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SHORT TERM SCHEDULING
Scheduling involve assigning specific dates to
job . It involves the allocation of resources
over time to accomplish tasks . As such , it is
the determination of the order in which jobs
need to be processed and the time to start
each job
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TYPES OF FLOW SYSTEMS
PRODUCT LAYOUT
ASSEMBLY LINES
TRANSFER LINES
PROCESS LAYOUT
FLOW SHOP (jobs go through same sequence)
JOB SHOP (each job has its own route)
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PROCESS LAYOUT FLOW SYSTEMS
PRODUCTS ARE RELEASED TO THE
PRODUCTION SYSTEM IN BATCHES
IF BATCHES VISIT SAME SEQUENCE OF
STATIONS --> FLOW SHOP
IF DIFFERENT BATCHES HAVE THEIR OWN
ROUTE --> JOB SHOP
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http://www.baskent.edu.tr/~kilter 4
Scheduling in Low-Volume Systems
Job-shop scheduling
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FEATURES OF JOB SHOPS
WIDE VARIETY OF PRODUCT REQUIREMENTS
MUST BE DESIGNED FOR MAXIMUM
FLEXIBILITY
INDIVIDUAL STATIONS MUST BE CAPABLE OF
WIDE VARIETY OF TASKS
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FEATURES OF JOB SHOPS
EXPERTISE IS PROCESS RELATED
ORGANIZED BY PROCESSING FUNCTION
UP TO 95% OF JOB TIME SPENT IN NON-PRODUCTIVE ACTIVITY
REMAINING 5% SPLIT BETWEEN LOT SETUP
AND PROCESSING
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KEY QUESTIONS
WHEN TO RELEASE ORDERS TO THE
PRODUCTION FACILITY?
HOW TO SEQUENCE JOBS AT A SINGLE
WORKSTATION?
HOW TO SCHEDULE JOBS THROUGH THE
ENTIRE FACILITY?
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NEED FOR SCHEDULING
For effective utilization of resource ( machine
time , operator time etc)
To determine the realistic delivery time of
spare part / finished goods
Advise the customer in case of delays
Determine bottle neck operations so thatcorrective action could be taken
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Scheduling methods and models
SEQUENCING: PROCESS OF DEFINING THEORDER IN WHICH JOBS ARE TO BE RUN ON A
MACHINE SCHEDULING: PROCESS OF ADDING START AND
FINISH TIME TO THE PROCESS DICTATED BY THESEQUENCE
Gantt Chart : it is a graphical tool whichrepresent a production schedule
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SCHEDULING:
Effective scheduling means faster movement of
goods and services through a facility . This means
greater use of assets and hence greater capacity
per every rupee invested which in turn lower cost Added capacity , faster throughput and the
related facility means better customer service
through faster delivery Good scheduling also contribute to realistic
commitment and hence dependable delivery
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SCHEDULING
Scheduling involves assigning due dates to specific job butmany jobs compete simultaneously for the same resources.Two type of scheduling techniques:
Forward schedulingstart the schedule as soon as jobrequirements are known . It is designed to produceschedule that can be accomplished even if it mean notmeeting the due date.
Backward scheduling begin with the due date , schedulingthe final operation first .Step in the job are then scheduledone at a time in reverse order . By subtracting the leadtime for each job, the start time is obtained . Note thenecessary resources may not be available
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SCHEDULING CRITERIA
The correct scheduling technique depend on
the volume of orders, the nature of the
operation and the overall complexity of the
jobs and the importance placed on each of the
four criteria :
(a) Minimise completion timeThis criterion is
evaluated by determining the averagecompletion time per job
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SCHEDULING CRITERIA
Maximize utilization this is evaluated by
determining the per cent of time that the
facility is utilized
Minimize work in progress inventory the
average number of job in the system.
Minimize customer waiting timethe average
number of late days
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SCHEDULING CRITERIA
A good scheduling approach should be simple
, clear , easily understood , easy to carry out ,
flexible and realistic
Conclusion : The overall objectives of
scheduling is to optimise the use of resources
so that production objectives could be met
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Loading
Loading means the assignment of job to work
or processing centres . Operation managers
assign jobs to work centre so that cost , idle
time or completion times are kept to aminimum . Loading work centres take two
forms : capacity oriented and assigning
specific jobs to work centres
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http://www.baskent.edu.tr/~kilter 16
INPUT OUTPUT CONTROL
Input/Output Control
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Loading Gantt Chart
Gantt charts are visual aids that are useful in
loading It shows the loading and idle times of
work centres
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Gantt chart (load)
Gantt Charts
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Gantt chart
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Assignment
The assignment method involve assigning
tasks or job to resourcesone job to one
machine
Objective minimize cost
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Assignment Method of Linear Programming
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The Assignment Problem
In many business situations, management needs toassign - personnel to jobs, - jobs to machines, -machines to job locations, or - salespersons toterritories.
