Concept explainers
A.
Interpretation: The network diagram representing the activities of the project is to be drawn and the critical path based on the most likely times is to be determined.
Concept Introduction: Program Evaluation and review technique is a planning and control tool, wherein the work flow of various activities of a project are graphically represented and analyzed. This technique is distinct in the way that it deals with uncertainty in the activity completion times.
B.
Interpretation: Theprobability that the project will be completed before 28 weeks and before 32 weeks is to be computed.
Concept Introduction: Program Evaluation and review technique is a planning and control tool, wherein the work flow of various activities of a project are graphically represented and analyzed. This technique is distinct in the way that it deals with uncertainty in the activity completion times.
C.
Interpretation: The number of weeks within which the project is to be completed given the completion probability of 0.95 is to be computed.
Concept Introduction: Program Evaluation and review technique is a planning and control tool, wherein the work flow of various activities of a project are graphically represented and analyzed. This technique is distinct in the way that it deals with uncertainty in the activity completion times.
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EBK PRODUCTION AND OPERATIONS ANALYSIS
- A solved PERT problem is detailed in the table below. The expected time and variance values and the critical activities are given in the table below. Answer the following questions by filling the blanks (WRITE YOUR ANSWERS TO 2 DECIMAL PLACES. DO NOT ROUND UP OR DOWN): a. The expected project completion time for this problem is and the standard deviation is . b. There is a 0.95 probability that the project will be completed by weeks. Activity Expected time Variance Critical? A 10 0.36 Yes B 7 0.11 No C 7 0.25 No D 3 0.48 Yes E 5 1.60 Yes F 7 0.69 No G 2 3.69 Yesarrow_forwardWhy might a probabilistic estimate of a project’s completion time based solely on the variance of the critical path be misleading? Under what circumstances would it be acceptable?arrow_forwardGiven the following network and activity time estimates, determine: The expected time and variance for each activity The critical path. This must be based on your calculations of the start and finish times and not by inspection. The expected project completion time, variance and standard deviation The probability that the project will be completed in 20 weeks or lessarrow_forward
- What is the value of the missing item labeled (a) in the table above? Round to the nearest integer. What is the value of the missing item labeled (b) in table above? Round to two decimals. Draw the network diagram for this project. Clearly label the earliest start, earliest finish, latest start, latest finish and slack for each activity. Specify the critical path and the critical activities. State the expected C.P. duration State the variance of the critical path. What is the probability that the dashboard will be delivered within 20 days?arrow_forwardWhat is the value of the missing item labeled (a) in the table above? Round to the nearest integer. What is the value of the missing item labeled (b) in table above? Round to two decimals. Draw the network diagram for this project. Clearly label the earliest start, earliest finish, latest start, latest finish and slack for each activity. Specify the critical path and the critical activities. State the expected C.P. duration State the variance of the critical path. What is the probability that the dashboard will be delivered within 20 days?arrow_forwardActivity E has an optimistic time of 9 days, a most likely time of 12 days, and a pessimistic time of 15 days. Estimate its expected time and standard deviation.arrow_forward
- The Farmer's American Bank of Leesburg is planning to install a new computerized accounts system. Bank management has determined the activities required to complete the project, the precedence relationships of the activities, and activity time estimates, as shown in the following table. Use POM- QM to analyze this project. According to the result of POM-QM, the expected project completion time is (type number only, no text) Activity a b C d C f 8 k Activity Description Position recruiting System development System training Equipment training Manual system test Preliminary system changeover Computer-personnel interface Equipment modification Equipment testing System debugging and installation Equipment changeover Activity Predecessor a a b, c b, c d, e d, e h f.g a 5 3 4 5 I 1 3 Time Estimates (weeks) 1 1 2 5 m 8 12 7 8 I 4 6 2.5 1. 2 8 b 17 15 10 23 1 13 9 7 1 2 11arrow_forwardThe following estimates of activity times (in days) are available for a small project: Activity Optimistic Most Probable Pessimistic A 4 5.0 6 B 8 9.0 10 C 7 7.5 11 D 7 9.0 10 E 6 7.0 9 F 5 6.0 7 An analyst determined that the critical path consists of activities B-D-F. Compute the expected project completion time and the variance of this path. What is the probability the project will be completed in 25 days?arrow_forwardConsider a project that has been modeled as in the table below. Part a) Draw the PERT/CPM network for this project and determine the project’s expected completion time μP and its critical path. Part b) Suppose the standard deviations of the activity durations are σA = 2, σB = 1, σC = 0, σD = 2, σE = 3, and σF = 0. Then please estimate the standard deviation of the overall project’s standard deviation σP . Part c) Suppose for the standard Normal random variable Z, we know P[−1 ≤ Z ≤ +1] ' 68%, P[−2 ≤ Z ≤ +2] ' 95%, and P[−3 ≤ Z ≤ +3] ' 99.7%. Then, approximately what time T is one for which there is only a less than 2.5% chance for the completion time to beat (be shorter than)? *Please answer a-c and type your work and answers or write them neatly please* Thank youarrow_forward
- Consider a project that has been modeled as in the table below. Part a) Draw the PERT/CPM network for this project and determine the project’s expected completion time μP and its critical path. Part b) Suppose the standard deviations of the activity durations are σA = 2, σB = 1, σC = 0, σD = 2, σE = 3, and σF = 0. Then please estimate the standard deviation of the overall project’s standard deviation σP . Part c) Suppose for the standard Normal random variable Z, we know P[−1 ≤ Z ≤ +1] ' 68%, P[−2 ≤ Z ≤ +2] ' 95%, and P[−3 ≤ Z ≤ +3] ' 99.7%. Then, approximately what time T is one for which there is only a less than 2.5% chance for the completion time to beat (be shorter than)? *Please answer a-c and either type your work and answers or write them neatly showing each step, please* NO EXCEL Thank you!arrow_forwardColeman Rich Control Devices, Inc., produces custom-built relay devices for auto makers. The most recent project undertaken by Rich requires 14 different activities. Rich's managers would like to determine the total project completion time (in days) and those activities that lie along the critical path. The appropriate data are shown in the following table: Activity A B с D E F G a) The expected completion time of the project = a 4 1 6 5 1 2 1 Time (days) m 6 2 6 8 9 3 7 b 7 3 6 11 18 6 8 Immediate Predecessor(s) A A B, C D D Activity a H 4 I 1 J 2 K 8 2 1 6 M N days (round your response to two decimal places). Time (days) = m 4 6 5 9 4 2 8 b 6 8 7 11 6 3 10 Immediate Predecessor(s) E, F G, H K L, M The activities that represent the project's critical path are b) If the time to complete the activities on the critical path is normally distributed, then the probability that the critical path will be finished in 53 days or less = decimal places). c) Using the standard normal table, the…arrow_forwardA project consists of seven activities, lettered A through F below. For each activity, the estimated normal time in number of weeks, crash time, normal cost, crash cost, and its preceding activity are given. Normal Time Crash Time Normal Cost Crash Cost Immediate Activity (weeks) (weeks) (Peso) (Peso) Predecessor(s) A 4 2,000 2,600 В 2 1 2,200 2,800 3 500 500 4 2,300 2,600 A E 3 900 1,200 В F 3 2 3,000 4,200 G 1,400 2,000 D, E 4 How much will the costs increase when this project is crashed at its maximum? O P 15,900.00 O P 12,300.00 O P 1,600.00 O Not in the choices O P 2,875.00arrow_forward
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