Project Scheduling Professor Stephen Lawrence Graduate School of Business Administration University of Colorado Boulder, CO

2 Project Management Management complex projects Many parallel tasks Deadlines and milestones must be met Difficult to know “what to do first” Difficult to know when project is in trouble Often have competition for limited resources When to use:

3 Examples Building a new airport Designing a new computer product Launching an advertising campaign Construction projects of all types Maintenance projects Curriculum reviews

4 Project Mgmt Techniques Critical Path Method (CPM) Developed by DuPont (1950’s) Plan and control maintenance of chemical plants Credited with reducing length of maintenance shutdown by 40% Project Evaluation and Review Technique (PERT) Developed by Navy (early 1960’s) Plan and control the Polaris missile project Credited with speeding up project by 2 years

Critical Path Method (CPM)

6 Graphical method of portraying relationship of project activities An activity is any discrete part or task of a project which takes resources and time to complete Activities exhibit precedence relations (some must be completed before others can start) Activities with their precedence relations form a project network Critical Path Method finds the longest path through the resulting project network

7 Precedence Relations ActivityImmediate PredecessorDuration (days) A(Start)BACADB, C

8 Simple Project Network A A B B C C D D

9 Activity Start/Finish Times ES LS EF LF Activity Name Activity Duration Early Finish Time Late Finish Time Early Start Time Late Start Time

10 Finding the Critical Path A D C B

11 CPM Terminology Critical Path: the chain of activities along which the delay of any activity will delay the project Early Start Time (ES): the earliest that an activity could possibly start, given precedence relations Late Start Time (LS): the latest that an activity could possibly start without delaying the project Early Finish Time (EF): the earliest that an activity could possibly finish Late Finish Time (LF): the latest that an activity could possibly finish without delaying the project Activity Slack: the amount of “play” in the timing of the activity; slack = LST-EST = LFT-EFT

12 Example Suppose you are an advertising manager responsible for the launch of a new media advertising campaign. The campaign (project) has the following activities: ActivityPredecessors Time A. Media bids none2 wks B. Ad concept none6 C. Pilot layouts B3 D. Select media A8 E. Client check-off A,C6 F. Pre-production B8 G. Final production E,F5 H. Launch campaign D,G0

13 Example Project Network A2A2 A2A2 B6B6 B6B6 F8F8 F8F8 D8D8 D8D8 C3C3 C3C3 E6E6 E6E6 G5G5 G5G5 H0H0 H0H0 Start

Program Evaluation and Review Technique (PERT)

15 PERT Similar to Critical Path Method (CPM) Accounts for uncertainty in activity duration estimates Provides estimates of project duration probabilities Best used for highly uncertain projects new product development unique or first-time projects research and development

16 Simple Project Network A A B B C C D D

17 A Simple Example Most Optimistic Most Likely Most Pessimistic Activity 210A 17B 46C D mab

18 Distribution Assumption Assume a “Beta” distribution activity duration density mab

19 Expected Duration & Variance Expected Time = Variance = a + 4m + b 6 (b - a) 2 36 For the Beta Distribution:

20 Distribution Assumption activity duration density mab expected duration

21 Expected Duration & Variance ET = Var = a + 4m + b 6 (b - a) 2 36 = 2+4(3)+10 6 = 4.0 = (10-2) 2 36 = Activity A

22 Critical Path of the Example A D C B Critical Path Duration =

23 Time and Variance Example Expected Time Variance Critical Path? Activity A 31.0B C D

24 Probability of Completion What is the probability that a project will be completed by a specified due date? Due Date - Expected Completion Date Sum of the Variances on the Critical Path z =z = Normal Distribution z Due Date Expected Completion

25 Completion Probability Example What is the probability of completing the project within 12 days? z = = From a Z-table for standard Normal distributions: Probability of completion =

26 Larger Example (a) (m) (b) Activity Preds Optimistic Likely Pessimistic A. none wks B. none 4 68 C. B D. A E. A,C 3 69 F. B G. E,F H. D,G 0 00 Suppose the duration of the activities of the ad campaign are, in fact, uncertain:

27 Activity D Suppose the duration of the activities of the ad campaign are, in fact, uncertain: (a) (m) (b) Activity Preds Optimistic Likely Pessimistic A. none wks B. none 4 68 C. B D. A E. A,C 3 69 F. B G. E,F H. D,G 0 00

28 Activity D Variance of Activity Duration for “D”: Var = (b - a) 2 36 = (10-2) 2 36 Expected Activity Duration for “D”: ET = a + 4m + b 6 = 2+4(8)+10 6

29 Example Project Network A2A2 A2A2 B6B6 B6B6 F8F8 F8F8 D D C3C3 C3C3 E6E6 E6E6 G5G5 G5G5 H0H0 H0H0 Start Critical Path Duration = 20 days 7.33

30 Project Duration Statistics A B C E F G H Activity Critical? Mean Var C.P. Var D

31 Using Project Statistics What is the probability that the ad campaign can be completed in 18 weeks? 20? 24? 18 weeks: Z = x -   sqrt(1.55) = Prob(x<18) = = Corresponding probability from standard normal Z-Table is :

32 Using Project Statistics What is the probability that the ad campaign can be completed in 18 weeks? 20? 24? 18 weeks: Z =-1.61Prob(x<18) = 20 weeks: Z =0.00Prob(x<20) = 24 weeks: Z =3.21Prob(x<24) =

33 Other Project Mgmt Techniques Project crashing where to devote extra resources to reduce activity/project durations while minimizing costs Resource leveling how to schedule resources (equipment, people) to minimizes peaks and valleys Multiple resource scheduling how to schedule resources when activities can require more than one resource type Cash flow and budgeting combine cash and budget information with project scheduling to track expenditures, project cash flows