2. 8 - 2 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Operations Management Framework Insert New Resource/Profit Model

3. 8 - 3 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. C H A P T E R 8 Timeliness L E A R N I N G O B J E C T I V E S ▬ Explain the effect time has on each profitability measure. ▬ Describe the impact of feedback delay on quality. ▬ Explain the common time reduction strategies. ▬ Construct a Gantt chart. ▬ Sequence orders using the traditional sequencing rules. ▬ Describe the physical features of queues and describe how they affect queue performance. ▬ Compute the probability of x arrivals per unit time for a queue. ▬ Describe the psychological approaches to managing perception of queue length. ▬ Construct a network diagram for a project. ▬ Identify the critical path for a project using CPM calculations ▬ Calculate the likelihood of completing a project in a specified time. ▬ Complete the calculations necessary to effectively crash a project.

4. 8 - 4 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Operations Management Framework Time is money -Influences Customer Value -Influences Net Income -Influences Return on Assets Cost Quality Timeliness Quality Tools

5. 8 - 5 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Time and Customer Value Speed and flexibility -Faster processes allow greater flexibility Deliver more options in the same amount of time -Customers will only wait so long. Start later, closer to demand -Better predictions of what will be needed

6. 8 - 6 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Time Really Is Money Time affects profitability through net income -Time-based value attributes - Increasing net sales Response time Delivery dependability

7. 8 - 7 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Time Really Is Money Managing timing of payments to make money (managing “float”) -Travel Agents You pay right away (on a credit card) -They pay in 30 days (business billing cycle) Keep the interest -Insurance companies -Collect as only much as (or less than) they will eventually pay in claims -Invest money while they are waiting to pay out claims

8. 8 - 8 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. The Effect of Time on ROA The cash-to-cash cycle -Waiting for supplies to arrive -- Opportunity cost of sales -Waiting to sell product -- Delay of return on investment in inventory and production -Waiting to collect from customer -- Financing the customer’s purchase Exhibit 8.1 The Cash-to-Cash Cycle

9. 8 - 9 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. The Effect of Time on ROA Suppose the transaction in exhibit 8.1 netted a $200 return on total expenditures of $1000 (a 20% return). What would happen to ROA if the cash-to-cash cycle went from 17 weeks to 13 weeks? With a 17 week cash-to-cash cycle, there are approximately three transactions per year for a return of $600 (60%). Reducing the cash-to-cash cycle time to 13 weeks (a 23.5% reduction in time) results in the $1000 being turned over four times instead of three. $800 will now be generated, a shift from a 60% to an 80% return (33% increase in return).

10. 8 - 10 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. The Effect of Time on ROA Shorter delivery lead-times from suppliers mean lower inventory requirements Weekly Delivery Average Inventory (Cases) = 400 cases Average Inventory (Investment) = $106,000 Daily Delivery Average Inventory (Cases) = 80 cases Average Inventory (Investment) = $21,200 Example from Chapter 2 Deliveries of 800 cases weekly (all are consumed) Cases cost $265, Sell for $300 Weekly Net Income is $28,000 ROA = Net Income Total Assets ROA = $28,000/$106,000 = 26.42%ROA = $28,000/$21,200 = 132.08%

11. 8 - 11 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Feedback Delay Elimination of causes of quality problems depends on timely information.

12. 8 - 12 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. General Time Reduction Strategies Compressing time of activities Concurrent tasks

13. 8 - 13 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. General Time Reduction Strategies Insert exhibit 8.3

14. 8 - 14 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. General Time Reduction Strategies Insert exhibit 8.4

15. 8 - 15 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. General Time Reduction Strategies Insert exhibit 8.5

16. 8 - 16 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Scheduling Definition: Determination of when something is to be done and the tasks and activities required to do it -Aids in on-time completion Direct link to value perceived by customers -Impacts utilization of firm’s resources Direct link to productivity Forward scheduling -When start date is known and completion needs determination Backward scheduling -When completion date is known and start date needs determination

17. 8 - 17 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Scheduling Gantt Charts -Layout of steps within job Clinical trials process -Layout multiple jobs that utilize a single resource.

