Scheduling

Scheduling of OperationsA planning tool for the short term Provides an opportunity to make use of new

information as we approach real time A methodology to fine tune planning and

decision making due to the occurrence of random events

Enables organisations to focus on micro-resources, a single machine, a set of workers and so on. Such a focus is neither possible nor warranted at the medium or long term planning.

Planning Context in the short term How do we assign the jobs to various work

centers? Within each work center, how do we rank

order the jobs? How do we assign other resources such as

skilled workers and material handling devices to the operating system?

How do we react to a breakdown in the system?

How do we measure the performance of the operating system?

SchedulingAlternative Terminologies Loading is defined as a planning methodology using

which the resources in an operating system are assigned with adequate number of jobs during the planning horizon (of say a week)

Scheduling is defined as the process of rank ordering the jobs in front of each resource with a view to maximise some chosen performance measure

Routing is defined as the order in which the resources available in a shop are used by the job for processing

Scheduling Context Number of jobs (n) Number of machines (m) Shop configuration

Flow shop Job Shop Cellular Manufacturing System

Job priorities FCFS, SPT, LPT, EDD, CR

Pure Flow ShopA graphical illustration

Machine 1

Machine 2

Machine 3

Machine m

. . . Job 1Job 2Job n

• In a flow shop, the resources are organised one after the other in the order the jobs are processed

• A pure flow shop is one in which all the jobs visit all the machines in the same order (beginning at machine 1 and ending at machine m)

• In a mixed flow shop, some jobs are allowed to skip machines in between

Job ShopA graphical illustration

Machine 1

Machine 2

Machine 3

Machine 6

Machine 5

Machine 4

Machine 7

. . . Job 1

Job 2

Job 3

In a job shop, machines are not organised in any processing order.

Scheduling Rules A sampleShortest processing time (SPT): Chooses the job with the least processing time among the competing list and schedules it ahead of the othersLongest processing time (LPT): The job with the longest processing time is scheduled ahead of other competing jobsEarliest Due Date (EDD): Establishes priorities on the basis of the due date for the jobs.Critical Ratio (CR): Critical ratio estimates the criticality of the job by computing a simple ratio using processing time information and due date. A smaller value of CR indicates that the job is more critical. Critical Ratio CR =

Remaining timeRemaining Work

=Due Date−Current Date

Remaining Pr oces sin g Time

First Cum First Served (FCFS): Schedules jobs simply in their order of job arrival

• for processing on one machine Suppose these four jobs arrive :

Priority Rules : Example

First Come, First Serve (FCFS)

Job ProcessingDue Date finish(in order time (in hours Time Lateness Slackof arrival) (in hours) from now)

A 2 8 2 0.0 6B 4 9 6 0.0 5C 7 29 13 0.0 22D 1 1.5 14 12.5 0.5E 5 22 19 0.0 17F 3 10 22 12.0 7

Total: 76 24.5Average: 12.67 4.08

• The job with the shortest processing time is processed first

Local Priority Rules

Shortest Operation Time (SOT)

Job Processing Due FinishSequence time Date Time Lateness Slack

D 1 1.5 1 0.0 0.5

A 2 8 3 0.0 6

F 3 10 6 0.0 7B 4 9 10 1.0 5

E 5 22 15 0.0 17

C 7 29 22 0.0 22

• Schedule job with smallest slack first

Local Priority Rules

Slack Time Remaining (STR)

Job Processing Due completionSequence time Date Time Lateness Slack

D 1 1.5 1 0.0 0.5

B 4 9 5 0.0 5

A 2 8 7 0.0 6F 3 10 10 0.0 7

E 5 22 15 0.0 17

C 7 29 22 0.0 22

• Used to schedule n-jobs through 2 sequential machines

© 1995 Corel Corp.

© 1995 Corel Corp.

Saw Drill

Job AJob A

Job BJob B

Job CJob C

Jobs (N = 3)

Oper. Sched.

Johnson’s Rule

All jobs are to be listed, and the time each requires on a machine shown.

Select the job with the shortest activity time. If the shortest time lies with the first machine, the job is scheduled first; if with the second machine, the job is scheduled last.

Once a job is scheduled, eliminate it.

Apply steps 2-3 to the remaining jobs, working toward the center of the sequence.

Oper. Sched.Johnson’s Rule

Johnson’s RuleAn illustration: Example 14.3.

Job No Processing timeMachine 1 Machine 2

1 4 72 6 33 2 34 7 75 8 6

Job 3 Job 1 Job 4 Job 5 Job 2

3 3 1 1 1 1 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 2 2 2 2 2 2

3 3 3 1 1 1 1 1 1 1 4 4 4 4 4 4 4 5 5 5 5 5 5 2 2 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Machine 2

Machine 1

Time units

Oper. Sched.Forward and Backward Scheduling

• Forward Scheduling– due dates determined by internal scheduler

• Backward Scheduling– for externally set due dates

Oper. Sched.

Workforce Scheduling in Services

• Need to know– forecasted staffing levels– specific skills needed during the time-frame– work-hour constraints

• Consecutive days-off requirements– methods exist to provide the staffing schedule

• Complex scheduling situations– computer programs used to find work schedules, given many

constraints

Input – Output ControlA schematic illustration

PendingOrders

CONWIP

Input rate control

Output rate control

CompletedOrders

ExistingLoad