Practical Operations Management
2nd Edition
ISBN: 9781939297136
Author: Simpson
Publisher: HERCHER PUBLISHING,INCORPORATED
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Chapter 7, Problem 25P
Summary Introduction
Interpretation:
The probability of the project will be completed within 3 weeks when only two path A-B-E of the probability of 55% and another path C-D-F of probability 90% being completed in 3 weeks.
Concept Introduction:
Probability is the field of mathematics concerning numerical description and which mainly deals with how likely an event is going to occur. The probability of a happening is a number between 0 and 1, where 0 indicates impossibility, and 1 indicates possibility.
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The following information has been computed from a project:
Expected total project time = T = 62 weeks
Project variance = 81
1- What is the probability that the project will be completed 18 weeks before its expected
completion date?
2- Draw Normal Curve & Analysis your solution with conclusion
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 type your work and answers or write them neatly please* Thank you
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!
Chapter 7 Solutions
Practical Operations Management
Ch. 7 - Prob. 1DQCh. 7 - Prob. 2DQCh. 7 - Prob. 3DQCh. 7 - Prob. 4DQCh. 7 - Prob. 5DQCh. 7 - Prob. 6DQCh. 7 - Prob. 1PCh. 7 - Prob. 2PCh. 7 - Prob. 3PCh. 7 - Prob. 4P
Ch. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - Prob. 9PCh. 7 - Prob. 10PCh. 7 - Prob. 11PCh. 7 - Prob. 12PCh. 7 - Prob. 13PCh. 7 - Prob. 14PCh. 7 - Prob. 15PCh. 7 - Prob. 16PCh. 7 - Prob. 17PCh. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - Prob. 24PCh. 7 - Prob. 25PCh. 7 - Prob. 26PCh. 7 - Prob. 27PCh. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Prob. 30PCh. 7 - Prob. 31PCh. 7 - Prob. 32PCh. 7 - Prob. 1.1QCh. 7 - Prob. 1.2QCh. 7 - Prob. 1.3QCh. 7 - Prob. 1.4QCh. 7 - Prob. 2.1QCh. 7 - Prob. 2.2QCh. 7 - Prob. 2.3Q
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- Why 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_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 3 2,000 2,600 B 1 2,200 2,800 3 500 500 D 8 4 2,300 2,600 A E 6 900 1,200 В F 3 3,000 4,200 G 4 1,400 2,000 D, E If you wish to reduce the time required to complete this project by one week, which activity should be crashed? O Activity C O Activity D O Activity E O Activity B O Activity Aarrow_forwardThe expected duration of a project is 26 weeks and the total project variance along the critical path is 11.555 Calculate the probability of completing the project in 25 weeks. Calculate the Z value which is used for finding the probability of completion of the project from the normal distribution table O a. + 0.0865 O b. + 0.2942 O C. - 0.0865 O d. - 0.2942arrow_forward
- A 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 3 2,000 2,600 2 1 2,200 2,800 3 500 500 D 8. 4 2,300 2,600 A E 6 3 900 1,200 F 3 2 3,000 4,200 G 4 2 1,400 2,000 D, E What is the maximum time that can be crashed? O Not in the choices Seven weeks Five weeks O Four weeks O Six weeksarrow_forwardThe managers at AllBirds have operations in multiple countries, which operate on different financial management systems. This has been increasingly challenging for the company, so the Justin is looking to consolidate and integrate the financial management across all locations into a single software system that can operate across the national boundaries. This is a new, complicated and lengthy project, so Justin has identified a set of activity categories that will need to be carefully managed, as noted in the table. What is the probability that project can be completed two months early?arrow_forwardA large Southeast city is requesting federal funding for a park-and-ride project. One of the requirements in the request application is a network plan for the design phase of the project. Sophie Kim, the chief engineer, wants you to develop a project network plan to meet this requirement. She has gathered the activity time estimates and their dependencies shown here. Description Survey Soils report C Traffic design D Lot layout E Approve design Illumination G Drainage H Landscape I Signage J Bid proposal ID A B The project is expected to take The critical path is: Early start for Activity E is: Late finish for Activity F is: Slack for Activity C is: Predecessor None A A A B, C, D E E E E F, G, H, I Time (days) 13 22 21 a 9 74 20 20 22 17 15 12 days. day(s).arrow_forward
- There are five critical paths in a network. A-B-C-D-X-E, A-F-U-Y-E, A-F-G-Y-E, A-H- J-K-L-E and A-S-T-Y-E. Each activity in this network can be crashed by 123 hours. The maximum possible reduction in the project duration will be: O a. 861 hour O b. 492 hours O c. 615 hours O d. 1722 hours e. Insufficient informationarrow_forwardConsider 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_forwardConsider the project described in the table below: Activity Duration A B C D E F G H 9 4 8 8 5 7 4 6 OEST-9 and LCT = 15 OEST=9 and LCT = 13 Immediate Predecessor What is the earliest start time (EST) and latest completion time (LCT) of activity B? OEST=9 and LCT = 20 OEST-9 and LCT-17 - A A A B B,C C,D E,F,Garrow_forward
- In the project considered below, activity crashing can take place over a wide range of reduction times. The cost per day of reduction is given: Activity Immediate Normal Time Cost/day Lower Time Predecessor (days) Limit A None 3 450 1 B None 4 300 2 A 3 200 D E 100 E A,B 500 1 F C.D 4 600 3 For example, activity C can be crashed from its normal time of 3 days down to as little as 1 day or anywhere in between; the cost per day to crash C is 200. a) Draw a network diagram for this project. What is the critical path? How long will the project take, if no crashing takes place? b) Determine the least cost way to crash activities in order to complete the project in 11 days; in 10 days; in 9 days; in 8 days. c) Suppose the due date for the project is 5 days and a penalty of $500 a day is assessed for each day late. What is the optimal number of days to crash the project? Why?arrow_forwardFrom the following data, calculate BAC, BCWS, BCWP, ACWP, EV, CV and SV when the Status Checking Date is May 5, 2017. Is the project over or under budget? By what percentage? Is the project behind or ahead of schedule? By what percentage? Project Status Status Checking Date 5/5/2017 Actual Effort Estimated Actual Completion Estimated Work Effort by Status Checking Date Completion Date Tasks Date (mm/dd/yy) (mm/dd/yy) (Person Days) (Person Days) 10 2/5/2017 2/5/2017 15 20 3/15/2017 3/25/2017 20 25 4/25/2017 4. 25 25 5/5/2017 4/1/2017 15 10 5/25/2017 10 5 6/10/2017 7 5 6/15/2017 HTML Editor 2. 3. 5.arrow_forwardA project being analyzed by PERT has 60 activities, 13 of which are on the critical path. If the estimated time along the critical path is 214 days with a project variance of 169, what is the probability that the project will be completed within 224 days? O 0.50 O 0.84 0.80 O 0.78arrow_forward
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