chapter 4 : scheduling
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CHAPTER 4 :CHAPTER 4 :SCHEDULINGSCHEDULING
Presented by:
HAMKA BIN TAIPMOHD SAFUAN BIN ANUARNUR AMIRA BINTI KHAMISPUVENDRAN A/L SUNDARAM
OUTLINE
4.1 Introduction4.2 Job Shop Scheduling Terminology4.3 Sequencing Rules
4.3.1 FCFS4.3.2 SPT4.3.3 EDD4.3.4 CR
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4.14.1 INTRODUCTIONINTRODUCTION
What is Scheduling ? Last stage of planning before production occurs Specifies when labor, equipment, facilities are
needed to produce a product or provide a service
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Operations SchedulingOperations Scheduling
Scheduling is an allocation decision Scheduling decisions allocate resources over relatively short
time periods: a few months, weeks, or hours. The results are time allocations of production resources to
different jobs All the orders can be completed while all production
resources are utilized with their loads being balance
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Production ManagementProduction Management
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Objectives of Operations SchedulingObjectives of Operations Scheduling
1. Meet customer due dates2. Minimize job lateness3. Minimize completion time4. Minimize idle time5. Minimize WIP inventory6. Minimize the average flow time through the system7. Reduce setup cost
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Typical Scheduling and Control FunctionsTypical Scheduling and Control Functions
The following functions must be performed in scheduling and controlling a shop floor:
Allocating orders, equipment, and personnel to work centers or other specified location-short term capacity planning
Determining the sequence of order performance Initiating performance of the scheduled work, commonly termed the
dispatching of jobs Shop-floor control, involving
Reviewing the status and controlling the progress of orders as they are being worked onExpediting the late and critical orders
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Scheduling OperationsScheduling Operations
Operations schedules are short-term plans designed to implement the master production schedule. Operations scheduling focuses on how best to use
existing capacity. Often, several jobs must be processed at one or
more workstations. Typically, a variety of tasks can be performed at each workstation.
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Cont… Scheduling OperationsCont… Scheduling Operations
1. Scheduling in High-Volume System – To obtain a smooth rate of flow of goods or customers through the system in order to get a high utilization of labor and equipment.
Often referred as flow systems; scheduling refer to flow shop scheduling
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Cont… Scheduling OperationsCont… Scheduling Operations
2. Scheduling in Intermediate-Volume System – Typically produce standard outputs. The run sizes are relatively small compared to flow shop.
3. Scheduling in Low Volume System – Job shop scheduling
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Low-Volume SystemLow-Volume System
Low-volume, job shop (batch) operations, are designed for flexibility.
Products are made to order and orders usually differ considerably in terms of processing requirements, materials needed, processing time and sequence and setup.
Each product or service may have its own routing (scheduling is much more difficult)
Many service operations have similar issues – how to distribute the workload among work centers and what job processing sequence to use
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Job ShopJob Shop
Turnning CenterDrilling Center
Milling CenterGrinding Center
A job shop is organized by machines which are grouped according to their functions.
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SequencingSequencing JobsJobs
Operations schedules are short-term plans designed to implement
the sales and operations plan
An operation with divergent flows is often called a job shop
Low-to medium-volume production
Utilizes job or batch processes
No similar pattern of movements of jobs from one machine to
the next
Difficult to schedule because of the variability in job routings
and the continual introduction of new jobs to be processed
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Sh
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Dep
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Raw
Mat
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Legend:Batch of partsWorkstation
Diagram of a Manufacturing Job Shop Process
Job Shop SequencingJob Shop Sequencing
Not all jobs are assumed to require exactly the same number of operations, and some jobs may require multiple operations on a single machine.
Each job may have a different required sequencing of operations.
Operations scheduling of shop floor usually means job shop scheduling;
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An operation with line flow is often called a flow shop Medium- to high-volume production Utilizes line or continuous flow processes All jobs follow the same paths from one machine to the
next Tasks are easier to schedule because the jobs have a
common flow pattern through the system
Cont…. SequencingCont…. Sequencing JobsJobs
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Flow Shop SequencingFlow Shop Sequencing
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Method of Shop Floor Planning and Control for Job ShopMethod of Shop Floor Planning and Control for Job Shop
1. Gantt Chart Used for variety of purposes related to loading and
Scheduling The purpose is to organize and visually display the
actual or intended use of resources in a time framework.
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2. Loading Refer to the assignments of jobs to processing (work) centers. Loading decisions involve assigning specific jobs to work
centers and to various machines in the work centers.
