Project Planning and Control

Project Planning and Control Jay Sounderpandian University of Wisconsin - Parkside

Part I INTRODUCTION

Historical Note • Until the 1940’s the Gantt Chart was the only tool available for Project Planning and Control. • During the 40’s, managers at Du Pont and (independently) engineers in the US Military invented the PERT/CPM method. • In the 90’s we have sophisticated computer programs for almost all aspects of Project Management. Sounderpandian

A Gantt Chart Project Title Week 1 Week 2 Week 3 Week 4 Week 5 W Task 1 Task 2 Task 3 Task 4 Sounderpandian

Gantt Chart Refinements Project Title Now Week 1 Week 2 Week 3 Week 4 Week 5 W Task 1 Task 2 Task 3 Task 4 Sounderpandian

Another Refinement Project Title Week 1 Week 2 Week 3 Week 4 Week 5 W Task 1 Task 2 Task 3 Task 4 Sounderpandian

Gantt Chart Limitations • Showing the interdependencies of tasks is cumbersome in a Gantt Chart. • If the chart is not computer driven, • Critical tasks are not readily identified. • Rescheduling and monitoring are difficult. • The amount of slack in the schedule of a task is difficult to calculate. Sounderpandian

The POLARIS Project • It had numerous tasks with intricate interdependencies. • It needed ready identification of critical tasks. • It needed close monitoring with frequent rescheduling. • No computer was available. Sounderpandian

Part II Project Network Diagrams

Task on Node (TON) Task on Arrow (TOA) A C B A C B Two Graphical Representations Sounderpandian

Advantages of TOA over TON • An arrow denotes passage of time and therefore is better suited (than a node) to represent a task. • Scheduling (manually) on a TOA diagram is easier than on a TON diagram. • In general, TOA needs fewer arrows than TON and therefore will be more clear. Sounderpandian

A Disadvantage of TOA • A TOA diagram often requires the use of dummy arrows, which represent dummy activities artificially introduced into the project. • Consider the project: • It needs a dummy arrow. Sounderpandian

C A End Start D B The need for Dummy Arrows • Consider the project: • The only way to draw a TOA diagram for it is: Dummy Sounderpandian

C A End Start D B The use of dummy arrows The dummy (broken) arrow is to be considered an additional (dummy) activity which takes zero time. It starts after A is finished. Since D starts after the end of B and the dummy activity, it has to wait, in effect, for A and B to be over. That is exactly the prerequisite for D. Sounderpandian

More on dummy arrows • Dummy arrows introduce additional tasks into the project and thus add complexity. • Therefore one should minimize the number of dummy arrows used in any project diagram. • Unfortunately, (and interestingly,) minimizing the number of dummy arrows is a very difficult problem. To wit, in a project with a large number of tasks, it may not be possible to know the minimum number of dummy arrows needed. Sounderpandian

TOA vs TON • Despite the difficulty with dummy arrows, the TOA diagram is better suited than the TON for manual work, because of its manual scheduling advantages. • Computer programs use the TON diagram, because of the trouble with dummy arrows. Sounderpandian

Steps in drawing a TOA diagram • 1. List all the activities in the project • 2. List all the precedence relationships among the tasks. • A precedence relationship may be due to resource constraint or due to a physical necessity. • 3. Estimate the duration of all the tasks. • 4. Draw the TOA diagram observing all conventions. Sounderpandian

Conventions in a TOA diagram • The length of an arrow need not be indicative of the task duration. • At most one arrow between any two nodes. • Exactly one Start node and one End node. • Avoid unnecessary dummy arrows. • Nodes are numbered such that every arrow goes from a smaller to a larger number. • Arrows go from left to right. Sounderpandian

Exercise 1 Draw a TOA diagram for the project: Sounderpandian

Exercise 5 Draw a TOA diagram for the project: (Tricky!) Sounderpandian

Part III Project Scheduling

Event Scheduling • The easiest way to schedule a project is by scheduling the events. Recall that events are represented by nodes in TOA diagrams. • While scheduling an event we will be interested in two things, namely, • the Earliest Time the event can occur assuming everything goes according to plan. • the Latest Time the event can occur without delaying the completion of the project. Sounderpandian

Earliest Time Estimate 10 + 9 = 19 13 + 5 = 18 8 + 14 = 22 Max = 22 10 22 9 13 5 14 8 Sounderpandian

Earliest Time Estimate • Assign time zero to start event (1). • Go to the next event (2, 3, ...). • Consider all incoming arrows. • Calculate the completion time of each arrow. • Pick the maximum. • Continue until all events are scheduled. Sounderpandian

