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Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Consider a project for which the following activities and time estimates in weeks apply
activity |
To |
tm |
tp |
1-2 |
3 |
5 |
8 |
1-3 |
2 |
3 |
5 |
1-5 |
2 |
3 |
4 |
2-3 |
1 |
2 |
5 |
2-6 |
7 |
8 |
9 |
3-4 |
1 |
3 |
6 |
3-5 |
2 |
4 |
6 |
4-5 |
1 |
2 |
4 |
5-6 |
1 |
2 |
3 |
- Draw the project network
- Compute the expected time and variance for each activity
iii. Compute slack for each event and find the critical path
- Find the length of the critical path and the project duration
- Approximate the probability that activity 3 – 4 will have positive slack. What is the
managerial implication of that probability?
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- A project has activities, durations, costs, and precedence relationships as shown in the following table. Accelerated Duration (Weeks) Immediate Predecessor Path A-C-E A-D-H-I B-F-H-I Activity B-G-I A B с D E F GJ H I Present Duration (Weeks) Project is reduced from Activity Crashed (1 week) Additional Cost for Crashing 8 13 8 18 13 15 10 7 5 $ to B B 7 I 11 4 16 8 13 8 6 4 $14,000 Develop a time-cost trade-off analysis. Detail the steps that you would use to accelerate or crash the project to its minimum duration at the lowest cost. Determine each step's cost and the duration of the project. Length of Path (weeks) H D, F A weeks at an additional cost (in $) of $ A U B B D, F G, H Present Cost D, F $11,000 $20,000 $9,000 $25,000 $20,000 $20,000 $15,000 $12,000 $10,000 Accelerated Cost $16,000 $26,000 $21,000 $29,000 $34,000 $31,000 $24,000 $17,000arrow_forwardEX6-6 (Algo) From the following information, develop... From the following information, develop an AON project network. Complete the forward and backward pass, compute activity slack, and identify the critical path. How many days will the project take? ID A Survey site B Description C Excavate site Install power lines. D Install drainage E Pour foundation The project will take The critical path is The late start on Activity C is The slack on Activity C is The slack on Activity D is The early start on Activity E is Predecessor None A B B C, D. Time 4 5 4 3 days. days. days. days, days.arrow_forwardA project has seven (7) main activities labelled A through G as shown in the below table which also shows their estimated duration times ( in weeks) and immediate predecessors. Activity a b Immediate Remarks predeccessor A 1 2 3 a = optimistic time 2 3 4 m = most likely time C 4 A b = pessimistic time 8 9 10 E 2 5 8 C,D 4 6. G 1 2 3 E (a) Develop a project network for this problem.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 Compute the expected activity completion times and the variance for each activity. 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.arrow_forward2. The time estimates (in weeks) for the activities of a PERT network are given below. (i) (ii) 1-2 1-3 1-4 2-5 3-5 4-6 5-6 18 9 10 8 16 7 Activity to 24 16 3 tm 7 9 20 14 2 tp 9 20 11 11 28 18 4 Draw the project network and calculate the project length. Calculate the standard deviation and variance along the critical path. (iii) Find the probability of completing the project one day earlier and 2 days later.arrow_forwardEvent Predecessor Event Time A - 6 B - 8 C A;B 12 D C 4 E C 6 F D;E 15 G E 12 H F;G 8 Specify : a) The project age b) Critical event and critical timearrow_forward
- In zuman Inc. The expected activity time is 7 weeks, whereas the optimistic time is 12 weeks and most likely time is 15 weeks , for an pert activity. Ascertain the pessimistic time and the variance of the activity.arrow_forwardThe Industrial and Systems Engineering Department at Sun University is moving from its old building to a new building. The move must be completed within the 14-day period between semesters. A list of tasks (activities) has been prepared. The activities and precedence requirements are presented in the table below. Three time estimates (in days) are given for each activity: optimistic time, most likely time, and pessimistic time. (a) Perform a forward pass and backward pass through the network to determine the critical path, and the expected duration of the project (b) What completion time should the department specify in its proposal in order to be 85% sure that it will complete the project on time? Activity Activity description Immediate predecessor Optimistic time (days) Most likely time (days) Pessimistic time (days) 1 Initiate move - 0 0 0 2 Prepare new building space 1 2 4 6 3 Pack faculty files and books 1 3 4 5 4…arrow_forwardGiven the following network and activity time estimates, determine: The expected time and variance for each activity Complete the chart showing bout the EF and LFarrow_forward
- A project consisting of the following activities: Activities predece.Activities day TE M K J H G E C B G KJ G I,F D D E,C B,A| B,A A 1 3 4 6. 5 2 3 9 6 2 4 3 5 1- Draw the network diagram of the project 2- Calculate (Es) and (Lc) the project events 3- Select the critical path 4 - What is the minimum time required to complete the project?arrow_forwardGiven the following network and probabilistic activity timeestimates, determine the expected time and variance foreach activity and indicate the critical path:arrow_forwardDave Fletcher was able to determine the activity times for constructing his laser scanning machine. Fletcher would like to determine ES, EF, LS, LF, and slack for each activity. The total project completion time and the critical path should also be determined. Here are the activity times: Activity A B с D Time (weeks) 5 8 2 1 Immediate Predecessor(s) A A Dave's earliest start (ES) and earliest finish (EF) are: Activity A Activity EFGH ES Time (weeks) 3 EF 5 5 10 7 Immediate Predecessor(s) B B C, E D, Farrow_forward
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