Project crashing and job Project 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 shortening is a method for shortening

project duration by reducing one or more project duration by reducing one or more critical activities critical activities to a time less than normal to a time less than normal activity time.activity time.

• The process of determining the job order on The process of determining the job order on some machine or in some work center is some 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 shortening Project crashing is a method for shortening the project duration by reducing the time of the project duration by reducing the time of one (or more)of the critical project activities one (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 is This reduction in the normal activity time is referred to as crashing.referred to as crashing.

Conti….Conti….

• Crashing is achieved by devoting more Crashing is achieved by devoting more resources, usually measures in terms of resources, 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 to The objective of project crashing project is to reduce project duration while minimizing the reduce project duration while minimizing the cost of crashing. cost of crashing.

THE GENERAL RELATIONSHIP OF TIME THE GENERAL RELATIONSHIP OF TIME AND COSTAND COST

• Crashing costs increase as project duration Crashing costs increase as project duration decreases.decreases.

• Indirect costs increase as production Indirect costs increase as production duration increases.duration increases.

• Reduce project length as long as crashing Reduce project length as long as crashing costs are less than indirect costs.costs are less than indirect costs.

Conti….Conti….

Conti….Conti….

• The objective of crashing was to reduce the The objective of crashing was to reduce the scheduled completion time to reap the scheduled completion time to reap the results of the projects sooner.results of the projects sooner.

• However, there may be other reasons for However, there may be other reasons for reducing project time.reducing project time.

• There also may be direct financial penalties There 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 more by allocating more reresources to them, sources to them, so that so that the time of one or more critical activities is the time of one or more critical activities is reduced to a time that reduced to a time that is lessis less than the normal than the normal activity activity time.time.

What criteria should it be based on What criteria should it be based on when deciding to crashing critical when 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 =11How? Path: 1-2-3 = 5+6=11 weeksHow? Path: 1-2-3 = 5+6=11 weeks

Path: 1-3 = 5 weeksPath: 1-3 = 5 weeksNow, how many days can we “crash” it?Now, how many days can we “crash” it?

13

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 • Should Should we use up all these 4 weeks?we use up all these 4 weeks?

13

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?

13

25 (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 same If the cost for path 1-2 and path 2-3 is the same

thenthen We can random pick them to crash so that its We can random pick them to crash so that its

completioncompletion Time is 8 weeksTime is 8 weeks

13

25 (1) 6(3)

8(0)

13

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 of Sequencing or priority sequencing: the process of determining which job is started first on some determining 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 job Priority rule: the rule used for btaining a job sequencing.sequencing.

Priority rule evaluation criteriaPriority rule evaluation criteriaTo meet corresponding objectives of To meet corresponding objectives of

scheduling.scheduling.Common standard measures:Common standard measures:

Meeting due date of customers or Meeting due date of customers or downstream operations.downstream operations.

Minimizing flow time (the time a job Minimizing 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 and Minimizing idle time of machines and

workers (Maximizing utilization).workers (Maximizing utilization).

Sequencing rulesSequencing rules

• FCFS FCFS (first come-first served)(first come-first served)

Jobs are processed in the sequence in which Jobs are processed in the sequence in which they entered the shop;they entered the shop;

The simplest and nature way of sequencing The 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 of Jobs 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 processing the 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 of Jobs are sequenced in increasing order of their due dates,their due dates,

The job with earliest due date is first, the The job with earliest due date is first, the one with the next earliest due date is one 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 time such 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 time CR will become smaller as the current time approaches due date, and more priority will given approaches 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 negative For 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 is If more than one jobs are later, higher priority is given to one that has shorter processing time given 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 local A machine center in a job shop for a local fabrication company has five unprocessed fabrication 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 the The jobs are labeled 1, 2, 3, 4, and 5 in the order that they entered the shop. The order that they entered the shop. The respective processing times and due dates respective 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 and Sequence 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 date11 1111 6161

22 2929 4545

33 3131 3131

44 11 3333

55 22 3232

Sequencing RulesSequencing Rules————FCFSFCFSMean Flow time=268/5=53.6Mean Flow time=268/5=53.6Average tardiness=121/5=24.2Average tardiness=121/5=24.2No. 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————SPTSPTMean Flow time=135/5=27.0Mean Flow time=135/5=27.0Average tardiness=43/5=8.6Average tardiness=43/5=8.6No. of tardy jobs=1.No. of tardy jobs=1.

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

Mean Flow time=235/5=47.0Mean Flow time=235/5=47.0Average tardiness=33/5=6.6Average tardiness=33/5=6.6No. of tardy jobs=4.No. of tardy jobs=4.

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=57.8Average tardiness=87/5=17.4Average tardiness=87/5=17.4No. of tardy jobs=4.No. of tardy jobs=4.

Both Jobs 4 and 5 are later, however Job 4 has shorter processing time 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.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, and EDD 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

CONCLUSION

CONCLUSION