Latest Time Estimate 25 - 5 = 20 28 - 14 = 14 23 - 13 = 10 Min = 10 25 5 10 28 14 13 23 Sounderpandian

Latest Time Estimate • Set the latest time equal to the earliest for the Finish event (n). • Go to the previous event (n-1, n-2, ...). • Consider all outgoing arrows. • Calculate the start time of each arrow. • Pick the minimum. • Continue until all events are scheduled. Sounderpandian

Critical Event • An event whose earliest and latest time estimates are equal is a Critical Event. • If there is a delay in a critical event, then the project completion will be delayed. Sounderpandian

Slack 5 10 23 29 13 Slack = 29 - 5 - 13 = 11 Sounderpandian

Critical Task • A task with zero slack is a Critical Task. • If a critical task is delayed, it would delay the project completion. • If a non-critical task is expedited, it would not expedite project completion. It would simply increase the slack of that task. Sounderpandian

Part IV The Critical Path

Exercise 7 Identify the critical path(s). 4 18 14 7 2 22 5 16 17 12 5 1 4 8 20 Start End 15 19 3 8 6 Sounderpandian

Critical Path • The critical path is the longest path from Start to Finish. • Its length is the project duration. • It consists of all and only the critical tasks and passes through all and only the critical events. • A project can have more than one critical path. Sounderpandian

When a critical task is expedited.. • The project duration may or may not decrease. • The critical path may cease to be critical, and a new critical path may emerge. • If another critical path already exists, it will remain critical. • The slack on any other task can only decrease or stay the same. Sounderpandian

When a critical task is delayed... • The project duration will increase. • The task will continue to be critical and its critical path will continue to be critical. • Another critical path may cease to be critical because it may not be one of the longest paths any more. • The slack on any other task can only increase or stay the same. Sounderpandian

If a non-critical task is delayed ... • As long as the delay is less than the slack: • the project duration would not increase • no changes would occur in critical path(s). • there could be some cost saving. • When the delay equals or exceeds the slack: • the task will become critical • changes in critical path(s) will occur • project cost may increase Sounderpandian

Exercise 8 • Refer to the project in Exercise 7. • 1. By how many days can the task 2-7 be delayed before it becomes critical? • 2. If the task 2-7 is delayed by 20 days what will be the new project duration? • 3. If a task has a slack of x days and is delayed by x + y days, what is the delay in the project? Sounderpandian

Exercise 9 • Refer to the project in Exercise 7. By how many days can the task 5-6 be expedited before the critical path changes? Note: This question is harder than those in the previous exercise because the new critical path can be any one of a number of possibilities. Sounderpandian

Part IV Expediting

Expediting a Project • When a project needs to be completed sooner, it needs to be expedited. • Expediting is beneficial (only) as long as the benefit exceeds the cost. • Sometimes a precedence relationship due to resource constraint can be removed by getting additional resources. That could greatly reduce project duration. Sounderpandian

Expediting a Project • In order to expedite a project, the lengths of all the critical paths need to be reduced. That is, if two parallel critical paths exist, then both paths need to be shortened. • An annoying complication is that critical path could change as some critical tasks are expedited. Thus, it has to be a trial-and-error process. Sounderpandian

Exercise 10 The figure shows the critical paths and expediting cost per day for each critical task. 8 $ 180 $ 210 $ 680 $ 520 1 4 15 18 Start End $320 $ 360 11 Assuming that no other task becomes critical, what is the least cost plan to expedite the project by 1 day? Sounderpandian

Exercise 10 Continued Assuming that no other task becomes critical, what is the least cost plan to expedite the project by 2 days? The assumption in the above question is crucial. If other tasks become critical, the problem becomes much harder. Sounderpandian

Exercise 11 Here is a whole project with critical path in red. Duration and crashing cost per day are shown for each task.. 2 $ 180 $ 210 7 14 5 1 4 End $50 Start 11 10 $ 360 $320 3 Find the minimum cost crashing plan for reducing the project duration by i) 1 day ii) 2 days. Sounderpandian

Part V PERT

PERT • PERT stands for Program Evaluation and Review Technique. • PERT is a refinement on CPM. It accommodates uncertainties in task durations. • In practice, almost all task durations are uncertain, and therefore PERT is useful and popular. Sounderpandian

Beta Distribution • Research shows that task durations follow a Beta distribution, which is right skewed. • To simplify the estimation of the distribution, a three-time estimate is used. The three estimates are: • the optimistic duration (a) • the most likely duration (m) • the pessimistic duration (b) Sounderpandian

Project Planning and Control