Order 1328631: Project Management

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2018-03-11

Project Management Class – 8

Resource Allocation

Learning Outcomes

Ø What is the fundamental trade-off between project cost and project time?

Ø Expediting a project Ø Resource leveling Ø How to allocate limited resources to specific

activities/projects when there are competing demands for the same limited resources?

Ø Case study review

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Expediting a Project

Ø Consider a “bridge construction” project. Ø Digging the drainage ditch takes 10 days with a team of 3

workers.

Ø There are 3 other workers that can be added if they stop their own task “concrete pouring”.

Ø They (i.e., 6 workers) can complete digging in 5 days at the cost of delaying the task “concrete pouring”.

Ø The PM can also rent an excavator machine to get the job done in 2 days.

Ø What is the key trade-off in making the decision?

Purchase and deliver equipment

Construct hospital

Develop information system

Install medical equipment

Train nurses and support staff

Select administration staff

Site selection and survey

Select medical equipment

Prepare final construction plans

Bring utilities to site

Interview applicants for nursing and support staff

Organizing and Site Preparation Physical Facilities and Infrastructure Level 1

Level 0

Level 2

Relocation of a Hospital

Expediting a Project: Example

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Relocation of Hospital Activity List, Duration, and Precedence Relationship

Activity Immediate Predecessors Activity times

(wks) START 0 Organizing and Site Preparation

A. Selecting administrative staff start 12 B. Site selection and survey start 9 C. Select medical equipment A 10 D. Prepare final construction plans B 10 E. Bring utilities to site B 24 F. Interview applicants for nursing and support staff A 10

Physical Facilities and Infrastructure G. Purchase and deliver equipment C 35 H. Construct hospital D 40 I. Develop information system A 15 J. Install medical equipment E, G, H 4 K. Train nurses and support staff F, I, J 6

FINISH K 0

FinishStart

0 9

9 33

9 19 19 59

22 5712 22

59 63

12 27

12 22 63 690 12

The Critical Path takes 69 weeks

Path Time (wks)

A-I-K 33 A-F-K 28 A-C-G-J-K 67 B-D-H-J-K 69 B-E-J-K 43

Developing the Schedule and Finding Critical Path

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Project Crashing

Project Crashing: Shortening (or expediting) some activities within a project to reduce overall project completion time.

Ø Project Costs

ü Direct Costs: Labor, materials, and any other costs directly related to activities

ü Indirect Costs: Administration, depreciation, financial, and other overhead costs that can be avoided by reducing total project time

ü Penalty Costs: If project extends beyond some specific date.

Cost to Crash

Cost to Crash Ø Normal time (NT) is the time necessary to complete an activity

under normal conditions. Ø Normal cost (NC) is the activity cost associated with the normal

time. Ø Crash time (CT) is the shortest possible time to complete an

activity. Ø Crash cost (CC) is the activity cost associated with the crash

time.

𝐂𝐨𝐬𝐭 𝐭𝐨 𝐜𝐫𝐚𝐬𝐡 𝐩𝐞𝐫 𝐩𝐞𝐫𝐢𝐨𝐝 = 𝐂𝐂 − 𝐍𝐂 𝐍𝐓 − 𝐂𝐓

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Which Activities to Crash?

Ø Which activities and for how long should be crashed?

FinishStart

0 9

9 33

9 19 19 59

22 5712 22

59 63

12 27

12 22 63 690 12

Path Time (wks)

A-I-K 33 A-F-K 28 A-C-G-J-K 67 B-D-H-J-K 69 B-E-J-K 43

Which Activities to Crash? Algorithm Ø Which activities and for how long should be crashed? Ø Determining the Minimum Cost Schedule:

1. Determine the project’s critical path(s). 2. Find the activity or activities on the critical path(s) with the lowest cost of

crashing per unit of time. 3. Reduce the time for this activity until…

a. It cannot be further reduced or b. Until another path becomes critical, or c. The increase in direct costs exceeds the savings that result from shortening

the project. 4. Repeat this procedure until the increase in direct costs is larger than the savings

generated by shortening the project.