18. 8 - 18 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Traditional Job Shop Sequencing Sequencing Rules for scheduling multiple jobs at a single resourceSequencing Rules -First Come, First Served -Earliest Due Date -Shortest Processing Time -Critical Ratio Time Remaining/effort remaining C.R. < 1 means there is no way to complete the job on time Other simple rule that often get used -“Squeaky wheel gets greased” Less disciplined contexts Very often used

19. 8 - 19 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Example 8.1 Job Sequencing Using EDD Insert exhibit 8.8 (Old version has ‘due day’ for ‘due date’) Exhibit 8.7 Process-Oriented Layout

20. 8 - 20 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Example 8.1 Job Sequencing Using EDD

21. 8 - 21 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Example 8.2 Job Sequencing Using SPT

22. 8 - 22 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Example 8.3 Job Sequencing Using Critical Ratio

23. 8 - 23 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Traditional Job Shop Sequencing Most traditional sequencing rules assume a single operation. Slack Time Remaining -Slack = Days to due date - Total processing time (all operations) -Slack per remaining operation = Slack / Number of remaining operations Exhibit 8.12: Slack per Remaining Operations

24. 8 - 24 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. People are not Products: Treating People “Fairly” Queue configuration: The physical design of the lines and servers in a queuing system. Server: A resource that is able to complete the process or service that customers or jobs wait in queue for. Phase: A distinct step in a process that requires a separate queue. Jockeying: When customers switch lines hoping to move faster. Queue Discipline: The rules that management enforces to determine the next customer served in a queue.

25. 8 - 25 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Managing Queue Arrivals Arrivals are “Poisson Distributed” -Bounded at the bottom but not the top. You can never have fewer than 0 visitors in a given hour, but you can have thousands if you're really unlucky in that hour. -Asymmetric distribution

26. 8 - 26 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Managing Queue Arrivals (continued) Call center receives 36 calls per hour, Poisson distributed -What is the probability of receiving 41 calls? Probability of having exactly 41 calls 4.46% Probability of having 41 or fewer calls 82.17% Probability of having more than 45 calls 100%-93.91% = 6.09% Probability of having  30 &  40 calls 77.71%-13.79% = 63.92%

27. 8 - 27 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. People are not Products: Treating People “Fairly” People generally have a sense of “social justice” when it comes to queues -First Come, First Served seems the most fair -Supermarket express lanes: deemed fair within purchase limits! Milwaukee 4/8/98 (USAToday 4/13/98): One customer is irritated that another in front has “too many items”, pulls out knife and cuts off half her nose!

28. 8 - 28 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. People are not Products: Serving Customers Psychological features of queues -Keep customers busy -Keep customers informed -Treat customers fairly -Start the service as soon as possible -Exceed the customer’s expectations

29. 8 - 29 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. People are not Products: Queue Alternatives Avoid Queues: Developing Alternate Procedures -Express check-in and check-out (hotels, rental cars) -Pay bills by mail and online, not in person Parking tickets paid online -Automatic Checking Account Debits Phone,Utilities, Credit Cards, Mortgages

30. 8 - 30 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. People are not Products: Queue Alternatives Make the Customer the Server! -Supermarket self-checkout stations -Gasoline “service” stations -Fast food soft drinks -WWW buying and selling -Print your own boarding pass online

31. 8 - 31 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Project Management with Certain Time Estimates Summary of steps: -Determine activities that need to be accomplished -Determine precedence relationships and completion times -Construct network diagram -Determine the critical path -Determine early start and late start schedules

32. 8 - 32 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Create Network Diagram -Based on order of precedence among activities Project Management: Scheduling Projects with Certain Time Estimates

33. 8 - 33 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculation of the Critical Path Network approach helps calculate project duration -A “path” is a sequence of activities that begins at the start of the project and goes to the end of the project 1,2,3,5,6,7,8 1,2,4,6,7,8 -The “critical path” is the path that takes the longest to complete and thus determines the minimum duration of the project 12 4 35 678

34. 8 - 34 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculation of the Critical Path Exhibit 8.17: Project Detail

35. 8 - 35 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculation of the Critical Path Critical Path -The path that takes the longest to complete 12 4 35 678 4 weeks10 weeks 4 weeks 2 weeks3 weeks 16 weeks4 weeks1 week Exhibit 8.17: Project Detail

36. 8 - 36 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculation of the Critical Path Critical Path -The path that takes the longest to complete 12 4 35 678 4 weeks10 weeks 4 weeks 2 weeks3 weeks 16 weeks4 weeks1 week C.P. = 40 weeks Exhibit 8.17: Project Detail

37. 8 - 37 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculation of the Critical Path It is possible for multiple Critical Paths to exist -New information suggests that Activity 4 will take 5 weeks instead of 4 12 4 35 678 4 weeks10 weeks 4 weeks 2 weeks3 weeks 16 weeks4 weeks1 week X 5 Exhibit 8.17: Project Detail

