CE 366 PROJECT MANAGEMENT AND ECONOMICS Robert G. Batson, Ph.D., P.E. Professor of Construction Engineering The Universi

1. CE 366PROJECT MANAGEMENT AND ECONOMICSRobert G. Batson, Ph.D., P.E.Professor of Construction EngineeringThe University of AlabamaRbatson@eng.ua.edu

2. Chapter 5:Project Scheduling

3. CPM and PERT Analytical Methods • CPM is standard method used for construction scheduling • Activity durations are expressed in working days, and are treated a deterministic (no statistical uncertainty) • CPM algorithm will identify “critical activities” along the project “critical path,” which determines estimated project duration • Slack times (flexibility in start/finish times) are determined • PERT (Project Evaluation and Review Technique) was created by U.S. Navy about the same time as CPM, for R&D projects • Activity times are treated as probability distributions • CPM algorithm is applied to mean activity durations • The PERT critical path yields mean and variance of project duration

4. Eight-step Procedure to Schedule a CPM Project • Estimate time duration of each activity. • Compute time period required for overall project completion. • Establish time intervals within which each activity must start & finish. • Identify critical path activities for careful management. • If necessary to meet the contract promise date, or for other reasons, explore shortening the project at minimum cost. • Adjust the start and finish times of certain (non-critical) activities to minimize resource conflicts and smooth out demand for manpower and equipment. • Make a working project schedule that show calendar dates planned to start and finish each activity. • Record the assumptions behind the schedule.

5. Rules for Estimating Activity Durations General Rules • Use the precedence diagram(s) already developed • Estimates are more reliable at a detail level, than at a summary level Specific Rules • Evaluate activities one at a time, independently, assuming resources will be available when required. • For each activity, assume a “normal” level of manpower and/or equipment – conventional crew sizes and equipment mix. • Assume a normal workday – do not assume overtime or multiple shifts unless contract says so. • Estimate the duration of the individual activity, not what must happen before, what will happen after the activity, or how it fits into some overall schedule plan(bar chart). • Use consistent time units, with conversions as necessary. • Assume normal weather conditions, e.g. temperatures and precipitation.

6. Estimating Activity Duration • Depend on those experienced with the type of work represented, at least to validate estimates • e.g., test duration estimated by test manager • subcontracted work estimated by manager or estimator at that firm • may be only way to estimate if crew or equipment production rates are not available • Quantity production rate • Total direct labor cost crew daily pay rate • See Figure 5.1 for working days and activity numbers entered in each activity box • Learning curves describe how construction time shortens with repetitive activity by a fixed crew

7. LEARNING CURVES • In many types of production, a reduction in labor hours per unit (Y) has been observed as a function of number of units produced • reduction as a constant factor when the number of units is doubled • factor is specific to industry • Yn = Y1n-b or lnYn = lnY1 - b ln n where Y1 = time it takes to make first unit Yn = time it takes to make nth unit b = “exponent” such that n-b = Yn/Y1, n = 2, 3, … • For example, if • then b = -ln (0.9)/ln (2) = 0.152. So, Y3 = 1000 (3 -.152 ) = 846.

8. Time Contingency Allowance • The project durations estimate provided by CPM is a forecast based on many assumptions • Each activity could experience “abnormal conditions” • Resources may be delayed or less productive than assumed • Weather may affect entire project, or portions of the project, depending on the timing, the type of work in-progress, and nature of the “weather day(s)” • Materials may be late, or on-time but damaged, or discovered wrong (upon inspection) • Time contingencies can be applied to specific activities, but typically a general allowance is made at milestones or for overall project completion time (as in Figure 5.1)

9. CPM “Activity-on-node” Notation and Assumption • Each activity j has a duration Dj and enough resources are available to conduct any activities simultaneously within the precedence constraints • Activities are represented by rectangles called “nodes” or “nodals”  • Arrows between activities are assumed to mean “finish-to-start” logic: • An activity cannot start until all the immediately preceding activities have finished • Once all preceding activities have been finished, the succeeding activity can immediately start • Other logic of lag and lead times to be discussed later

10. DefinitionsAn activity is critical to the project if any change in its duration (+ or -) would change the overall project duration by the same amount. Another way to say this is that if the start of the critical activity is advanced or delayed, the project completion is advanced or delayed by the same amount. A noncritical activity allows some scheduling flexibility or slack—the start time may be advanced or delayed within limits without affecting the project completion date. A critical path is a path from start to finish node consisting only of critical activities. This turns out to be the path of “maximum length” through the network, and determines project duration. The algorithm to identify critical activities and the critical path is called the critical path algorithm or sometimes, the critical path method.

11. CPM Activity Time Notation and Definitions Earliest start time for node j, ESj = max { ESi + Di } for all nodes i that immediately precede node j. These ESj are calculated for each node in the network by making a forward pass through the network and writing ESj in the upper left corner of the node. To start ES1 = 0. If n is the terminal node, then ESn is the earliest time to complete the project. Earliest finish time for node j is the earliest possible time that it can be completed: EFj = ESj + Dj. Write EFj in the upper right corner of the node j box. Notice that ESj = max {EFi}, over all i immediately preceding j.

12. CPM Activity Time Notation and Definitions A backward pass is now executed, from finish node to the start node, and the latest finish time for activity j (LFj) is defined to be the latest time activity j can complete without delaying the completion of the project beyond its earliest time ESn: LFj = min {LFi - Di} for all nodes i immediately following node j. To start the backward pass, set LFn=ESn; write LFj in the lower right corner of the node j box. Latest start time for activity j is the latest possible time activity j can be started without delaying the earliest completion of the project: LSj = LFj – Dj; write LSj in the lower left corner of node j. Notice that LFj= min {LSi}, all i immediately succeeding j.