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Hospital Example: Finding Cost to Crash

DIRECT COST AND TIME DATA FOR THE HOSPITAL PROJECT Activity Normal

Time (NT) (weeks)

Normal Cost (NC)($)

Crash Time (CT)(weeks)

Crash Cost (CC)($)

Maximum Time Reduction (week)

Cost of Crashing per Week ($)

A 12 $12,000 11 $13,000 1 1,000 B 9 50,000 7 64,000 2 7,000 C 10 4,000 5 7,000 5 600 D 10 16,000 8 20,000 2 2,000 E 24 120,000 14 200,000 10 8,000 F 10 10,000 6 16,000 4 1,500 G 35 500,000 25 530,000 10 3,000 H 40 1,200,000 35 1,260,000 5 12,000 I 15 40,000 10 52,500 5 2,500 J 4 10,000 1 13,000 3 1,000 K 6 30,000 5 34,000 1 4,000

Totals $1,992,000 $2,209,500

CC – NC NT – CT

Analyzing Cost – Time Trade-Offs Hospital Example

Ø Project completion time was 69 weeks (Critical Path Analysis)

Ø Suppose that project indirect costs are $8,000 per week

Ø After 65 weeks, the Regional Hospital Board imposes cost of $20,000 per week if the hospital is not fully operational.

Ø Question: What is the saving per week shortening the project?

ü Saving per week (up to week 65) = $28,000

ü Saving per week (beyond week 65) = $8,000

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Analyzing Cost – Time Trade-Offs Hospital Example Ø Determine the minimum-cost schedule for the Hospital project.

Ø Project completion time = 69 weeks Ø Project cost = $2,624,000

Direct = $1,992,000 Indirect = 69($8,000) = $552,000 Penalty = (69 – 65)($20,000) = $80,000

A–I–K 33 weeks A–F–K 28 weeks A–C–G–J–K 67 weeks B–D–H–J–K 69 weeks B–E–J–K 43 weeks

DIRECT COST AND TIME DATA FOR THE HOSPITAL PROJECT Activity Normal

Time (NT) (weeks)

Normal Cost (NC)($)

Crash Time (CT)(weeks)

Crash Cost (CC)($)

Maximum Time Reduction (week)

Cost of Crashing per Week ($)

Totals $1,992,000 $2,209,500

Hospital Example Which Activity To Crash?

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Analyzing Cost – Time Trade-Offs: Hospital Example

STAGE 1 Ø Step 1. The critical path is B–D–H–J–K. Ø Step 2. The cheapest activity to crash per week is J at $1,000. Ø Step 3. Crash activity J by its limit of three weeks because the critical path remains unchanged. The new expected path times are

A–C–G–J–K: 64 weeks B–D–H–J–K: 66 weeks B–E–J–K: 40 weeks

Ø The net savings are 3($28,000) – 3($1,000) = $81,000. Ø The total project costs are now $2,624,000 - $81,000 = $2,543,000.

Path Time (wks)

A-I-K 33 A-F-K 28 A-C-G-J-K 67 B-D-H-J-K 69 B-E-J-K 43

Analyzing Cost – Time Trade-Offs: Hospital Example

Finish

K 6

I 15

F 10

C 10

D 10

H 40

J 1

A 12

B 9

Start G 35

E 24

STAGE 1

The critical path does not change

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DIRECT COST AND TIME DATA FOR THE HOSPITAL PROJECT Activity Normal

Time (NT) (weeks)

Normal Cost (NC)($)

Crash Time (CT)(weeks)

Crash Cost (CC)($)

Maximum Time Reduction (week)

Cost of Crashing per Week ($)

Totals $1,992,000 $2,209,500

Analyzing Cost – Time Trade-Offs: Hospital Example

STAGE 2 Ø Step 1. The critical path is B–D–H–J–K with 66 weeks. Ø Step 2. The cheapest activity to crash per week is now D at $2,000. Ø Step 3. Crash D by two weeks.

