PM592 Week 4 Lecture

7/11/13 Proj Cost & Schedule Control

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Week 4: Advanced Scheduling and Crashing - Lecture

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Scheduling, Schedule Crashing, and Resource Allocation and Leveling

Introduction | CPM and Time Cost Trade Off (Crashing) | CPM Crashing ... Demonstration Problem | PERT Network Processes |CCPM Network Processes | Resource Allocation and Leveling | Resource Leveling ... Demonstration Problem

Introduction

The network process that is the basis for developing project schedules was introduced last week. We will now present some additionalvariations on the basic network process that will allow us to improve on the scheduling process. We will look at the concepts of CriticalPath Method (CPM) with schedule crashing based upon a time/cost trade off, statistical evaluation of project schedules, program evaluationand review technique (PERT) for projects with risky schedules, and the theory of constraints concept with Critical Chain Path Method(CCPM).

Our second major topic for this week is the allocation of resources to the project tasks. As the project manager we have to determine howto have just the right amount of resources available at just the right time. This is a lofty but obtainable goal which gives a hint to thecomplexity of assigning human and other resources to the project. The complexity arises because both quantity and timing must becoordinated in an environment of shifting project and organizational demands. For this reason, we will also look at some tools to levelresources and adapt work flows to make things run more efficiently.

CPM and Time Cost Trade Off (Crashing)

We will work with the time/cost trade off called crashing, used to reduce the duration of a project schedule.

Crashing a Project Schedule: CPM ... two types of time/cost combinations:

1. Normal ... the schedule that is typically estimated as the most likely for each task. An estimate for the cost of each task will be madeconsidering this normal schedule.

2. Crashed ... the result of expediting the activity by the application of additional resources. Crashing is usually undertaken on critical path(the longest paths) activities to shorten project duration. Note: When crashing, only reduce the critical path to the point of the next longestpath. At that point you have created/added a new critical path and now must repeat the process with multiple critical paths in mind.

Other Definitions:

Time limited ... project must be finished on time, using as few resources as possible.Resource limited ... project must be finished as soon as possible, without exceeding some specific level of resource use, or somegeneral resource constraint.System-constrained task ... fixed time and resource crashing activities, a process to reduce the schedule duration with added cost:

1. Develop cost slope for each activity; cost slope is "$ per day" or other cost/time combination.2. Look for activity on the critical path with lowest slope (i.e. cost/time unit).3. Iteratively crash activities on the critical path until the desired combination of time/cost for project is achieved.

Crashing a project schedule costs money. It should only be done when the benefit/cost has have been analyzed and it is determined to beof value to the business.

CPM Crashing ... Demonstration Problem

Crashing a Project Schedule ... Problem 4-3

The Cost Slope: Optimizing Crashing SchedulesGiven a project with the data below:

Task PredecessorNormalTime

CrashTime

NormalCost

CrashCost

A -- 8 6 1000 1500



B -- 6 3 150 600

C A 4 3 400 500

D B 5 3 500 700

E C 7 5 800 900

F D 4 4 250 250

G E, F 10 8 1500 1900

Total Budget: $4,600

Question: Calculate the most cost-effective way tomeet the goal.

Goal: Reduce the schedule duration on this project to22 days.

Solution:

1. Draw the project network diagram.

2. Calculate the critical path.

Paths and durations for this project are:

Path 1: Start, A, C, E, End = 8 + 4 + 7 + 10 = 29 days

Path 2: Start, B, D, F, G, End = 6 + 5 + 4 + 10 = 25 days

What is the critical path?

Click to view answer

3. Calculate the crash cost per day for each critical task.

Normal time - crash time = days available for crashingCrash cost - normal cost = cost of crashingCost of crashing/days available = crash cost per day

Task PredecessorNormalTime

CrashTime

NormalCost

CrashCost

Crash Cost perDay

cp PathTime

2nd PathTime

A - 8 6 1000 1500 250 8



B - 6 3 150 600 150 6

C A 4 3 400 500 100 4

D B 5 3 500 700 100 5

E C 7 5 800 900 50 7

F D 4 4 250 250 4

G E, F 10 8 1500 1900 200 10 10

TotalBudget = 4600 29 25

4. Look for the activity on cp with the lowest cost per unit. Crash it as required to reduce the project duration.

5. Continually crash activities until desired combination of time/cost for project is achieved.

6. Be aware that if dual critical paths are created, multiple tasks must be crashed to continue to reduce the project duration.

