1. Quick Recap Monitoring and Controlling

2. 2 Control Project Cost

3. 3 Cost Analysis Using the Expected Value Approach Spending extra money, in general should decrease project duration. Is this operation cost effective? The expected value criterion is used to answer this question.

4. 4 Analysis indicated: –Completion time within 180 days yields an additional profit of $1 million. –Completion time between 180 days and 200 days, yields an additional profit of $400,000. –Completion time reduction can be achieved by additional training. XYZ. COMPUTERS - Cost analysis using probabilities

5. 5 Two possible activities are considered for training. –Sales personnel training: Cost $200,000; New time estimates are a = 19, m= 21, and b = 23 days. –Technical staff training: Cost $250,000; New time estimates are a = 12, m = 14, and b = 16. Which option should be pursued? XYZ. COMPUTERS - Cost analysis using probabilities

6. 6 Evaluation of spending on sales personnel training. –This activity (H) is not critical. –Under the assumption that the project completion time is determined solely by critical activities, this option should not be considered further. Evaluation of spending on technical staff training. –This activity (F) is critical. –This option should be further studied as follows: Calculate expected profit when not spending $250,000. Calculate expected profit when spending $250,000. Select the decision with a higher expected profit. XYZ. COMPUTERS - Cost analysis using probabilities

7. 7 –Case 1: Do not spend $250,000 on training. Let X represent the project’s completion time. Expected gross additional profit = E(GP) = P(X 200)(0). Use Excel to find the required probabilities: P(X 200) =.25841 Expected gross additional profit =..065192(1M)+.676398(400K)+.25841(0) = $335,751.20 XYZ. COMPUTERS - Cost analysis using probabilities

8. 8 –Case 2: Spend $250,000 on training. The revised mean time and standard deviation estimates for activity F are:  F = (12 + 4 (14) + 16)/6 = 14  F = (16 -12)/6 =0.67  F  = 0(.67) 2 =0.44 Using the Excel PERT-CPM template we find a new critical path (A-B-C-G-D-J), with a mean time = 189 days, and a standard deviation of = 9.0185 days. XYZ. COMPUTERS - Cost analysis using probabilities

9. 9 –The probabilities of interest need to be recalculated. From Excel we find: P(X < 180) =.159152; P(180 < X < 200) =.729561 P(X > 200) =.111287 –Expected Gross Additional Revenue = P( X 200)(0) =.159152(!M)+.729561(400K)+.111287(0) = $450,976.40 XYZ. COMPUTERS - Cost analysis using probabilities

10. 10 The expected net additional profit = 450,976-250,000 = $200,976 < $335,751 Expected additional net profit when spending $250,000 on training Expected profit without spending $250,000 on training Conclusion: Management should not spend money on additional training of technical personnel. XYZ. COMPUTERS - Cost analysis using probabilities

11. 11 Cost Analyses Using The Critical Path Method (CPM) The critical path method (CPM) is a deterministic approach to project planning. Completion time depends only on the amount of money allocated to activities. Reducing an activity’s completion time is called “crashing.”

12. 12 There are two crucial completion times to consider for each activity. –Normal completion time (T N ). –Crash completion time (T C ), the minimum possible completion time. Crash time/Crash cost The cost spent on an activity varies between –Normal cost (C N ). The activity is completed in T N. –Crash cost (C C ). The activity is completed in T C.

13. 13 Crash time/Crash cost – The Linearity Assumption The maximum crashing of activity completion time is T C – T N. This can be achieved when spending C N – C C. Any percentage of the maximum extra cost (C N – C C ) spent to crash an activity, yields the same percentage reduction of the maximum time savings (T C – T N ).