38. 8 - 38 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculation of the Critical Path It is possible for multiple Critical Paths to exist -New information suggests that Activity 4 will take 5 weeks instead of 4 12 4 35 678 4 weeks10 weeks 5 weeks 2 weeks3 weeks 16 weeks4 weeks1 week X 5 C.P. = 40 weeks Exhibit 8.17: Project Detail

39. 8 - 39 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculation of the Critical Path Critical Path may also shift if non-critical activity is lengthened or Critical Path activity is shortened -Another update indicates it will actually take 6 weeks for Activity 4 12 4 35 678 4 weeks10 weeks 4 weeks 2 weeks3 weeks 16 weeks4 weeks1 week X 6 Exhibit 8.17: Project Detail

40. 8 - 40 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculation of the Critical Path 12 4 35 678 4 weeks10 weeks 6 weeks 2 weeks3 weeks 16 weeks4 weeks1 week X 6 C.P. = 41 weeks Critical Path may also shift if non-critical activity is lengthened or Critical Path activity is shortened -Another update indicates it will actually take 6 weeks for Activity 4 Exhibit 8.17: Project Detail

41. 8 - 41 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Determining Slack Slack - The amount of time an activity on a non-critical path can be delayed without affecting the duration of the project (i.e., without putting it on the critical path) -Uses four calculated values Early start - Earliest an activity can start (based on prerequisites) Early finish - Earliest it can finish (based on prerequisites & duration) Late start - Latest an activity can start and not delay the project Late finish - Latest an activity can finish and not delay the project

42. 8 - 42 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculating Early Start (ES) and Early Finish (EF) Move from left to right in network -ES for 1st activity usually zero -EF equals ES plus activity duration -ES is latest of the EF times of an activity’s predecessors Exhibit 8.17: Project Detail

43. 8 - 43 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Move from right to left in network -LF for last activity equals EF for last activity Or target date if different -LS equals LF minus activity duration -LF is earliest of the LS times of an activity’s followers Calculating Late Start (LS) and Late Finish (LF) Exhibit 8.17: Project Detail

44. 8 - 44 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculating Slack Slack - The amount of time an activity on a non-critical path can be delayed without affecting the duration of the project (i.e., without putting it on the critical path) Computed by either: Late Start - Early Start or Late Finish - Early Finish Activities that have zero slack are, by definition, on the critical path Exhibit 8.21: ES, EF, LS, LF, and Slack Values

45. 8 - 45 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Project Scheduling with Uncertain Time Estimates Summary of steps: -Determine activities that need to be accomplished -Determine precedence relationships and completion times -Construct network diagram -Determine the critical path -Determine early start and late start schedules -Calculate the variances for the activity times -Calculate the probability of completing by the desired due date

46. 8 - 46 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Project Scheduling with Time Uncertainty “Heuristic” approach to dealing with timing uncertainty -Based on understanding of individual activities as conforming to a “beta” distribution Take three time estimates -Optimistic - What is the (realistic) fastest we can get an activity done? -Pessimistic - What is the (realistic) worst case scenario for delay? -Most likely - What is our “most likely” estimate?

47. 8 - 47 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Project Scheduling with Time Uncertainty Calculate the “expected time” for the activity Where: T e = Expected Time o = Optimistic estimate m= Most likely estimate p = Worst-case (pessimistic) estimate

48. 8 - 48 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Project Scheduling with Time Uncertainty Activity #1 weeks Activity #3 weeks Activity #2 weeks

49. 8 - 49 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 12 4 35 678 4 weeks10 weeks 4.17 weeks 2.17 weeks3 weeks 16.17 weeks4.17 weeks1.17 weeks C.P. = 40.68 weeks Using Variation in Time Estimates to Assess Duration Probabilities How do we interpret this estimate??? Probabilistically: 50% chance we will finish faster, 50% chance we will finish slower Probability theory (“central limit theorem”) dictates that we assume that finish times across entire project are distributed “normally”

50. 8 - 50 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Using Variation in Time Estimates to Access Duration Probabilities So, if the “expected” duration ( T e ) of the project is 40.68 weeks, how can I tell the probability of actually finishing it in 39 weeks (or less)? -I take advantage of estimates of T e and make an estimate of  2 … -… draw on my knowledge of statistics (especially Normal distributions),… -… and use the “standard normal probability” table along with the following equation:

51. 8 - 51 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Using Variation in Time Estimates to Access Duration Probabilities Where: Z = Number of standard deviations D is from T e T e = Expected Time D = Project duration I am thinking about Note that this is , not  2, We have to take the square root of the “variance” to get the standard deviation