Note: 1) When crashing two or more critical paths with common activities, we must consider crashing a common task as the most cost-effective solution as opposed to crashing individual activities on each path.

2) Each task is limited in the number of days it can be crashed due to physical or other constraints. As you crash, we can no longer crashan activity once it is reduced to its crash time.

The table below shows the six crash steps to reduce the project duration from the normal time of 29 days to the desired crashed durationgoal of 22 days.

TaskCrashDays Cost/Day Cost

CPTime

Additional CrashCost

ProjectCost 2nd Path Time

Initial schedule and cost 29 $4,600 25

E 2 50 100 27 100 $4,700 25

C 1 100 100 26 200 $4,800 25

G 2 200 400 24 600 $5,200 23

A 1 250 250 23 850 $5,450 23

At this point, the CP A-C-E-G is equal in length to the next longest path. To further reduce the projectschedule, we will have to reduce both paths.

A 1 250 250 22 $1,100 $5,700 23

D 1 100 100 22 $1,200 $5,800 22

Solution

In this project, the lowest cost crashing solution is to crash E, C, G, A, and D. This will reduce the schedule to the desired 22 days.

What is the additional cost to reduce the duration to 22 days?

Click to view answer

There are many ways to crash a task and here we added resources, at a cost. This allows the tasks on the critical path to get finishedquicker.

Expert Says

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CPM cost duration history ... a graph showing the increase in cost per unit for crashing a project is useful for demonstrating to clients ormanagers the increased costs associated with speeding up a project. This can also be used to evaluate the effects of crashing on projectswith incentive and penalty clauses, or with resource availability and utilization options. The graph aboves portrays the solution for ourdemonstration problem with a resulting $5,800 crash cost and 22 days. At this point we have met our goal and do not need to crash anyfurther.

Another approach is to start by fully crashing all tasks in the schedule; that is, use the crash duration values in the network and calculatethe schedule. Then "relax" activities starting with the most costly, non-critical path activities until the desired combination of duration andcost is reached.

PERT Network Processes

CPM is a de-facto standard for project scheduling. There are other types of network analyses that are important to understand. You will notneed these in all projects, but when you do you need to be aware they exist and what their advantages are.

A schedule may be improved where there is considerable risk or uncertainty in the task estimates by using the PERT process.

Example Problem 4-4

Given a project with the following data and the Z Value Table on page 254:

Activity Optimistic Pessimistic Most Likely Expected

Time(a) Time(b) Time(m) Time (TE)

A 5 10 7 7.17

B 7 14 12 11.50

C 4 7 5 5.17

D 6 12 8 8.33

E 15 26 22 21.50

F 18 23 20 20.17

G 17 29 24 23.67

H 14 22 17 17.33

I 4 7 6 5.83

J 8 11 10 9.83

K 5 9 8 7.67

L 3 6 4 4.17

The critical path for this project is: B - F - J

A: Calculate the expected time (TE) for critical path activities.B: Calculate the scheduled duration (S) for the project using the TE of critical path tasks.C: What is the probability of the project being complete in a desired time (D) of 44 days?D: What is the probability of the project being complete in a desired time (D) of 38 days?

Answer

A B C D

Activity TE Variance -(a + (4m) + b) / 6 ((b-a)/ 6) squared

B 11.50 1.36F 20.17 0.69J 9.83 0.25

Schedule = 41.5 DaysSum of variance for CP= 2.31Square root ofvariance for CP = 1.52

44 DaysZ = (D-S) / 1.52 =1.65Probability (fromtable) = 0.45010.4501 +0.500 = 95%

38 DaysZ = (D-S) / 1.52 =-2.31Probability (fromtable) = (0.4896)0.4896 +0.500 = 1%

This process is usually a part of project management software such as MS Project.

Expert Says



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CCPM Network Processes

Critical chain project management (CCPM) is based upon the theory of constraints (TOC) developed by Eliyahu Goldratt. It was initiallyused in manufacturing environments but was expanded for use in project management. Our text covers this process so I will not go intodetails here. I will say that it is different and unique in some of the principles it uses. It uses the basic critical path process but introducesdifferent concepts on how to manage the project using the CPM process. It also requires all levels of management to accept these differentphilosophies and processes to manage a project. I believe it has merit, but of course, it will not be for everyone.

