7. Scheduling of Operations

7/30/2019 7. Scheduling of Operations

1/26

Scheduling of Operations


2/26

What is scheduling?

Last stage of planning before production occurs Planning and control issues pertaining to short-term

(ranging from a day/shift to utmost a week or two)

In short-term several questions need to beanswered. How can the jobs be assigned to various work centers? Within each work center, how can the jobs be rank ordered? How can other resources such as skilled workers and

special gadgets be assigned to the operating system?

A collective framework to address these questions isreferred to as scheduling of operations.


3/26

Objectives in Scheduling

Meet customer due dates

Minimize job lateness

Minimize completion time

Minimize overtime

Maximize machine or labor utilization

Minimize idle time

Minimize work-in-process inventory


4/26

Terminologies

Loading: Resources in an operating system are assigned with

adequate number of jobs during the planning horizon. Ensures thatthe resources in an operating system are utilized in the best possibleway.

Routing: The technological order in which resources available in ashop are used by the job for processing.

Scheduling & Sequencing: Process of rank ordering the jobs

according to some chosen performance measures for each resource.

Dispatching: Administrative process of authorizing processing of jobsby resources in the operating system, as identified by the schedulingsystem, in the form of shop order or information communicatedelectronically.

Expediting: Administrative process of reviewing the progress of thejob in the operating system and ensuring that it travels throughvarious stages of the process as indicated in routing, without harmingthe performance measures. If there are deviations and delays, it callsfor pushing the job forward through the system.


5/26

Loading

Process of assigning work to limited resources

Perform work on most efficient resources

Use assignment method of linear programmingto determine allocation


6/26

Assignment Method

1. Perform row reductions1. subtract minimum value in each row from all other row values

2. Perform column reductions1. subtract minimum value in each column from all other column

values

3. Cross out all zeros in matrix1. use minimum number of horizontal and vertical lines

4. If number of lines equals number of rows in matrix thenoptimum solution has been found. Make assignments wherezeros appear

5. Else modify matrix1. subtract minimum uncrossed value from all uncrossed values2. add it to all cells where two lines intersect3. other values in matrix remain unchanged

6. Repeat steps 3 through 5 until optimum solution is reached


7/26

Assignment Method: Example

Row reduction Column reduction Cover all zeros

5 0 1 5 3 0 1 4 3 0 1 4

4 0 2 4 2 0 2 3 2 0 2 32 1 0 1 0 1 0 0 0 1 0 0

5 1 0 6 3 1 0 5 3 1 0 5

Number lines number of rows so modify matrix

Initial PROJECT

Matrix 1 2 3 4

Bryan 10 5 6 10

Kari 6 2 4 6

Noah 7 6 5 6Chris 9 5 4 10


8/26

Assignment Method: Example (cont.)

Modify matrix Cover all zeros1 0 1 2 1 0 1 20 0 2 1 0 0 2 10 3 2 0 0 3 2 01 1 0 3 1 1 0 3

Number of lines = number of rows so at optimal solution

1 2 3 4

Bryan 1 0 1 2

Kari 0 0 2 1Noah 0 3 2 0

Chris 1 1 0 3

PROJECT

1 2 3 4

Bryan 10 5 6 10

Kari 6 2 4 6Noah 7 6 5 6

Chris 9 5 4 10

PROJECT

Project Cost = 5 + 6 + 6 + 4 = 21


9/26

Scheduling Context

The following parameters adequately describethe scheduling problem. Number of machines/resources Number of jobs Shop configuration: the manner in which machines

are organized on the shop floor and the flow patternof the jobs utilizing the machines. Flow shop resources are organized one after other in the

order the jobs are processes. If there are n jobs, there aren

! ways in which one can draw up alternative schedule. Job shop machines are not organized in processing

order, rather similar type of resources is grouped together.If there are n jobs andmmachines, there are (n!)mways inwhich one can draw up alternative schedule.


10/26

Scheduling Rules

SPT - shortest processing time

LPT - longest processing time

EDD - Earliest Due Date

CR - critical ratio Considers both processing time and due date information.

CR estimates the criticality of the job as

CR = Remaining time / Remaining work= (Due date Current date) / Remaining processing time

Smaller the value of CR indicates the job is more critical.

If CR < 1, indicates the available time is not sufficient and the job is alreadyrunning late and if CR > 1, indicates some slack is available for the job.

FCFS - first-come, first-served

LCFS - last come, first served RAN Random order

CUSTPR - highest customer priority

SETUP - similar required setups


11/26

Job

No

Processing

time

Order

of

arrival Due by

1 12 1 23

2 9 2 24

3 22 3 30

4 11 4 20

CR Order

1.917 3

2.667 4

1.364 1

1.818 2

SPT LPT EDD FCFS

3 2 2 1

1 4 3 2

4 1 4 3

2 3 1 4

Random No RAN

0.8403 3

0.9930 4

0.6439 2

0.4418 1

Current time = 0

EXAMPLE


12/26

Performance criterion

Completion-based measures

Assessment of the processing time is done.

Frequently used measures:

Flow Time the elapsed time between releasing a job into the

shop and the time of completion of processing of the job. It isequal to the sum of processing time of all operations of the joband other non-productive time including waiting and moving time.