52. 8 - 52 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Using Variation in Time Estimates to Access Duration Probabilities We recognize that there is variation around our estimates -We are estimating “most likely” or “expected” not “exact” -Commonly assume a “Beta” distribution Another asymmetric distribution (because duration is never less than zero) Calculating variance of the activity’s duration estimate:

53. 8 - 53 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Activity #1weeks Activity #2 weeks Activity #3weeks Using Variation in Time Estimates to Access Duration Probabilities

54. 8 - 54 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Using Variation in Time Estimates to Assess Duration Probabilities Calculate Critical Path using T e Accumulate the variances of the individual activities Apply formula to estimate project duration probabilities Where: Z = Number of standard deviations D is from T e T e = Expected Time D = Activity duration I am thinking about

55. 8 - 55 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Using Variation in Time Estimates to Assess Duration Probabilities Exhibit 8.22: Expected Values and Variances of Time Estimates

56. 8 - 56 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 12 4 35 678 4 weeks10 weeks 4.17 weeks 2.17 weeks3 weeks 16.17 weeks4.17 weeks1.17 weeks Using Variation in Time Estimates to Assess Duration Probabilities What is the probability of finishing in 39 weeks or less? Exhibit 8.22: Expected Values and Variances of Time Estimates

57. 8 - 57 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 12 4 35 678 4 weeks10 weeks 4.17 weeks 2.17 weeks3 weeks 16.17 weeks4.17 weeks1.17 weeks C.P. = 40.68 weeks Sum of Variances = 2.56 weeks Using Variation in Time Estimates to Assess Duration Probabilities What is the probability of finishing in 39 weeks or less? Exhibit 8.22: Expected Values and Variances of Time Estimates

58. 8 - 58 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Using Variation in Time Estimates to Assess Duration Probabilities So, I look up the cumulative probability [G(z)] of the activity being completed before -1.05 standard deviations from the “most likely” estimate… -… and find out I have a 14.686% chance of finishing within 39 weeks!! Where: Z = Number of standard deviations D is from T e T e = Expected Time D = Activity duration I am thinking about 1.6 = the square root of 2.56!!! Standard deviation difference between “most likely” and desired duration

59. 8 - 59 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Using Variation in Time Estimates to Access Duration Probabilities - One Last Thought So, what if I want to be 90 percent sure that I hit the project duration that I tell my boss I will (or she will fire me)? -Reconfigure “Z” equation to solve for D -Pick the value of “Z” that corresponds to the level of certainty I want (90% = +1.30) -Solve weeks!!! What if I can stand to be only 80% sure?? Find probability under G(z) in Appendix B and translate to number of standard deviations

60. 8 - 60 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Crashing Projects A methodical approach to reducing project duration -Focus on the time of activities on the critical path -Looking for greatest improvement with least cost Additional labor, machinery Overtime and temporary employees Premiums paid to outside contractors for early delivery Steps -Create network -Identify critical path -Identify costs of reducing each activity on path -Reduce most cost effective activity -Look for critical path changes Beware of multiple critical paths -Crash next activity

61. 8 - 61 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Crashing Projects: Create the Network Exhibit 8.24: Network to Crash

62. 8 - 62 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. A8A8 B7B7 D 10 E 12 C7C7 F8F8 G9G9 H5H5 Crashing Projects: Identify the Critical Path C.P. = 35 days

63. 8 - 63 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Crashing Projects: Identify Costs of Crashing Each Activity Exhibit 8.25: Crash Time and Costs

64. 8 - 64 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. A8A8 B7B7 D 10 E 12 C7C7 F8F8 G9G9 H5H5 Crashing Projects: Reduce Most Cost Effective Activity 6 X

65. 8 - 65 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. A8A8 B7B7 D 10 E 12 C7C7 F8F8 G9G9 H5H5 Crashing Projects: Look for Critical Path Changes C.P. = 34 days 6 X

66. 8 - 66 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. A8A8 B7B7 D 10 E 12 C7C7 F8F8 G9G9 H5H5 Crashing Projects: Look for Critical Path Changes C.P. = 34 days 6 X Multiple Critical Paths Appear!!!

67. 8 - 67 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Crashing Projects: Crash Next Activity Both C.P.Path 1 OnlyPath 2 Only Exhibit 8.25: Crash Time and Costs

68. 8 - 68 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Crashing Projects: Summary Solution Exhibit 8.26: Crashing Summary

69. 8 - 69 McGraw-Hill/Irwin Operations Now, 2/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Caveats Time estimates are frequently wrong Early finishes are absorbed Cushions get wasted Resources aren’t always available when needed