Resource Allocation and Leveling

"How do you have just the right amount of resource available at just the right time?" Resource needs vary as the projectprogresses which means the amount of resources required will fluctuate, making the task even more difficult. It is beneficial to the projectnot only that the right resources be available when needed but also that, to the best of our ability, we schedule the resources on an evenbasis to reduce the changes in the team's work schedule. This example will illustrate how to accomplish this.

Resource Load Diagram - Demonstration Problem 4-1

Task Duration (days) Predecessor (units) Number of Programmers Required

A 10 n/a 5

B 5 n/a 5

C 10 B 10

D 10 A 5

E 15 D 5

F 5 D 5

The dark line with the arrows shows the tasks that must be done on time (Tasks A, D, E, and F) or the entire project will be delayed. TasksB and C are not on the critical path and may be delayed (but not any longer than the tasks on the critical path) without affecting the projectlength.

Problem Data Solution



Level this project given the constraint that only 10 programmers areavailable.

Resource Load Diagram:

1. Determine the critical and other paths.CP = A - D - E = 35 daysB - C - F = 15 daysA - D - F = 25 days

2. Plot resource loading against time for each activity. Startwith the CP:

Task A uses 5 and takes days 1 through 10.Task D uses 5 and takes days 10 through 20, afterits predecessor, A.Task E uses 5 and takes days 20 through 35, afterits predecessor, D.Task B uses 5 and takes days 1 through 5,concurrently with A; (as resource use is cumulative,plot B on top of A).Task C uses 10 and takes days 5 through 15,concurrently with A and D, and after its predecessor,B.Task F uses 5 and takes days 20 through 25,concurrently with E, after its predecessor, D.

Total resource use:

Total resource demand

Days Unleveled Leveled

1...5 10 10

5...10 15 10

10...15 15 10

15...20 5 10

20...25 10 10

25...30 5 10

30...35 5 5

Note that leveling in this case assumes task C can be:

1. slowed down; and2. split.

If C cannot be split, task F could be delayed to start on day25 after C is complete.If C cannot be slowed down, it will have to be delayed tostart on day 35 and the project completion will be delayeduntil day 45.

Resource Load Diagram: Leveling will force Task C to be completed later in the project; this could change the critical path and delay the entire project.

Gantt Chart Per Initial Project Plan

Task DurationWeek#

5 10 15 20 25 30 35 40 45

A 10 R = 5 R = 5

B 5 R = 5

C 10 R =10 R = 10

D 10 R = 5 R = 5

E 15 R = 5 R = 5 R = 5

F 5 R = 5

CP = 11 WEEKS

Total Resources 10 15 15 5 10 5 5 0 0

15 C C

10 B C C F

5 A A D D E E F

Gantt Chart After Resources are Leveled

Task DurationWeek#

5 10 15 20 25 30 35 40 45

A 10 R = 5 R = 5

B 5 R = 5



C 10 R =5 R = 5 R = 5 R =5

D 10 R = 5 R = 5

E 15 R = 5 R = 5 R = 5

F 5 R = 5

CP = 11 WEEKS

Total Resources 10 15 15 5 10 5 5 0 0

15

10 B C C C F C

5 A A D D E E F

Expert Says

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Week # Weekly Cash Flow Before Leveling Weekly Cash Flow After Leveling

1 $20,000 $20,000

2 $30,000 $20,000

3 $30,000 $20,000

4 $10,000 $20,000

5 $20,000 $20,000

6 $10,000 $20,000

7 $10,000 $10,000

Note that leveling resources provides a much more even cash flow and leads to more manageable financial management and control.

Conclusion



Resource leveling ... shifting tasks within their slack time to even out demands on resources which are common to different tasks.Advantages:

Less management is required when resource use is constant.If the resource is people, leveling improves morale.

Constrained resource scheduling: If the quantity of resources available is limited we have a resource constrained project. If theresources available are less than required it will result in an increased schedule or additional cost to resolve.

Two approaches to solve the problem

Heuristic methods ... this will produce a solution but not necessarily the best solution. Start with the PERT/cpm schedule andanalyze resource use period by period, resource by resource; if resource supply is exceeded in a given period, examine tasks andallocate resources to them sequentially, according to some priority rules.

Priority rules: (examples)shortest task firstmost resources firstminimum slack firstmost critical followersmost successors

If excess resources are left idle, they can be reassigned in the organization or used to accomplish future tasks.If resources are exhausted, tasks must be slowed or delayed.

Optimization ... this will produce the best solution based upon the project requirements and objectives. There are two types ofoptimization: mathematical (linear) programming and enumeration. These are complex and we will not address these methods here.

