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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Production and Operations Analysis, Seventh Edition
- Problem 2: Chicago Project You are asked to manage an upcoming project for a client based in Chicago. Your supervisor, Susan, asked you to determine if the project will be completed in 2 months (60 days). Susan sent you the estimated time durations (in days) for the project. The information is given below: Compute the expected time and variance for each activity. What is the critical path and the expected duration of the project? What is the probability that the project will take longer than 58 days to complete?arrow_forwardConsider a project that has been modeled as in Table 1 Draw the PERT/CPM network for this project and determine the project’s expected completion time µP and its critical path. 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 . 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)?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_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_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_forward
- Draw CPM network of activities tabulated below: 1. Calculate the expected duration and the standard deviation for the critical path. 2. Compute the followings: (a) The probability that the project will finish by the end of day 50 (b) The probability that the project will finish at day 52 (c) The probability that the project will finish before the start of day 49. (d) The completion date with at least a 95% confidence levelarrow_forwardThe 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_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 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_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_forwardThere are four activities on the critical path, and they have standard deviations of 1, 3, 9, and 3 days. Determine the standard deviation of the critical path.arrow_forward
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