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7/30/2019 7. Scheduling of Operations
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Scheduling of Operations
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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.
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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
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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.
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Loading
Process of assigning work to limited resources
Perform work on most efficient resources
Use assignment method of linear programmingto determine allocation
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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
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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
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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
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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.
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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
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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
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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 }
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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)
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PROCESSING DUE
JOB TIME DATE
A 5 10B 10 15
C 2 5
D 8 12
E 6 8
Example
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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
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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
SEQUENCE TIME TIME TIME DATE TARDINESS
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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
SEQUENCE TIME TIME TIME DATE TARDINESS
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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
SEQUENCE TIME TIME TIME DATE TARDINESS
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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
SEQUENCE TIME TIME TIME DATE TARDINESS
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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
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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
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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.
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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
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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
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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
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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