Project crashing and job sequencing

Project crashing and jobProject crashing and job
sequencingsequencing
Presented by :Presented by :
Payal Buha (014)Payal Buha (014)
Ibtisam Sorthia (048)Ibtisam Sorthia (048)
Khushbu Dhorajiya (018)Khushbu Dhorajiya (018)
Krupali Suhagiya (050)Krupali Suhagiya (050)
Chandrika Makwana (032)Chandrika Makwana (032)
Submitted to :Submitted to : Mr. Vishal SondagraMr. Vishal Sondagra

INTRODUCTIONINTRODUCTION
• Project crashingProject crashing is a method for shorteningis a method for shortening
project duration by reducing one or moreproject duration by reducing one or more
critical activitiescritical activities to a time less than normalto a time less than normal
activity time.activity time.
• The process of determining the job order onThe process of determining the job order on
some machine or in some work center issome machine or in some work center is
known as sequencing or priority sequencing.known as sequencing or priority sequencing.

Project crashingProject crashing
• Project crashing is a method for shorteningProject crashing is a method for shortening
the project duration by reducing the time ofthe project duration by reducing the time of
one (or more)of the critical project activitiesone (or more)of the critical project activities
to less than its normal activity time.to less than its normal activity time.
• This reduction in the normal activity time isThis reduction in the normal activity time is
referred to as crashing.referred to as crashing.

Conti….Conti….
• Crashing is achieved by devoting moreCrashing is achieved by devoting more
resources, usually measures in terms ofresources, usually measures in terms of
dollars, to the activities to be crashed.dollars, to the activities to be crashed.
• The objective of project crashing project is toThe objective of project crashing project is to
reduce project duration while minimizing thereduce project duration while minimizing the
cost of crashing.cost of crashing.

THE GENERAL RELATIONSHIP OF TIMETHE GENERAL RELATIONSHIP OF TIME
AND COSTAND COST
• Crashing costs increase as project durationCrashing costs increase as project duration
decreases.decreases.
• Indirect costs increase as productionIndirect costs increase as production
duration increases.duration increases.
• Reduce project length as long as crashingReduce project length as long as crashing
costs are less than indirect costs.costs are less than indirect costs.

Conti….Conti….
• The objective of crashing was to reduce theThe objective of crashing was to reduce the
scheduled completion time to reap thescheduled completion time to reap the
results of the projects sooner.results of the projects sooner.
• However, there may be other reasons forHowever, there may be other reasons for
reducing project time.reducing project time.
• There also may be direct financial penaltiesThere also may be direct financial penalties
for not completing a project on time.for not completing a project on time.

Trade-off conceptTrade-off concept
Here, we adopt the “Trade-off” concept.Here, we adopt the “Trade-off” concept.
• WWe attempt to “crash” some “e attempt to “crash” some “criticalcritical” events” events
by allocating moreby allocating more reresources to them,sources to them, so thatso that
the time of one or more critical activities isthe time of one or more critical activities is
reduced to a time thatreduced to a time that is lessis less than the normalthan the normal
activityactivity time.time.

What criteria should it be based onWhat criteria should it be based on
when deciding to crashing criticalwhen deciding to crashing critical
times?times?
The critical path is 1-2-3, the completion time =11The critical path is 1-2-3, the completion time =11
How? Path: 1-2-3 = 5+6=11 weeksHow? Path: 1-2-3 = 5+6=11 weeks
Path: 1-3 = 5 weeksPath: 1-3 = 5 weeks
Now, how many days can we “crash” it?Now, how many days can we “crash” it?
1
3
25 (1) 6(3)

Conti…Conti…
• The maximum time that can be crashed for:The maximum time that can be crashed for:
Path 1-2-3 = 1 + 3 = 4Path 1-2-3 = 1 + 3 = 4
Path 1-3 = 0Path 1-3 = 0
• ShouldShould we use up all these 4 weeks?we use up all these 4 weeks?
1
3
25 (1) 6(3)
5(0)

• If we used all 4 days, then path 1-2-3 has
(5-1) + (6-3) = 7 completion weeks
Now, we need to check if the completion time for path 1-3
has lesser than 7 weeks (why?)
Now, path 1-3 has (5-0) = 5 weeks
Since path 1-3 still shorter than 7 weeks, we used up all 4
crashed weeks
• Question: What if path 1-3 has, say 8 weeks completion
time?
1
3
2
5 (1)
6(3)
5(0)
4(0) 3(0)

• Now, we cannot use all 4 days (Why?)
Because path 1-2-3 will not be critical path anymore
path 1-3 would now has longest hour to finish
• Rule: When a path is a critical path, it will not stay as
a critical path
• So, we can only reduce the path 1-2-3 completion
time to the same time
• as path 1-3. (HOW?)
1 3
25 (1) 6(3)
8(0)

• We can only reduce total time for path 1-2-3 =We can only reduce total time for path 1-2-3 =
path 1-path 1-33,,
that is 8 weeksthat is 8 weeks
If the cost for path 1-2 and path 2-3 is the sameIf the cost for path 1-2 and path 2-3 is the same
thenthen
We can random pick them to crash so that itsWe can random pick them to crash so that its
completioncompletion
Time is 8 weeksTime is 8 weeks
1
3
25 (1) 6(3)
8(0)

1
3
25 (1)5 (1) 6(3)6(3)
8(0)8(0)
1
2
3
5 (1)5 (1)
6(3)6(3)
8(0)8(0)
OR
4(0)4(0) 4(1)4(1)
3(0)3(0)

JOB SEQUENCINGJOB SEQUENCING
 Sequencing or priority sequencing: the process ofSequencing or priority sequencing: the process of
determining which job is started first on somedetermining which job is started first on some
machines or work center by priority rule.machines or work center by priority rule.
 Priority rule: the rule used for btaining a jobPriority rule: the rule used for btaining a job
sequencing.sequencing.