13. Project Duration • Calendar days = (working days) × 7/5 + holiday allowance [no contingency allowance] • Calendar days = (working days + contingency) × 7/5 + holiday allowance [a more realistic method] • If calendar days ≤ Construction Period, good news! • If calendar days > Construction Period, must re-evaluate and perhaps increase resources to shorten the CPM-based working days estimate.

14. Total Float and Critical Activities For activity j, Total Float j = LSj – ESj = LFj – EFj Another way to understand Total Float j uses LSj = LFj − Dj and EFj = ESj + Dj to rewrite the definition as Total Float j = (LFj – ESj) – Dj, that is, Total Float j = (maximum time available) j – Dj. Activity j is critical if Total Float j = 0, which means LSj= ESj, LFj= EFj, and LFj – ESj = Dj. A critical path is a path from project start to finish consisting only of critical activities (may be more than one).

15. Activity Paths and Critical Paths • A path in a CPM network is an unbroken sequence of precedence arrow from start node to finish node • All paths in a CPM network must be traversed during the actual project • The critical path has the longest total duration of any path through the network, and this is the minimum possible time (estimated) to complete the project • Identified by activities with zero total float • Not activities that are judged “difficult” or “important” • Critical (path) activities • Generally make up 20% or less of the total network • Must be monitored closely for on-time performance

16. Free Float For activity j, Free Floatj is an upper limit on the delay in starting activity j which will not affect earliest start time of any immediately following activity: Free Float j = [min {ESi}, i immediately succeeds j] –EFj Notes: • Free Float j ≤ Total Float j • Free Float j is a “local” measure of slack or spare time; Total Float j is larger, but is shared among activities along each path containing j • If FFj = TFj, then activity j can be scheduled anywhere in its [ESj, LFj] span, without causing project delay nor impacting any succeeding activity i.

17. Early-Start (Normal) Schedule • Convert network calculations to calendar date schedules • Schedule each activity j as follows: • Start on day ESj + 1, on calendar • End on day EFj, on calendar • Enter dates on one or all of: • precedence diagram (Figure 5.6) • tabular time schedule (Figure 5.7) • Gantt (bar) chart (Figure 5.15) • These dates are preliminary • “scheduled” or “estimated” • resource limitations, weather allowances, etc. to be resolved

20. Sorts applied to Project Activities • Activity number sort • Early-start sort • free float is better conserved • designers, vendors, subcontractors are better controlled • Late-start sort • Late-finish sort • Total float sort (ascending order of criticality, like Figure 5.8) • Project responsibility (organization or person responsible) • Combined sorts as project manager directs

22. Lags between Activities • Lags are a collection of more complex relationships between two activities, and the associated precedence notation • Lag time can be designated on the precedence arrow as a positive, negative, or zero value • Arrows are no longer restricted to finish-to-start • Forward-pass and backward-pass computations are adjusted appropriately by the logic and lag amount • Lag types are shown in Figure 5.9: Finish-to-Start, Start-to-Start, Finish-to-Finish, Start-to-Finish, Combination

24. Pipeline Relocation Project • Precedence diagram, CPM computations, and critical path are shown in Figure 5.10 • Summary diagram of repetitive operation projects • it condenses a large network to a more manageable size, but sacrifices internal logic • lag logic becomes quite complex (Figure 5.11) • The combined activity nodes may be on critical path (activity 40) entirely, or partially (activities 10, 20, 50, 60) • Site managers and personnel would react more favorably to the detail diagram, and it would be more useful for control and handling of “work-arounds”

27. Special CPM Network Logic • Interface Computations • At interface activity (activity 110 in Figure 5.12), LS110 set equal to EF170 = LF 170 = 20 (in general, EF) ES110 set equal to LS 110 = 20, as well • A forward pass to Activity 140 (finish) • A backward pass to Activity 0 (start) • A forward pass to Activity 110 • The path with TF=3 is the “critical path” with 3 days contingency, starting crossing structure at time 0 • Hammock Activity -- consumes resources, no estimated duration, inherits ES, LS, EF, LF • Milestone Events -- zero time duration box (rounded) established as reference points (See Figure 5.1) by management for monitoring

29. Time-Scaled Networks • Arrows on precedence diagrams represent logic, hence their length is meaningless • Time-scaled networks (Figure 5.14) depict • precedence logic • scheduled working days and dates for each activity • activities progressing in parallel • critical path and floats • Early-start schedule has • each activity scheduled in span [ES, EF] horizontally • each activity is a solid line segment, its free float dotted, and both labeled with number of days • circles are added to represent events, separate scheduled time from float time, and to aid in capturing network logic; numbers inside circle are (expired)working days

30. Nature and Significance of Floats • The free float of an activity is extra time associated with that activity that can be consumed (due to starting later than ESj, duration longer than Dj, or both) without affecting the early start time of any succeeding activity • However, when free float is used for a given activity j, total float is also used in the same amount • Total float is length of time EFj can be delayed, and not delay project completion • Total float consumption is more complex because groups of activities share it; the entire group loses it and moves to the right (if not already completed) • If all of an activity’s total float is consumed, the activity becomes critical and a new critical path is created

31. Gantt Charts • A popular visual aid in project schedule management due to Henry Gantt (1861-1919) • Activities in rows • Time increments in columns • Bars depict start date, duration, and end date of activities • Triangles depict milestones • Colors or shading used for critical path; also for progress in completing activities once they begin • Weaknesses • Interdependencies difficult to show • May not identify critical activities, critical path, floats • Ineffective for project time acceleration & resource management • Computer software permits Gantt charts to be created from CPM networks, for use on-site and in managerial briefings