3. Scheduling Forward scheduling and Backward scheduling
Cont……Method of Shop Floor Planning and Control for Cont……Method of Shop Floor Planning and Control for Job ShopJob Shop
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Cont……Method of Shop Floor Planning and Control Cont……Method of Shop Floor Planning and Control for Job Shopfor Job Shop
1. Gantt Charts Developed in the early 1900’s by Henry Gantt 1.1 Load charts
- Illustrates the workload relative to the capacity of a resource - Shows job schedule by employee
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1.2 Progress charts: - Illustrates the planned schedule compared to actual performance - Brackets show when activity is scheduled to be finished. Note that design and pilot run both finished late and feedback has not started yet.
Cont……Method of Shop Floor Planning and Control Cont……Method of Shop Floor Planning and Control for Job Shopfor Job Shop
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2. Loading
2.1 Infinite loading: Ignores capacity constraints,
but helps identify bottlenecks in a proposed schedule to enable proactive management
2.2 Finite loading: Allows only as much work to
be assigned as can be done with available capacity – but doesn’t prepare for inevitable slippage
Cont……Method of Shop Floor Planning and Control for Cont……Method of Shop Floor Planning and Control for Job ShopJob Shop
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3. Scheduling
3.1 Forward Scheduling Scheduling ahead from a point in time If the issue is “How long will it take to complete this job?”
3.2 Backward Scheduling Scheduling backward from a due date If the issue is “When the latest the job can be started and still be
completed by the due date?”
Cont……Method of Shop Floor Planning and Control Cont……Method of Shop Floor Planning and Control for Job Shopfor Job Shop
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Start processing when order is received regardless of due date
Schedule the job’s last activity so it is finished right before the due date
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4.24.2 Job Shop Scheduling TerminologyJob Shop Scheduling Terminology
1. Parallel processing versus sequential processing Sequencing Processing: the m machines are distinguishable, and
different operations are performed by different machines. Parallel processing: The machines are identical, and any job can be
processed on any machine.
M1 M2
M3 M4
Job A
Job B
M1, M2, M3, and M4 are different; Job A has 2 operations which should be
processed on different Machines: M1and M2;
Job B has 3 operations which should be processed on different Machines: M3, M2 and M4;
M1 M2
M3 M4
Job A
Job B
M1, M2, M3, and M4 are identical;
Jobs A and B can be processed on any one of the 4 machines
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2 Flow time The flow time of job i is the time that elapses from the initiation of
that job on the first machine to the completion of job i. The mean flow time, which is a common measure of system
performance, is the arithmetic average of the flow times for all n jobs
Job 1 Job 2
Job 1
Job 3
Job 2 Job 3
Machines
M1
M2
TimeF1: FT of Job 1
F2: FT of Job 2
F3: FT of Job 3
Mean Flow Time=(F1+F2+F3)/3
Cont… Job Shop Scheduling TerminologyCont… Job Shop Scheduling Terminology
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3. Make-span The make-span is the time required to complete a group of jobs (all n
jobs). Minimizing the make-span is a common objective in multiple-machine
sequencing problems.
Job 1 Job 2
Job 1
Job 3
Job 2 Job 3
Machines
M1
M2
TimeF1: FT of Job 1
F2: FT of Job 2
F3: FT of Job 3
Make-span of the 3 jobs
Cont… Job Shop Scheduling TerminologyCont… Job Shop Scheduling Terminology
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4. Tardiness and lateness Tardiness is the positive difference between the completion time and the
due date of a job. Lateness refers to the difference between the job completion time and its
due date and differs from tardiness in that lateness can be either positive or negative.
If lateness is positive, it is tardiness; when it is negative, it is earliness
Due date of Job i
Completion time of Job i
Tardiness of Job iDue date
of Job i
Completion time of Job i
When the completion of Job is earlier than due date, the tardiness is 0
Lateness>0---Tardiness
Lateness<0---Earliness
Cont… Job Shop Scheduling TerminologyCont… Job Shop Scheduling Terminology
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4.34.3 Sequencing RulesSequencing Rules
FCFS (first come-first served) Jobs are processed in the sequence in which they entered the shop; The simplest and nature way of sequencing as in queuing of a bank
SPT (shortest processing time) Jobs are sequenced in increasing order of their processing time; The job with shortest processing time is first, the one with the next
shortest processing time is second, and so on;
EDD (earliest due date)
Jobs are sequenced in increasing order of their due dates;
The job with earliest due date is first, the one with the next earliest due date is second, and so on;
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CR (Critical ratio) Critical ratio is the remaining time until due date divided by processing
time; Scheduling the job with the smallest CR next;
Processing time of Job i
Due date of Job iCurrent time Remaining time of Job i
CRi=Remaining time of Job i/Processing time of Job i
=(Due date of Job i-current time)/Processing time of Job i
CR provides the balance between SPT and EDD, such that the task with shorter remaining time and longer processing time takes higher priority; CR will become smaller as the current time approaches due date, and more priority will given to one with longer processing time; For a job, if the numerator of its CR is negative ( the job has been already later), it is naturally scheduled next; If more than one jobs are later, higher priority is given to one that has shorter processing time (SPT).
