Unit 7 Scheduling, Allocating Resources, Monitoring and - PDF document

Unit 7 Scheduling, Allocating Resources, Monitoring and Controlling, Evaluating and Terminating the Project Source: Project Management in Practice, 5th Edition, Mantel, Meredith, Shafer, Sutton, Wiley, 2014. Project Management: A Systems Approach to Planning, Scheduling, and Controlling, 10th Edition, Harold Kerzner, Wiley, 2009. 1 Project Scheduling  Project planning, budgeting, and scheduling is interdependent on each other.  Project scheduling is the discipline of organizing and time‐phasing the activities required to complete the objectives of an effort.  Project schedule is the project plan in an altered format for monitoring and controlling project activities. 2

PERT and CPM  Both PERT and CPM were developed in the late 1950s  Program Evaluation and Review Technique (PERT) • by U.S. Navy, Booz‐Allen Hamilton, and Lockheed Aircraft • used probabilistic activity durations  Critical Path Method (CPM) • by Dupont De Nemours Inc. • used deterministic activity durations  Both employed networks to schedule and display task sequences.  While theyuse slightly different ways in drawing the networks, anything one can do with PERT, could also do with CPM and vice versa. 3 The Language of PERT/CPM  Activity • a task or set of tasks • uses resources and time  Event • an identifiable state resulting from completion of one or more activities • consumes no resources or time • predecessor activities must be completed before an event can be achieved. 4

The Language of PERT/CPM continued  Milestones • identifiable and noteworthy events that mark significant progress  Network • a diagram of nodes (activities or events) and arrows (directional arcs) that illustrate the technological relationships of activities • usually drawn with a “Start” node on the left and a “Finish” node on the right.  Path • a series of connected activities between any two events 5 The Language of PERT/CPM concluded  Critical Path • the set of activities on a path (from the project’s start event to its finish event) that, if delayed, will delay the completion date of the project  Critical Time • the time required to complete all activities on the critical path 6

Building the Network It’s necessary to know the predecessor/successor relationship (technological dependences) in building the network  Two ways of displaying a project network • Activities on Arrows (AOA) network … in which the activities are shown as arrows and events as nodes, usually associated with PERT. • Activities on Nodes (AON) network … in which each task (activity) is shown as a node and the technological relationship is shown by the arrows, usually associated with CPM. (will use in this course) 7 Example – Table 7‐1 A Sample Set of Project Activities and Precedencies Task Predecessor a -- b -- c a d b e b f c, d g e 8

AON Network Stage 1 Start with task a and b , because they have no predecessors 9 AON Network ‐ Stage 2 Next, connect task c with a (its predecessor), and d, e with b (their predecessor). 10

AON Network ‐ Complete Next, connect task f with c, d (its predecessors), and g with e (its predecessor). Since there is no other tasks, f and g are connected to the “finish” node. 11 Example ‐ Table 7‐2 A Sample Problem for Finding the Critical Path and Critical Time Activity Predecessor Duration a -- 5 days b -- 4 c a 3 d a 4 e a 6 f b, c 4 g d 5 h d, e 6 i f 6 j g, h 4 As AON is easier to deal with, will be using AON notations mostly (adopted by most project management software.) 12

Example ‐ Figure 7‐1 Stage 1 of a Sample Network Start with task a and b , also noted their durations. Next, connect task c, d, e with a (their predecessor). 13 Example ‐ Figure 7‐2 A Complete Network Connect tasks g and h with task d ; h with task e ; j with task g, h ; and i with task f. Since there is no other tasks, i and j are connected to the “finish” node. 14

Example ‐ Figure 7‐3 Information Contents in an AON Node 15 Example ‐ ES, EF calculation (forward pass) For task a , its ES is day 0, EF is (0 + 5) = 5. Task c , d , e cannot start before a is completed on day 5, their ESs. Adding their respective durations to their ESs, give their EFs. 16

Example ‐ ES, EF calculation (forward pass) Task f cannot start until both b and c are completed, giving its ES = 8 and EF = 12. Task g cannot start until d is completed, giving its ES = 9 and EF = 14. Task h cannot start until both d and e are completed, giving its ES = 11 and EF = 17. 17 Example ‐ ES, EF calculation (forward pass) Task j cannot start until both g and h are completed, giving its ES = 17 and EF = 21. Task i cannot start until f is completed, giving its ES = 12 and EF = 18. The shortest time for completion is the longest path through the network, in this case, a- e-h-j , and the critical time is 21 days. 18