14. 14 Time Cost ($100) 20 18 16 14 12 10 8 6 4 2 5 10 15 20 25 30 35 40 45 Normal C N = $2000 T N = 20 days Add to the normal cost... …and save on completion time Add more to the normal cost... Crashing C C = $4400 T C = 12 days …and save more on completion time Add 25% of the extra cost... … to save 25% of the max. time reduction Total Cost = $2600 Job time = 18 days A demonstration of the Linearity Assumption

15. 15 Marginal Cost = Additional Cost to get Max. Time Reduction Maximum Time reduction = (4400 - 2000)/(20 - 12) = $300 per day M = E R Crash time/ Crash cost - The Linearity Assumption

16. 16 If the deadline to complete a project cannot be met using normal times, additional resources must be spent on crashing activities. The objective is to meet the deadline at minimal additional cost. Crashing activities – Meeting a Deadline at Minimum Cost

17. 17 XYZ fast food restaurants. It is planning to open a new restaurant in 19 weeks. Management wants to –Study the feasibility of this plan, –Study suggestions in case the plan cannot be finished by the deadline. XYZ Restaurants – Meeting a Deadline at Minimum Cost

18. 18 XYZ Restaurants – Without spending any extra money, the restaurant will open in 29 weeks at a normal cost of $200,000. When all the activities are crashed to the maximum, the restaurant will open in 17 weeks at crash cost of $300,000. Determined by the PERT.xls template

19. 19 A D C B E FG I H XYZ Restaurants – Network presentation L O J N M K P

20. 20 XYZ Restaurants – Marginal costs R = T N – T C = 5 – 3 = 2 E = C C – C N = 36 – 25 = 11 M = E/R = 11/2 = 5.5

21. 21 XYZ Restaurants – Heuristic Solution Three observations lead to the heuristic. –The project completion time is reduced only when critical activity times are reduced. –The maximum time reduction for each activity is limited. –The amount of time a critical activity can be reduced before another path becomes critical is limited. Small crashing problems can be solved heuristically.

22. 22 Linear Programming Approach –Variables X j = start time for activity j. Y j = the amount of crash in activity j. –Objective Function Minimize the total additional funds spent on crashing activities. –Constraints No activity can be reduced more than its Max. time reduction. Start time of an activity takes place not before the finish time of all its immediate predecessors. The project must be completed by the deadline date D. XYZ Restaurants – Linear Programming

23. 23 Min 5.5Y A +10Y B +2.67Y C +4Y D +2.8Y E +6Y F +6.67Y G +10Y H + 5.33Y I +12Y J +4Y K +5.33Y L +1.5Y N +4Y O +5.33Y P Minimize total crashing costs XYZ Restaurants – Linear Programming

24. 24 Min 5.5Y A +10Y B +2.67Y C +4Y D +2.8Y E +6Y F +6.67Y G +10Y H + 5.33Y I +12Y J +4Y K +5.33Y L +1.5Y N +4Y O +5.33Y P Maximum time-reduction constraints H F E D C B A 0.5 2.0 0.5 2.5 1.0 1.5 Y Y Y Y Y Y Y        Y G 1.5  …….. 19FINX  )( ST Meet the deadline Linear Programming

25. 25 XAXA Min 5.5Y A +10Y B +2.67Y C +4Y D +2.8Y E +6Y F +6.67Y G +10Y H + 5.33Y I +12Y J +4Y K +5.33Y L +1.5Y N +4Y O +5.33Y P Activity can start only after all the Predecessors are completed. X B  X A +(5 – Y A ) B XBXB A -YA-YA X A +5-Y A A X A +5 B XBXB B XBXB B XBXB Linear Programming B XBXB

26. 26 X B  X A +(5 – Y A ) X C  X A +(5 – Y A ) X D  X A +(5 – Y A ) X e  X A +(5 – Y A ) X F  X A +(5 – Y A ) X B  X B +(1 – Y B ) X F  X C +(3 – Y C ) X G  X F +(1 – Y F ) X(FIN)  X N +(3 – Y N ) X(FIN)  X O +(4 – Y O ) X(FIN)  X P +(4 – Y P ) Min 5.5Y A +10Y B +2.67Y C +4Y D +2.8Y E +6Y F +6.67Y G +10Y H + 5.33Y I +12Y J +4Y K +5.33Y L +1.5Y N +4Y O +5.33Y P Activity can start only after all the predecessors are completed. …….. Linear Programming