Priority rule evaluation criteriaPriority rule evaluation criteria
To meet corresponding objectives ofTo meet corresponding objectives of
scheduling.scheduling.
Common standard measures:Common standard measures:
 Meeting due date of customers orMeeting due date of customers or
downstream operations.downstream operations.
 Minimizing flow time (the time a jobMinimizing flow time (the time a job
spends in the shop flow).spends in the shop flow).
 Minimizing WIP.Minimizing WIP.
 Minimizing idle time of machines andMinimizing idle time of machines and
workers (Maximizing utilization).workers (Maximizing utilization).

Sequencing rulesSequencing rules
• FCFSFCFS (first come-first served)(first come-first served)
 Jobs are processed in the sequence in whichJobs are processed in the sequence in which
they entered the shop;they entered the shop;
 The simplest and nature way of sequencingThe simplest and nature way of sequencing
as in queuing of a bankas in queuing of a bank

Conti….Conti….
• SPT (shortest processing time)SPT (shortest processing time)
 Jobs are sequenced in increasing order ofJobs are sequenced in increasing order of
their processing time,their processing time,
 The job with shortest processing time is first,The job with shortest processing time is first,
the one with the next shortest processingthe one with the next shortest processing
time is second, and so on,time is second, and so on,

Conti…Conti…
• EDD (earliest due date)EDD (earliest due date)
 Jobs are sequenced in increasing order ofJobs are sequenced in increasing order of
their due dates,their due dates,
 The job with earliest due date is first, theThe job with earliest due date is first, the
one with the next earliest due date isone with the next earliest due date is
second, and so on,second, and so on,

Conti…Conti…
• CR (Critical ratio)
 Critical ratio is the remaining time until due date
divided by processing time;
 Scheduling the job with the smallest CR next,
• CRi = Remaining time of Job I /
Processing time
of Job i
• = (Due date of Job i-current time) /
Processing time
of Job i

Conti…Conti…
 CR provides the balance between SPT and EDD,CR provides the balance between SPT and EDD,
such that the task with shorter remaining timesuch that the task with shorter remaining time
and longer processing time takes higher priority,and longer processing time takes higher priority,
 CR will become smaller as the current timeCR will become smaller as the current time
approaches due date, and more priority will givenapproaches due date, and more priority will given
to one with longer processing time,to one with longer processing time,
 For a job, if the numerator of its CR is negativeFor a job, if the numerator of its CR is negative
( the job has been already later), it is naturally( the job has been already later), it is naturally
scheduled next,scheduled next,
 If more than one jobs are later, higher priority isIf more than one jobs are later, higher priority is
given to one that has shorter processing timegiven to one that has shorter processing time
(SPT).(SPT).

Example of n jobs one machineExample of n jobs one machine
 A machine center in a job shop for a localA machine center in a job shop for a local
fabrication company has five unprocessedfabrication company has five unprocessed
jobs remaining at a particular point in time.jobs remaining at a particular point in time.
The jobs are labeled 1, 2, 3, 4, and 5 in theThe jobs are labeled 1, 2, 3, 4, and 5 in the
order that they entered the shop. Theorder that they entered the shop. The
respective processing times and due datesrespective processing times and due dates
are given in the table below.are given in the table below.
 Sequence the 5 jobs by above 4 rules andSequence the 5 jobs by above 4 rules and
compare results based on mean flow time,compare results based on mean flow time,
average tardiness, and number of tardy jobsaverage tardiness, and number of tardy jobs

Conti…Conti…
Job numberJob number Processing timeProcessing time Due dateDue date
11 1111 6161
22 2929 4545
33 3131 3131
44 11 3333
55 22 3232

Sequencing RulesSequencing Rules————FCFSFCFS
Mean Flow time=268/5=53.6Mean Flow time=268/5=53.6
Average tardiness=121/5=24.2Average tardiness=121/5=24.2
No. of tardy jobs=3.No. of tardy jobs=3.
1 11 61 0
2 40 45 0
3 71 31 40
4 72 33 39
5 74 32 42
Total 268 121

Sequencing RulesSequencing Rules————SPTSPT
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
Total 135 43

Sequencing RulesSequencing Rules————EDDEDD
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
Total 235 33

Sequencing RulesSequencing Rules————CRCR
Current time should be reset after scheduling one jobCurrent time should be reset after scheduling one job

Sequencing RulesSequencing Rules————CRCR Mean Flow time=289/5=57.8Mean Flow time=289/5=57.8
Both Jobs 4 and 5 are later, however Job 4 has shorter processing timeBoth Jobs 4 and 5 are later, however Job 4 has shorter processing time
and thus is scheduled first; Finally, job 1 is scheduled last.and thus is scheduled first; Finally, job 1 is scheduled last.

Sequencing RulesSequencing Rules————SummarySummary
DiscussionsDiscussions
 SPT results in smallest mean flow time;SPT results in smallest mean flow time;
 EDD yields the minimum maximum tardiness (42, 43, 18, andEDD yields the minimum maximum tardiness (42, 43, 18, and
31 for the 4 different rules);31 for the 4 different rules);
 Always true? Yes!Always true? Yes!

Example by videoExample by video
Sequencing n jobs on 1 machine - Example 4.mp4

Project crashing and job sequencing

Project crashing and job sequencing

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Project crashing and job sequencing