Ø The first week of reduction in activity D saves $28,000. Ø Crashing D by a second week saves only $8,000 in indirect costs. Ø Updated path times are

A–C–G–J–K: 64 weeks and B–D–H–J–K: 64 weeks Ø The net savings are $28,000 + $8,000 – 2($2,000) = $32,000. Ø Total project costs are now $2,543,000 – $32,000 = $2,511,000.

Path Time (wks)

A-I-K 33 A-F-K 28 A-C-G-J-K 64 B-D-H-J-K 66 B-E-J-K 40

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Finish

K 6

I 15

F 10

C 10

D 8

H 40

J 1

A 12

B 9

Start G35

E 24

STAGE 2

Analyzing Cost – Time Trade-Offs: Hospital Example

There are two critical paths

STAGE 3 Step 1. The critical paths are B–D–H–J–K and A-C-G-J-K with 64 weeks Step 2. Activities eligible to be crashed:

Finish

K 6

I 15

F 10

C 10

D 8

H 40

J 1

A 12

B 9

Start G35

E 24

A, B $8,000 A, H $13,000 C, B $7,600 C, H $12,600 G, B $10,000 G, H $15,000

K $4,000

Analyzing Cost – Time Trade-Offs: Hospital Example

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Analyzing Cost – Time Trade-Offs: Hospital Example

STAGE 3 Ø Step 1. The critical paths are B-D-H-J-K and A-C-G-J-K with 64 weeks Ø Step 2. Activities eligible to be crashed:

(A, B); (A, H); (C, B); (C, H); (G, B); (G, H) or to crash Activity K ü Candidates are those whose costs of crashing are less than the potential

savings; $8,000 per week.

Ø Step 3. We choose activity K to crash 1 week at $4,000 per week. Updated path times are: A–C–G–J–K: and B–D–H–J–K with 63 weeks

Ø Net savings are $8,000 - $4,000 = $4,000 Ø Total project costs are $2,511,000 – $4,000 = $2,507,000

Finish

K 5

I 15

F 10

C 10

D 8

H 40

J 1

A 12

B 9

Start G 35

E 24

STAGE 3

Analyzing Cost – Time Trade-Offs: Hospital Example

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STAGE 4 Step 1. The critical paths are B–D–H–J–K and A-C-G-J-K with 63 weeks Step 2. Activities eligible to be crashed:

A, B $8,000 A, H $13,000 C, B $7,600 C, H $12,600 G, B $10,000 G, H $15,000

Finish

K 5

I 15

F 10

C 10

D 8

H 40

J 1

A 12

B 9

Start G35

E 24

Analyzing Cost – Time Trade-Offs: Hospital Example

STAGE 4

Ø Step 1. The critical paths are still B-D-H-J-K and A-C-G-J-K with 63 weeks

Ø Step 2. Activities eligible to be crashed: (B,C) @ $7,600 per week.

Ø Step 3. Crash activities B and C by two weeks. Updated path times are

A–C–G–J–K: 61 weeks and B–D–H–J–K: 61 weeks

Ø The net savings are 2($8,000) – 2($7,600) = $800.

Ø Total project costs are now $2,507,000 – $800 = $2,506,200.

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Analyzing Cost-Time Trade-Offs: Hospital Example

Stage Crash Activity Time Redu ction

Resulting Critical Path(s)

Project Duration

Project Direct Costs

Crash Cost

Added

Total Indirect Costs

Total Penalty Costs

Total Project Costs

0 — — B-D-H-J-K 69 1,992.0 — 552.0 80.0 2,624.0

1 J 3 B-D-H-J-K 66 1,992.0 3.0 528.0 20.0 2,543.0

2 D 2 B-D-H-J-K A-C-G-J-K

64 1,995.0 4.0 512.0 0.0 2,511.0

3 K 1 B-D-H-J-K A-C-G-J-K

63 1,999.0 4.0 504.0 0.0 2,507.0

4 B, C 2 B-D-H-J-K A-C-G-J-K

61 2,003.0 15.2 488.0 0.0 2,506.2

Resource Leveling

Ø When the project is large and contains many resource over-allocations, resource leveling must be accomplished:

Ø A technique in which start and finish dates are adjusted based on resource constraints with the goal of balancing demand for resources with the available supply.