Cont… Sequencing RulesCont… Sequencing Rules
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Example 5.1 A machine center in a job shop for a local fabrication company has five unprocessed jobs remaining at a particular point in time. The jobs are labeled 1, 2, 3, 4, and 5 in the order that they entered the shop. The respective processing times and due dates are given in the table below. Sequence the 5 jobs by above 4 rules and compare results based on mean flow time, average tardiness, and number of tardy jobs
Job number Processing Time Due Date
1
2
3
4
5
11
29
31
1
2
61
45
31
33
32
Cont… Sequencing RulesCont… Sequencing Rules
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1. First Come First Serve (FCFS)
Job number Processing Time Due Date
1
2
3
4
5
11
29
31
1
2
61
45
31
33
32
Job Completion Time Due Date Tardiness
1 11 61 0
2 40 45 0
3 71 31 40
4 72 33 39
5 74 32 42
Totals 268 121
Mean Flow time=268/5=53.6Average tardiness=121/5=24.2
No. of tardy jobs=3.
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2. 2. Shortest Processing Time (SPT) Processing Time (SPT)
Job number Processing Time Due Date
1
2
3
4
5
11
29
31
1
2
61
45
31
33
32
Job Processing Time Completion Time Due Date Tardiness
4 1 1 33 0
5 2 3 32 0
1 11 14 61 0
2 29 43 45 0
3 31 74 31 43
Totals 135 43
Mean Flow time=135/5=27.0Average tardiness=43/5=8.6
No. of tardy jobs=1.
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3. Earliest Due Date (EDD)
Job number Processing Time Due Date
1
2
3
4
5
11
29
31
1
2
61
45
31
33
32
Job Processing Time Completion Time Due Date Tardiness
3 31 31 31 0
5 2 33 32 1
4 1 34 33 1
2 29 63 45 18
1 11 74 61 13
Totals 235 33
Mean Flow time=235/5=47.0Average tardiness=33/5=6.6
No. of tardy jobs=4.
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4. Critical Ratio (CR)
Current time: t=0
Job number Processing Time Due Date Critical Ratio
12345
11293112
6145313332
61/11(5.545)45/29(1.552)31/31(1.000)33/1 (33.00)32/2 (16.00)
Current time: t=31
Job number Processing Time Due Date-Current Time Critical Ratio
1245
112912
30 14 2 1
30/11(2.727)14/29(0.483) 2/1 (2.000)1/2 (0.500)
Current time should be reset after scheduling one job
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Cont … 4. Critical Ratio (CR)
Current time=60
Job number Processing Time Due Date-Current Time
Critical Ratio
1
4
5
11
1
2
1
-27
-28
1/11(0.0909)
-27/1<0
-28/2<0
Job number Processing Time Completion Time Tardiness
3
2
4
5
1
31
29
1
2
11
31
60
61
63
74
0
15
28
31
13Totals 289 87
Mean Flow time=289/5=57.8Average tardiness=87/5=17.4
No. of tardy jobs=4.
Both Jobs 4 and 5 are later, however Job 4 has shorter processing time and thus is scheduled first; Finally, job 1 is scheduled last.
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Sequencing RulesSequencing Rules————SummarySummary
Rule Mean Flow Time Average Tardiness
Number of
Tardy Jobs
FCFS
SPT
EDD
CR
53.6
27.0
47.0
57.8
24.2
8.6
6.6
17.4
3
1
4
4
Discussions SPT results in smallest mean flow time EDD have the minimum tardiness (42, 43, 18, and 31 for the 4 different
rules)
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Exercise
There are five sheet metal jobs are waiting to be assigned at a company work centre.Their work (processing) time and due dates are given below. Then, determine the sequence of processing according to (FCFS,SPT,EDD and CR)
Figure 1: Jobs are assigned as below:
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Job Processing Time Due Date
A 6 8
B 2 6
C 8 18
D 3 15
E 9 23
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