Sequencing Problems

Abu Bashar

Sequencing???

• It is the selection of an appropriate order in which a number of jobs (Operations) can be assigned to to a finite number of service facilities (Machines or equipments) so as to optimize the outputs in terms of time, cost or profit.

Common Sequencing Rules• FCFS. First Come First Served. Jobs

processed in the order they come to the shop.• SPT. Shortest Processing Time. Jobs with the

shortest processing time are scheduled first. • EDD. Earliest Due Date. Jobs are sequenced

according to their due dates.• CR. Critical Ratio. Compute the ratio of

processing time of the job and remaining time until the due date. Schedule the job with the largest CR value next.

Two Work Center Sequencing

• Johnson’s Rule: technique for minimizing completion time for a group of jobs to be processed on two machines or at two work centers.

• Minimizes total idle time

• Several conditions must be satisfied

Johnson’s Rule Conditions

• Job time must be known and constant

• Job times must be independent of sequence

• Jobs must follow same two-step sequence

• Job priorities cannot be used

• All units must be completed at the first work center before moving to the second

Sequencing Problems

• One machine, many jobs

• Two machines, many jobs

• Three machines, many jobs

• Many machines, many jobs

One machine, many jobs

• Total time is independent of sequence

• Sequencing minimizes idle time

Two machines, many jobs

• All Jobs follow same sequence – Johnson’s Rule

• Jobs have different sequence – Jackson’s Rule

• Johnson’s 3 machine rule

Johnson’s Rule• Johnson’s rule: A procedure that minimizes idle time

when scheduling a group of jobs on two workstations.• Step 1. Find the shortest processing time among the

jobs not yet scheduled. If two or more jobs are tied, choose one job arbitrarily.

• Step 2. If the shortest processing time is on workstation 1, schedule the corresponding job as early as possible. If the shortest processing time is on workstation 2, schedule the corresponding job as late as possible.

• Step 3. Eliminate the last job scheduled from further consideration. Repeat steps 1 and 2 until all jobs have been scheduled.

Eliminate M3 from consideration. The next shortest time is M2 at Workstation 1, so schedule M2 first.

Eliminate M5 from consideration. The next shortest time is M1 at workstation #1, so schedule M1 next.Eliminate M1 and the only job remaining to be scheduled is M4.

Example 16.5 Johnson’s RuleJohnson’s Rule at the at the Morris Machine Co.Morris Machine Co.

Time (hr)Time (hr)

MotorMotor Workstation 1Workstation 1 Workstation 2Workstation 2

M1M1 1212 2222M2M2 44 55M3M3 55 33M4M4 1515 1616M5M5 1010 88

Sequence = Sequence = M1M1M2M2 M3M3M4M4 M5M5

Shortest time is 3 hours at workstation 2, so schedule job M3 last.

Eliminate M2 from consideration. The next shortest time is M5 at workstation #2, so schedule M5 next to last.

Workstation

M2 (4)

M1 (12)

M4 (15)

M5 (10)

M3 (5)

Idle—available for further work

0 5 10 15 20 25 30Day

35 40 45 50 55 60 65

Idle2 M2 (5)

M1 (22)

M4 (16)

M5 (8)

M3 (3)Idle

1

Gantt Chart for the Morris Machine Company Repair Schedule

The schedule minimizes the idle time of workstation 2 and gives the fastest repair time for all five motors.

No other sequence will produce a lower makespan.

Example 16.5 Johnson’s RuleJohnson’s Rule at the at the Morris Machine Co.Morris Machine Co.

Problem

Job 1 2 3 4 5 6 7 8

A 4 5 8 10 6 5 10 6

B 8 10 2 4 5 7 6 6

Example

Johnson’s 3 Machine Rule• Domination – Largest on B is not greater

than smallest on A or C. Domination guarantees optimality

• Conversion – Convert into a 2 M/C problem as M1 = A + B, M2 = B + C

• Find optimal sequence for this 2 machine problem

• Schedule on 3 machines based on the sequence above

Job 1 2 3 4 5 6A 8 6 10 7 9 7B 7 4 6 5 5 4

C 13 12 11 12 13 10

M1 15 10 16 12 14 11

M2 20 16 17 17 18 14

Classwork

j 1 2 3 4 5

tj1 8 11 7 6 9

tj2 3 2 5 7 11

tj3 6 5 7 13 10

Classwork

Thank You Very Much