Consider the situation of assigning n jobs to nmachines.
When a job i (=1,2,....,n) is assigned to machine j
(=1,2, .....n) that incurs a cost Cij. The objective is to assign the jobs to machines at the
least possible total cost.
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The Assignment Problem
This situation is a special case of the
Transportation Model And it is known as the
assignment problem.
Here, jobs represent sources and machines
represent destinations.
The supply available at each source is 1 unit
And demand at each destination is 1 unit.
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The Assignment Problem
The assignment model can be expressed
mathematically as follows:
Xij= 0, if the job j is not assigned to machine i
1, if the job j is assigned to machine i
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The Assignment Problem Example
Ballston Electronics manufactures small electricaldevices.
Products are manufactured on five differentassembly lines (1,2,3,4,5).
When manufacturing is finished, products aretransported from the assembly lines to one of thefive different inspection areas (A,B,C,D,E).
Transporting products from five assembly lines tofive inspection areas requires different times (inminutes)
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The Assignment Problem Example
Under current arrangement, assignment of
inspection areas to the assembly lines are 1 to A, 2
to B, 3 to C, 4 to D, and 5 to E.This arrangement requires 10+7+12+17+19 = 65 man
minutes.
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The Assignment Problem Example
Management would like to determine whethersome other assignment of production lines toinspection areas may result in less cost.
This is a typical assignment problem. n = 5 Andeach assembly line is assigned to each inspectionarea.
It would be easy to solve such a problem when n
is 5, but when n is large all possible alternativesolutions are n!, this becomes a hard problem.
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The Assignment Problem Example
Assignment problem can be either formulated
as a linear programming model, or it can be
formulated as a transportation model.
However, An algorithm known as Hungarian
Methodhas proven to be a quick and efficient
way to solve such problems.
This technique is programmed into many
computer modules
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Hungarian Method Example
Step 1: Select the smallest value in each row.
Subtract this value from each value in that row
Step 2: Do the same for the columns that do not
have any zero value.
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Hungarian Method Example
If not finished, continue
with other columns.
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Hungarian Method Example
Step 3: Assignments are made at zero values.
Therefore, we assign job 1 to machine 1; job 2
to machine 3, and job 3 to machine 2.
Total cost is 5+12+13 = 30.
It is not always possible to obtain a feasible
assignment as in here.
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Hungarian Method Example 2
A feasible assignment is not possible at this
moment.
In such a case, The procedure is to draw a
minimum number oflines through some of
the rows and columns, Such that all zero
values are crossed out.
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Hungarian Method Example 2
The next step is to select the smallest uncrossed out element. This
element is subtracted from every uncrossed out elementand added
to every element at the intersection of two lines.
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Hungarian Method Example 2
We can now easily assign to the zero values.
Solution is to assign (1 to 1), (2 to 3), (3 to 2)
and (4 to 4).
If drawing lines do not provide an easy
solution, then we should perform the task of
drwaing lines one more time.
Actually, we should continue drawing lines
until a feasible assignment is possible.
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http://www.baskent.edu.tr/~kilter 35
Sequencing
Possible priority rules:
First come, first served (FCFS): Jobs are processed in the order in which they arrive ata machine or work center.
Shortest processing time (SPT): Jobs are processed according to processing time at amachine or work center, shortest job first.
Earliest due date (EDD): Jobs are processed according to due date, earliest due datefirst.
Critical ratio (CR): Jobs are processed according to smallest ratio of time remaininguntil due date to processing time remaining.
Slack per operation (S/O): Jobs are processed according to average slack time (time
until due date minus remaining time to process). Compute by dividing slack timeby number of remaining operations, including the current one.
Rush: Emergency or preferred customers first.
LPT : longest processing timethe longer, bigger job are often more important andthey are selected first
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Sequencing
Assumptions of priority rules:
The set of jobs is known; no new jobs arrive after processing begins; and no jobs are
canceled.
Setup time is independent of processing sequence.
Setup time is deterministic.
Processing times are deterministic rather than variable.
There will be no interruptions in processing such as machine breakdowns, accidents,
or worker illness.
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Performance Measures:
Performance Measures:
Job flow time. This is the length of time a job is at a particular workstation or work
center.
Job lateness. This is the length of time the job completion date is expected to exceed
the date the job was due or promised to a customer.