27. 27 XYZ Restaurants – Deadline Spreadsheet

28. 28 XYZ has the policy of not funding more than 12.5% above the “normal cost” projection. Crash budget = (12.5%)(200,000) = 25,000 Management wants to minimize the project completion time under the budget constraint. XYZ Restaurants – Operating within a fixed budget

29. 29 5.5Y A + 10Y B + 2.67Y C + 4Y D + 2.8Y E + 6Y F + 6.67Y G + 10Y H + 5.33Y I + 12Y J + 4Y K + 5.33Y L + 1.5Y N + 4Y O + 5.33Y P  25 The crash funds become a constraint Minimize 5.5Y A + 10Y B + 2.67Y C + 4Y D + 2.8Y E + 6Y F + 6.67Y G + 10Y H + 5.33Y I + 12Y J + 4Y K + 5.33Y L + 1.5Y N + 4Y O + 5.33Y P The completion time becomes the objective function X(FIN)  19 Minimize X(FIN) The other constraints of the crashing model remain the same. XYZ Restaurants – Operating within a fixed budget

30. 30 XYZ Restaurants – Budget Spreadsheet

31. 31 PERT/COST PERT/Cost helps management gauge progress against scheduled time and cost estimates. PERT/Cost is based on analyzing a segmented project. Each segment is a collection of work packages. PROJECT Work Package 1 Activity 1 Activity 2 Work Package 2 Activity 3 Activity 5 Work Package 3 Activity 4 Activity 6

32. 32 –Once started, a work package is performed continuously until it is finished. –The costs associated with a work package are spread evenly throughout its duration. Work Package - Assumptions

33. 33 For each work package determine: –Work Package Forecasted Weekly cost = Budgeted Total Cost for Work Package Expected Completion Time for Work Package (weeks) –Value of Work to date = p(Budget for the work package) where p is the estimated percentage of the work package completed. –Expected remaining completion time = (1 – p)(Original Expected Completion Time) Monitoring Project progress

34. 34 Completion Time Analysis Use the expected remaining completion time estimates, to revise the project completion time. Cost Overrun / Underrun Analysis For each work package (completed or in progress) calculate Cost overrun = [Actual Expenditures to Date] - [Value of Work to Date]. Monitoring Project progress

35. 35 A project may be found to be behind schedule, and or experiencing cost overruns. Management seeks out causes such as: –Mistaken project completion time and cost estimates. –Mistaken work package completion times estimates and cost estimates. –Problematic departments or contractors that cause delays. Monitoring Project Progress – Corrective Actions

36. 36 Possible Corrective actions, to be taken whenever needed. –Focus on uncompleted activities. –Determine whether crashing activities is desirable. –In the case of cost underrun, channel more resources to problem activities. –Reduce resource allocation to non-critical activities. Monitoring Project Progress – Corrective Actions

37. 37 Twenty weeks before the election the campaign remaining activities need to be assessed. If the campaign is not on target or not within budget, recommendations for corrective actions are required. Election CAMPAIGN

38. 38 Work packages to focus on CAMPAIGN – Status Report

39. 39 –The remaining network at the end of week 20. I9I9 Finish F 7.8 H 15 (1-p)(original expected completion time)=(1-0.25)(20)=15 20+15=35 20+7.8=27.8 27.8+9=36.8.8 The remaining activities are expected to take 0.8 weeks longer than the deadline of 36 weeks. CAMPAIGN – Completion Time Analysis

40. 40 Estimated work value to date=(13,000)(0.40)=$5,200 Cost overrun = 5600 - 5200 = 400 CAMPAIGN – Project Cost Control

41. 41 CAMPAIGN – Results Summary The project is currently.8 weeks behind schedule There is a cost over-run of $3900. The remaining completion time for uncompleted work packages is: –Work package F: 7.8 weeks, –Work package H: 15 weeks, –Work package I: 9 weeks. Cost over-run is observed in –Work package F: $400, –Work package H: $500.