Release time of the job be Ri, Completion time of the job be Ci, thenFlow time Fi = Ri Ci

Make span the time taken to complete all the jobs released into

the shop for processing. It is the completion time of the last job inthe shop.

Make span (maximum completion time) Cmax = max { Ci }


13/26

Due date-based measures

Efficacy of the scheduling rule is evaluated with reference to thedue date of the jobs.

Measures:

Lateness: The difference between completion time and due date.

If the due date is denoted as Di, then lateness Li = Ci Di

Tardiness: Captures information of only those jobs that are late.Negative values of lateness are considered to be 0.

Tardiness Ti = max(0, Li)

Number of tardy jobs nT

Utilization-based measures Based on actual inventory build up in the shop or utilization of the shop

resources.

Measures include the mean number of jobs waiting, mean number offinished jobs,

Simulation models are typically used such scheduling problems.

Performance criterion (cont)


14/26

PROCESSING DUE

JOB TIME DATE

A 5 10B 10 15

C 2 5

D 8 12

E 6 8

Example


15/26

Sequencing Rules: FCFS

A 0 5 5 10 0

B 5 10 15 15 0

C 15 2 17 5 12

D 17 8 25 12 13

E 25 6 31 8 23

FCFS START PROCESSING COMPLETION DUE

SEQUENCE TIME TIME TIME DATE TARDINESS


16/26

Sequencing Rules: EDD

C 0 2 2 5 0E 2 6 8 8 0

A 8 5 13 10 3

D 13 8 21 12 9

B 21 10 31 15 16

EDD START PROCESSING COMPLETION DUE



17/26

A(10-0)

5 = 5B(15-0) - 10 = 5

C(5-0) 2 = 3

D(12-0) 8 = 4

E(8-0) 6 = 2

Sequencing Rules: SLACK

E 0 6 6 8 0

C 6 2 8 5 3D 8 8 16 12 4

A 16 5 21 10 11

B 21 10 31 15 16

SLACK START PROCESSING COMPLETION DUE



18/26

A(10)/5 = 2.00

B(15)/10 = 1.50

C (5)/2 = 2.50D(12)/8 = 1.50

E (8)/6 = 1.33

Sequencing Rules: CR

E 0 6 6 8 0

D 6 8 14 12 2

B 14 10 24 15 9

A 24 5 29 10 19

C 29 2 31 5 26

CR START PROCESSING COMPLETION DUE



19/26

Sequencing Rules: SPT

C 0 2 2 5 0

A 2 5 7 10 0

E 7 6 13 8 5

D 13 8 21 12 9

B 21 10 31 15 16

SPT START PROCESSING COMPLETION DUE



20/26

Sequencing Rules: Summary

FCFS 18.60 9.6 3 23DDATE 15.00 5.6 3 16

SLACK 16.40 6.8 4 16

CR 20.80 11.2 4 26

SPT 14.80 6.0 3 16

AVERAGE AVERAGE NO. OF MAXIMUM

RULE COMPLETION TIME TARDINESS JOBS TARDY TARDINESS


21/26

A manufacturer is in the process of assessing the

usefulness of SPT and EDD rules for the purpose

of scheduling four jobs on a machine. The table

below gives the related information. Compute

relevant performance measures and comment.

Job No Process time Due by

1 4 6

2 7 9

3 2 194 8 17


22/26

A flow process with two machines and nnumber of jobs to be scheduled.

Johnsons Rule List time required to process each job at each machine.

Set up a one-dimensional matrix to represent desired sequencewith number of slots equal to number of jobs.

Select smallest processing time at either machine.

If that time is on machine 1, put the job as near to beginning ofsequence as possible.

If smallest time occurs on machine 2, put the job as near to theend of the sequence as possible.

Remove job from list. Repeat until all slots in matrix are filled and all jobs are sequenced.

The resulting sequence of the jobs is the best schedule tominimize the make span of the jobs.


23/26

EXAMPLE: Using Johnsons Rule

JOB PROCESS 1 PROCESS 2

A 6 8B 11 6

C 7 3

D 9 7

E 5 10

CE A BD


24/26

Johnsons Rule (cont.)

A B CDE

E A D B C Process 1(sanding)

5 11 20 31 38

E A D B C Process 2(painting)

5 15 23 30 37 41

Idle time

Completion time = 41

Idle time = 5+1+1+3=10


25/26

Guidelines for Selecting a Sequencing Rule

1. SPT most useful when shop is highly congested2. Use SLACK for periods of normal activity3. Use EDD when only small tardiness values can be

tolerated4. Use LPT if subcontracting is anticipated5. Use FCFS when operating at low-capacity levels6. Do not use SPT to sequence jobs that have to be

assembled with other jobs at a later date


26/26

1 2 3 4 5 6 8 9 10 11 12 Days

1

2

3

Todays Date

Job 32B

Job 23C

Job 11C Job 12A

Fac

ility

Key: Planned activity

Completed activity

Behind schedule

Ahead of schedule

On schedule

Gantt Chart

Documents

7. Scheduling of Operations