that sched­uled work actu­ally starts.

For­ward sched­ul­ing

Sched­ul­ing from the present date onward to find the ear­li­est com­ple­tion.

Back­ward sched­ul­ing

Sched­ul­ing back­wards from the due date so that work fin­ishes just in time.

Flow time

The time a job spends in the shop, from its arrival until its com­ple­tion.

Crit­i­cal ratio

Time remain­ing until the due date divided by work time remain­ing.

Makespan

The total time needed to com­plete a group of jobs.

Gantt chart

A bar chart that shows activ­i­ties against time, used for load­ing and sched­ul­ing.

Com­mon ques­tions#

Which sequenc­ing rule is best?#

No sin­gle rule is best for every mea­sure. SPT always min­imises aver­age flow time on a sin­gle machine, while EDD min­imises the max­i­mum late­ness. Man­agers choose accord­ing to their main objec­tive.

What does a crit­i­cal ratio of 0.8 mean?#

The job has less time left than the work it still needs, so it is behind sched­ule and should get pri­or­ity.

When is John­son's rule used?#

When a set of jobs must pass through two machines or work cen­tres in the same order and the aim is to min­imise the total com­ple­tion time.

How is for­ward sched­ul­ing dif­fer­ent from back­ward sched­ul­ing?#

For­ward sched­ul­ing starts from today and finds the ear­li­est fin­ish; back­ward sched­ul­ing starts from the due date and finds the lat­est start. Back­ward sched­ul­ing keeps inven­tory lower but leaves less slack.

What is the dif­fer­ence between sched­ul­ing and dis­patch­ing?#

Sched­ul­ing pre­pares the time plan, for exam­ple Job A starts at 10 AM. Dis­patch­ing tells the worker or depart­ment to begin Job A at 10 AM.

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. Chary, S. N. Pro­duc­tion and Oper­a­tions Man­age­ment. McGraw-Hill Edu­ca­tion (India).
5. Pan­neer­sel­vam, R. Pro­duc­tion and Oper­a­tions Man­age­ment. PHI Learn­ing.

Related read­ing#

• What is Plant Lay­out in Oper­a­tions Man­age­ment?
• Pro­duc­tion Plan­ning and Con­trol (PPC) in Oper­a­tions Man­age­ment
• Sup­ply Chain Man­age­ment in Oper­a­tions Man­age­ment