Ø Purpose is to create a smoother distribution of resource usage. Ø Resource leveling aims to minimize the period-by-period variations in

resource loading by shifting tasks within their slack allowances.

Ø Leveling is done by delaying or splitting tasks until the resources assigned to them are no longer over-allocated.

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Activity Slack Allowance

FinishStart

0 9

9 33

9 19 19 59

22 5712 22

59 63

12 27

12 22 63 690 12

48 63

53 63

59 63

24 59

19 59

35 59

14 24

9 19

2 14

0 9

63 69

S = 0

S = 2

S = 26

S = 0

S = 36

S = 2

S = 41 S = 0

S = 0 S = 0

S = LF – EF or LS – ES Question: How long each activity can be delayed without delaying the entire project?

Resource Leveling Example

Ø Consider the following project. Ø Find the project completion

time, all the paths from start to end, and critical path.

Ø Find the number of required resources (people) in every week.

Ø Suggest a resource leveling plan to smoothen the resource allocation over project schedule.

Activity Immediate Predecessor

Duration (Week)

# of resources (People)

A - 4 2 B - 4 1 C - 4 2 D A 2 5 E B 3 2 F C 2 2 G D 3 5 H G 5 3

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Resource Leveling Example (Cont.)

S t a r t

FI N IS H

B E

G HD

Path Completion

Time ADGH 14 BE 7 CF 6

Resource Leveling Example (Cont.)

A (2)

D (5) G (5) H (3)

B (1) E (2)

C (2) F (2)

Resources (people) 5 5 5 5 9 9 7 5 5 3 3 3 3 3

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Over-allocated period

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Resource Leveling Example (Cont.)

A (2)

D (5) G (5) H (3)

B (1) E (2)

C (2) F (2)

Resources (people) 5 5 5 5 9 9 7 5 5 3 3 3 3 3

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Over-allocated period

Activity slack

Resource Leveling Example (Cont.)

A (2)

D (5) G (5) H (3)

B (1) E (2)

C (2) F (2)

Resources (people) 5 5 5 5 9 9 7 5 5 3 3 3 3 3

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Activity slack

7 7 5 5 5

Activity slack

5 5 55 5

We can hire 5 workers at the beginning without laying off and hiring over time!

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Allocating Scare Resources to Several Projects

Ø When the allocating scarce resources is extended to where several projects are being carried out concurrently, the size and complexity of the problem increase

Ø With several projects, we can link them together with pseudoactivities

Ø Pseudoactivities have duration but require no resources

Ø The use of pseudoactivities allows a set of projects to be linked and dealt with as though it were a single project

§ The individual projects are interrelated by specifying predecessor/successor relationships

§ They appear to be parts of one project

Multiple Projects Connected with Pseudoactivities

Ø Project manager faces the problem of choosing between different outcomes that result from different priority rules

Ø Must also deal with different arrangements and durations of pseudoactivities (i.e., leveling rule)

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Criteria of Priority Rules

There are many measurable criteria to help select a priority rule 1. Schedule slippage

§ Amount project or set of projects delayed by application of a leveling rule § The PM must trade-off penalty costs or displeasure of clients against the

cost of adding resources 2. Resource utilization: extent to which resources are over or underworked 3. In-process inventory: amount of unfinished work in the system Ø The minimum slack rule is probably the best overall priority rule according to research. Ø It gives the best combination of minimum project slippage, minimum resource idle-time, and minimum in-process inventory.

Problems with Traditional Project Management

Ø When planning for a project, estimates for task durations are required. Ø To increase the probability and high-confidence that the task completing on

time we consider additional safety time beyond the work content time required to be embedded within the task duration.