Resource Leveling ... Demonstration Problem

Demonstration Problem 4-2

This example introduces the cost factor into the resource leveling problem in a resource-constrained project. In the case where we need toadd resources to avoid increasing the project schedule, we need to understand how to determine the additional cost involved. Use the Ganttchart to determine and resolve resource conflicts.

Example:

Problem Data Solution

Activity Predecessor Duration Resources Required

A --- 6 Weeks 3 Drill Rigs, 6 Laborers

B --- 2 Weeks 4 Trucks, 1 Laborer

C A 1 Week 2 Backhoes, 2 Laborers

D B 3 Weeks 2 Drill Rigs, 4 Laborers

E C & D 4 Weeks 3 Trucks, 1 Laborer

Resource Constraints Resource Cost (per unit)

3 Drill Rigs $2,000 per week

4 Trucks $1,000 per week

2 Backhoes $3,000 per week

8 Laborers $10.00 per hour

Calculate:

1. the total budget for the project. Are there any resourceconflicts?

2. the most cost-effective method of resolving the conflict ...either by adding or leveling resources (additional resourcescan be obtained at a 50% cost premium).

Activity Resources Cost Calculation Total Cost

A Drill Rigs 6 x 3 x $2,000 = $36,000

$50,400Laborers 6 x 6 x 40 x $10 =$14,400

B Trucks 2 x 4 x $1,000 = $8,000$8,800

Laborers 2 x 1 x 40 x $10 = $800

C Backhoe 1 x 2 x $3,000 = $6,000$6,800

Laborers 1 x 2 x 40 x $10 = $800

D Drill Rigs 3 x 2 x $2,000 = $12,000$16,800

Laborers 3 x 4 x 40 x $10 = $4,800

E Trucks 4 x 3 x $1,000 = $12,000$13,600

Laborers 4 x 1 x 40 x $10 = $1,600

Total Budget = $96,400

GANTT Chart

The line for each task shows the number of weeks needed to complete each task as well as


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Resource

which tasks must be done first before the next task can start. Task A and B can be done atthe same time at the start of the project (week 0), Task D must wait until Task B iscomplete before starting at week 2; Task C must wait until week 6 when Task A iscomplete. Task E cannot start until Task C is complete at week 7.

Resource Use (cumulative) by Week

Week Number

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

Drill Rigs 3 3 5 5 5 3

Trucks 4 4 3 3 3 3

Backhoes 2

Laborers 7 7 10 10 10 6 2 1 1 1 1

Resource conflict exists between tasks A and D. These tasks need five drill rigs and 10 laborers; only three drill rigs and eight laborers areavailable. The time frame of the conflict is weeks 3, 4, and 5.

The Effect of Adding or Leveling Resources:

We can add resources, level the resources, or a combination of the two.

Adding Resources:

Adding resources at a 50% premium:

2 Drill Rigs x 3 weeks x $2,000 x 0.50 = $6,0002 Laborers x 3 weeks x 40 hrs. x 0.50 = $1,200Adds a total of $7,200 to the budget. The schedule remains the same.Note that only the premium (50%) is added; the original budget included all resources required, including those in conflict.

Leveling:

Delay D to weeks 7, 8, and 9 using slack. This will delay the start of E by 2 weeks and the project completion by 2 weeks until week 13.There are no extra costs.

Combining Leveling and Adding Resources:

The third option is a combination. Shift the start of D to week 5 within the slack for the task. We now have reduced the conflict from 3 to 2weeks. We then add resources to cover those 2 weeks. The extra cost at a 50% premium is:

2 Drill Rigs x 2 weeks x $2,000 x 0.50 = $4,0002 Laborers x 2 weeks x 40 hrs. x 0.50 = $800Adds a total of $4,800 to the budget. The schedule remains the same.Note that only the premium (50%) is added, the original budget included all resources required, including those in conflict.

This option preserves the schedule, but at a reduced cost because we also used the slack available to level the resources.

Discussion

To solve these problems, draw the Gantt chart and use a grid like that shown to accumulate resources of each type. Compare resource useto constraints to determine if conflicts exist. When leveling, if you move a task you have to recalculate total resource use from the start ofthe moved task to make sure additional conflicts have not been made.

The needs of the project and business will dictate which of the solutions the project manager should use.

Note: This is the method used by Microsoft Project and other PM software to determine and level resource conflicts. Software can be ahelpful tool to resolve complex resource conflict problems.

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PM592 Week 4 Lecture