Makespan.Makespan is the total time needed to complete a group of jobs. It is the
length of time between the start of the first job in the group and the completion of
the last job in the group.
Average number of jobs. Jobs that are in a shop are considered to be work-in-process
inventory.Average number of jobs = Total flow time Makespan
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Performance Measures:
Average completion time = Sum of flowtime/number of jobs
Utilization=Total job work(processing) time/
sum of flow time Average number of jobs in the system =Sum of
total flow time /Total job work(processing)time
Average job lateness=Total late days/numberof jobs
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http://www.baskent.edu.tr/~kilter 39
Example
Processing times (including setup times) and due dates for six jobs waiting to be
processed at a work center are given in the following table. Determine the
sequence of jobs, the average flow time, average tardiness, and average number
of jobs at the work center, for each of these rules:
FCFS
SPTEDD
CR
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FCFSThe FCFS sequence is simply A-B-C-D-E-F. The measures of effectiveness are as follows (see
table):1. Average flow time: 1206 = 20 days.
2. Average tardiness: 546 = 9 days.
3. The makespan is 41 days.
Average number of jobs at the work center: 12041 = 2.93.
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http://www.baskent.edu.tr/~kilter 41
SPTUsing the SPT rule, the job sequence is A-C-E-B-D-F (see the following table). The resulting
values for the three measures of effectiveness are1. Average flow time: 1086 = 18 days.
2. Average tardiness: 406 = 6.67 days.
3. Average number of jobs at the work center: 10841 = 2.63.
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http://www.baskent.edu.tr/~kilter 42
EDDUsing earliest due date as the selection criterion, the job sequence is C-A-E-B-D-F. The
measures of effectiveness are as follows (see table):1. Average flow time: 1106 = 18.33 days.
2. Average tardiness: 386 = 6.33 days.
3. Average number of jobs at the work center: 11041 = 2.68.
Using the critical ratio we find
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At day 4 [C completed], the critical ratios are
At day 16 [C and F completed], the critical ratios are
At day 18 [C, F, and A completed], the critical ratios are
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At day 23 [C, F, A, and E completed], the critical ratios are
At day 18 [C, F, and A completed], the critical ratios are
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At day 23 [C, F, A, and E completed], the critical ratios are
The job sequence is C-F-A-E-B-D, and the resulting values for the measures of effectiveness are
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as follows:
1. Average flow time: 1336 = 22.17 days.
2. Average tardiness: 586 = 9.67 days.
3. Average number of jobs at the work center: 13341 = 3.24.
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Performance
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Example
Use the S/O rule to schedule the following jobs. Note that processing time includes
the time remaining for the current and subsequent operations. In addition, you
will need to know the number of operations remaining, including the current one.
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Determine the difference between the due date and the processing time for each
operation. Divide the difference by the number of remaining operations, and rank
them from low to high. This yields the sequence of jobs:
Sequencing Jobs through Two Work
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Sequencing Jobs through Two WorkCenters
For the technique to work, several conditions must be satisfied:
Job time (including setup and processing) must be known and constant for each job at
each work center.
Job times must be independent of the job sequence.
All jobs must follow the same two-step work sequence.
Job priorities cannot be used.
All units in a job must be completed at the first work center before the job moves on
to the second work center.
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Johnson rule
The next step in complexity is the case in which N jobs (where N is2 or more) must go
through two different machines or job centres in the same owner
Determination of the optimum sequence involves these steps:
List the jobs and their times at each work center.
Select the job with the shortest time. If the shortest time is at the first work center,
schedule that job first; if the time is at the second work center, schedule the job
last. Break ties arbitrarily.
Eliminate the job and its time from further consideration.
Repeat steps 2 and 3, working toward the center of the sequence, until all jobs havebeen scheduled.
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Example
A group of six jobs is to be processed through a two-machine flow shop. The first
operation involves cleaning and the second involves painting. Determine a
sequence that will minimize the total completion time for this group of jobs.
Processing times are as follows:
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Select the job with the shortest processing time. It is job D, with a time of two hours.
Since the time is at the first center, schedule job D first. Eliminate job D from further
consideration.
Job B has the next shortest time. Since it is at the second work center, schedule it last
and eliminate job B from further consideration. We now have
The remaining jobs and their times are
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The shortest remaining time is six hours for job E at work center 1. Thus, schedule that
job toward the beginning of the sequence (after job D). Thus,
Job C has the shortest time of the remaining two jobs. Since it is for the first work
center, place it third in the sequence. Finally, assign the remaining job (F) to thefourth position and the result is