Example – Figure 7‐4 The Critical Path and Time for Sample Project 19 Example ‐ LS, LF calculation (backward pass) Task j and i must be completed by day 21, giving their LFs = 21, where the LS for j = 21-4 = 17, and LS for i = 21-6 = 15. Task g and h could have their LFs = 17, and LS for g = 17-5 = 12, and LS for h = 17-6 = 11. 20

Example ‐ LS, LF calculation (backward pass) Task f must be completed by day 15, giving its LF = 15, where the LS for f = 15-4 = 11. Task b has thus its LF = 11, and LS = 11-4 = 7. Task d, e, c have their LFs = 11, and LSs = 7, 5, and 8 respectively. Task a has its LF = 5, and LS = 0 21 Calculating Activity Slack  Latest Start Time (LS) – Earliest Start Time (ES) = Slack  Latest Finish time (LF) – Earliest Finish time (EF) = Slack Example – Activity a, e, h, and j, all on the critical path, has no slack. Activity i has a slack = 15 – 12 = 3 days, Activity f has a slack = 11 – 8 = 3 days, Activity g has a slack = 12 – 9 = 3 days, Activity d has a slack = 7 – 5 = 2 days, Activity c has a slack = 8 – 5 = 3 days, and Activity b has a slack = 7 – 0 = 7 days, 22

Building the Network with MSP See Example 1 in supplemental Material 23 Building the Network with MSP See Example 1 in supplemental material 24

Building the Network with MSP View Total Slack & Free Slack Total slack = LF – EF = LS – ES. For task b, total slack = 7 – 0 = 7 Free Slack = the time an activity can be delayed without affecting the start time of any successor activity. For task b, free slack = ES of (f) – EF (b) = 8 – 4 = 4 25 Calculating Probabilistic Activity Times Assume that all possible durations for some tasks could be represented by the beta distribution as shown in figure 5‐13  The expected time (T E ) is based on three time estimates • pessimistic ( a ) – the actual duration of the task will be a or lower less than 1 percent of the time • most likely ( m ) – the mode of the distribution • optimistic ( b ) – the actual duration of the task will be b or higher less than 1 percent of the time   ( 4 ) a m b  T E 6 26

The Beta Distribution Figure 7‐4 The Beta Distribution of all Possible Times for an Activity 27 The Beta Distribution The general formula for the probability density function of the beta distribution defined on the interval (a, b) parameterized by two positive shape parameters, α and β is where p and q are the shape parameters, a and b are the lower and upper bounds, respectively, of the distribution, and B ( p , q ) is the beta function. The beta function has the formula Mathematical Expectations, By approximation,   ( 4 ) a m b   6  ( ) b a   6 With  = (b-a)/6, it assumes that the range between a and b will cover 99.7% of all durations. 28

The Probabilistic Network An Example Table 7‐3 A Sample Set of Project Activities with Uncertain Durations Opt. Norm. Pess. T E Var. ((b ‐ a)/6) 2 Activity Pred a m b (a + 4m + b)/6 A ‐ 8 10 16 10 4/6 1.78 B a 11 12 14 12 1/6 .25 C b 7 12 19 12 2/6 4.00 D b 6 6 6 6 .00 E b 10 14 20 14 2/6 2.78 F c,d 6 10 10 9 2/6 .44 G d 5 10 17 10 2/6 4.00 H e,g 4 8 11 7 5/6 1.36 29 The Probabilistic Network An Example Figure 7‐5 An AON network from Table 5‐4. 30

The Probabilistic Network An Example The critical path is a-b-d-g-h The critical time is 47 days Some concerns - o Since 47 days is the mean, it means that the project has a 50% chance to complete before 47 days and 50% chance to be more than 47 days. o The critical path may not be a-b-d-g-h if an activity on another path might have a longer duration (for example a-b-c-f, if activity c or f or both got delayed.) 31 The Probabilistic Network An Example – MSP View See Example 2 in supplemental material 32

The Probabilistic Network An Example – MSP Network View See Example 2 in supplemental material 33 The Probability of Completing the Project on Time Critical time = 47 days, to complete the project by this time requires that all paths in the project’s network be completed by the specified time. The probability that the a‐b‐d‐g‐h path will be completed on or before a desired day, D, is   ( ) D    Pr .( ) Pr .( ) x D Z   where D = the desired project completion time  = the sum of T E activities on the path being investigated  = the sum of variances of the activities on the path     = the standard deviation 34