Ø The more safety in a task the more there is a tendency to behave in the following ways: § Not starting the task until the last moment (Student Syndrome) § Delaying (or pacing) completion of the task (Parkinson’s Law)

Ø As a result, the safety which was included at the planning stage is wasted and tasks over-run.

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Goldratt’s Critical Chain

Ø Critical Chain Project Management was developed by Eli Goldratt in response to many projects being dogged by poor performance manifested in § Longer than expected durations § Frequently missed deadlines § Increased costs in excess of budget § Substantially less deliverables than originally promised

Ø Goldratt’s focus in the Critical Chain is on a single project with multiple demands on a scarce resource

Ø The logic extends to the multiproject case without alteration

Goldratt’s Critical Chain (Cont.)

Ø Consider the three AOA network diagrams.

Ø In scenario 1, there is only 1 path.

Ø In scenario 2, completion of BCDE depends on three activities.

Ø In scenario 3, there are two completely independent paths each consisting of 5 tasks.

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How Long?

Ø Each task takes 10 days

Ø What is the completion time for each project?

§ All three would have the same duration of 50 days

Ø Simple project with five tasks takes the same time as complex one with 11 tasks!

Part of Problem

Ø Part of the problem is the assumption that the activity times are known with certainty

Ø Assume all activities are normally distributed § Mean of 10 § Standard deviation of three

Ø Each is simulated 200 times

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Analysis

Ø This example clearly demonstrates how the commonly made assumption of known activity times in practice can lead to quite unrealistic project deadlines

Ø The results would have been even more dramatic had the activities required some common resources

Ø Similarly, the results would have been more dramatic and realistic had a nonsymmetrical distribution been used to model the activity times

Multitasking

Ø Multitasking is assigning team members to multiple projects and having them allocate their time across these projects

Ø There is typically a penalty or cost associated with switching from working on one project to another

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Multitasking (Cont.)

Ø Alternative Gantt Charts for Projects A and B

Switching from project to project is likely to extend activity times. Eliminating such switching costs further increases the benefits associated with the Gantt chart shown in Figure (b).

Resolving These Problems

Ø Goldratt suggests that the key to resolving this is to schedule the start of new projects based on the availability of bottleneck resources

Ø He further suggests that time buffers be created between the bottleneck resource and the resources that feed it

Ø He also suggests reducing the amount of safety time added to individual tasks and then adding some fraction of the safety time reduced back into the system as safety buffer for the entire project

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The Critical Chain

Ø Another limitation is the dependency between resources and tasks is often ignored

Ø Using traditional approaches, A1-C1 is the critical path

Ø What if A1 and A2 are not independent

Ø Then path A1-C1 increases to 22 days, or path A2-B1 increases to 18 days

If A1 is done first è A2-B1 will be finished in 7 + 5 + 6 = 18 If A2 is done first è A1-C1 will be finished in 5 + 7 + 10 = 22

Addressing Problem

Ø Need to consider both precedence relationships and resource dependencies

Ø Goldratt proposes thinking in terms of the longest chain of consecutively dependent tasks where such dependencies can arise

§ Referred to as critical chain

Ø There are two potential sources that can delay the project § Delay in the tasks that make up the critical chain § Delay in activity feeding the critical chain that results in delay of the

critical chain

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Project and Feeder Buffers

Project Buffer: A project buffer is inserted at the end of the project network between the last task and the completion date.

§ Any delays on the longest chain of dependent tasks will consume some of the buffer but will leave the completion date unchanged and so protect the project.

Feeding Buffers: delays on paths of tasks feeding into the longest chain can impact the project by delaying a subsequent task on the Critical Chain.

§ To protect against this, feeding buffers are inserted between the last task on a feeding path and the Critical Chain.

§ The feeding buffer is typically recommended to be half the size of the safety time taken out of the feeding path.

Project and Feeder Buffers

Project buffer

Feeding buffer