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
- Draw the network diagram. Calculate the expected duration and variance of each activity. Calculate the expected duration and variance of the critical path. Calculate the probability that the project will be completed in less than 28 weeks.arrow_forwardA project has the activity duration and cost information indicated in the table where all times are in weeks. What is the total cost for completing this project in 50 days? Activity Predecessor Normal Time Normal Cost Crash Time Crash Cost A -- 8 $12,000 5 $21,000 B A 12 $20,000 9 $30,000 C A 15 $24,000 10 $60,000 D B 3 $10,000 2 $15,000 E C 9 $17,000 6 $34,000 F E 7 $5,000 6 $6,000 G D 8 $14,000 6 $20,000 H A 12 $22,000 10 $30,000 I H 6 $50,000 5 $55,000 J F, G, I 11 $33,000 9 $50,000arrow_forwardtheir is no predecessors Draw the network diagram for this project. Clearly label the earliest start, earliest finish, latest start and latest finish 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 dinner will be ready within 3 minutes early?arrow_forward
- Consider a project that has been modeled as in the table below: a. Draw the PERT/CPM network for this project and determine the project’sexpected completion time μP and its critical path. 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 standarddeviation of the overall project’s standard deviation σP . 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 forthe completion time to beat (be shorter than)? *Please solve a-c and neatly write or type your answers, showing your steps, NO EXCEL*arrow_forwardtheir is no predecessor Draw the network diagram for this project. Clearly label the earliest start, earliest finish, latest start and latest finish 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 dinner will be ready within 3 minutes early?arrow_forwardFor each of the following network diagrams, determine both the critical path and the expected project duration. The numbers on the arrows represent expected activity times.a. AOA diagram b. AON diagram c. AOA diagram d. AON diagramarrow_forward
- Use the Program Evaluation and Review Technique to represent the project in an activity network. In conjunction with the Critical Path Method, use the activity network to find the shortest time possible to complete the project, to identify the critical jobs in the project, and to determine the earliest and latest that each activity can start and finish without making the project completion longer.a=1, b=1, c=6, d=5, e=2, f=5; andab=1x1=1, bc=1x6=6, cd=6x5=30, de=5x2=10, ef=2x5=10, af=1x5=5.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_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 either type your work and answers or write them neatly showing each step, please* NO EXCEL Thank you!arrow_forward
- A project has 7 activities P, Q, R, S, T, U, and V. Three time estimates (optimistic, most-likely, pessimistic) are used for each activity. Write down your answers to all parts of the question in the box given below. Give your answer to 3 decimal places. (Note (a) has of 2 parts and (b) has of 3 parts) For activity Q, these time estimates are as follows: optimistic time = 9, most-likely time = 14, pessimistic time = 20. Write down the average activity time for Q the variance of activity time for Q. The critical path of this project has a mean project time of 44 days and a standard deviation of 5 days. Assume project completion time is normally distributed. Find the probability that the project will be completed in 47 days. Find the probability that the project will take more than 40 days. We want to set a deadline for this project completion. If the probability of meeting this set deadline is 0.88, what will be the deadline for this project.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_forwardYou are provided with the following information for a project, with activity durations given in weeks: Activity Immediate Optimistic Most Likely Pessimistic Predecessor Time (a) Time (m) Time (b) A ____ 2 3 4 B ____ 2 4 6 C A 1 2 3 D B 3 6 9 E C, D 7 8 9 F D 4 7 10 G E 3 4 5 H E, F…arrow_forward
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