Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 10.3, Problem 8P
a.
Summary Introduction
Interpretation: The direct cost of the project is to be computed after the successive reduction of the project time by one week.
Concept Introduction: Network diagram is a graphical representation of tasks and events happening in a project. It depicts the workflow and is used to compute the total duration of the project.
B.
Summary Introduction
Interpretation: The optimal project completion time and the total project cost are to be computed when the indirect costs amount to $150.
Concept Introduction: Network diagram is a graphical representation of tasks and events happening in a project. It depicts the workflow and is used to compute the total duration of the project.
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The North Carolina Department of Transportation is undertaking a construction project to widen a large section of interstate highway near Charlotte, NC, which includes the construction of a number of new bridges, interchanges, and overpasses. The first step in the project is the appointment of a project manager and the development of a project team, some of which will be departmental employees and others will be private consultants and operatives. The team of a project of this size also requires a large support staff with varying technical skills. Once the team is selected and the staff is in place the first task is to select a primary contractor to manage and oversee the actual construction. The following table gives the standard activities required for the planning and scheduling of this process.
Activity
Description
Predecessor
Time (weeks)
Optimistic
a
Most Likely
m
Pessimistic
b
a
b
c
d
e
f
g
h
i
j
k
L
M
Select project manager
Develop a team recruitment…
Consider Table 6-3. All duration estimates or estimated times are in weeks, and the networkproceeds from Node 1 to Node 8. (Note that you can easily change this table to createmultiple exercises.)a. Draw an AOA network diagram representing the project. Put the node numbers in circlesand draw arrows from node to node, labeling each arrow with the activity letter andestimated time.b. Identify all of the paths on the network diagram and note how long they are, using Figure 6-8as a guide for how to represent each path.c. What is the critical path for this project and how long is it?d. What is the shortest possible time needed to complete this project?
Consider the AON graph of a project shown in Figure 19.18.The activity times are 3, 4, 2, 5, 7, 2, 2, and 3 days for activities A1 through A8, respectively. What is the earliest completion time of the project?
Chapter 10 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 10.2 - Prob. 1PCh. 10.2 - Prob. 2PCh. 10.2 - Prob. 3PCh. 10.2 - Prob. 4PCh. 10.2 - Prob. 5PCh. 10.2 - Prob. 6PCh. 10.3 - Prob. 7PCh. 10.3 - Prob. 8PCh. 10.3 - Prob. 9PCh. 10.3 - Prob. 10P
Ch. 10.4 - Prob. 11PCh. 10.4 - Prob. 12PCh. 10.4 - Prob. 13PCh. 10.4 - Prob. 14PCh. 10.4 - Prob. 15PCh. 10.4 - Prob. 16PCh. 10.5 - Prob. 17PCh. 10.5 - Prob. 18PCh. 10.5 - Prob. 19PCh. 10.5 - Prob. 20PCh. 10.5 - Prob. 21PCh. 10.6 - Prob. 22PCh. 10.6 - Prob. 23PCh. 10.6 - Prob. 24PCh. 10.6 - Prob. 25PCh. 10 - Prob. 26APCh. 10 - Prob. 27APCh. 10 - Prob. 28APCh. 10 - Prob. 29APCh. 10 - Prob. 30AP
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- Consider the following activity information and the constraint that the project must be completed in 16 weeks. (refer to the first pic) In addition, activities c, f, h, and i may be crashed as follows. Assume partial crashing. (refer to the second pic) Question : Find the best schedule and its costarrow_forwardA contractor needs to complete a project. The project involves 10 activities (labeled A, B, ..., J) with precedence relationship in network below. The estimate (in weeks) of the duration of each activityis in the table below. a. The mean and variance of the activity time for A~F are given in the table. Find the mean and variance of the activity time for the remaining arcs.b. Identify the critical path and then compute the mean and variance of the project completion time.c. What is the probability that the project is completed between 32 and 36 weeks?d. What completion time should the contractor claims to be 95% sure of completing the project by then?arrow_forwardConsider the following table of activities A through E in which A is the start node and E is the stop node. Assume all activities require the same resource. On a piece of scratch paper, draw the early-start Gantt Chart associated with this table and determine the following. Assume the project is resource-constrained but not time-constrained. Assume only one resource is available and that resource can only do one activity at a time. Activities B, C and D all have the same early start date (time). Since there is only one resource, only one of the activities B, C, D can be started on the early start date. Which should be started first?arrow_forward
- A project consisting of eight activities satisfies the following precedence constraints: a. Construct a network for this project. (You should need only one pseudoactivity.)b. Compute the earliest and the latest starting and finishing times for each activity and identify the critical path.c. Draw a Gantt chart of the schedule for this project based on earliest starting times.arrow_forwardDraw the following project schedule (See textbook section 8.8 and exhibits 8.11-8.15) Task A duration 12 days Task B duration 4 days, the predecessor is task A Task C duration 6 days, the predecessor is task A Task D duration 8 days, the predecessor is task C Task E duration 6 days, the predecessor is task B Task F duration 4 days, the predecessor is task C Task G duration 8 days, predecessors are tasks D, E, and F Indicate the ES, EF, LS, LF and slack time (format as displayed in examples) and provide a legend with the diagram. Highlight/Identify the critical path on the diagram. Show the enumeration method to determine the critical path. Be sure that both methods indicate the same critical path.arrow_forwardYou may need to use the appropriate technology to answer this question. Use the following network with activities and times estimated in days to answer the questions. A project network with 13 activities and 17 directed arcs is shown. Activity Start is connected to activity A, to activity B, and to activity C. Activity A is connected to activity D, to activity E, and to activity F. Activity B is connected to activity F. Activity C is connected to activity G and to activity H. Activity D is connected to activity K. Activity E is connected to activity I. Activity F is connected to activity I. Activity G is connected to activity I. Activity H is connected to activity J. Activity I is connected to activity K. Activity J is connected to activity K. Activity K is connected to activity Finish. Activity Finish has no arcs directed to other activities. Activity Optimistic Most Probable Pessimistic A 2 5 6 B 1 3 7 C 5 6 9 D 5 12 14 E 3 4 5 F 9 10 13 G 4 6 8 H 3 6 8 I 5 7 12 J 11 12 13 K 1 3 4…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_forwardAn IT company must complete a project with the following tasks listed A to G. ACTIVITY NORMAL DURATION (DAYS) CRASHED DURATION (DAYS) NORMAL COST ($) CRASHED COST ($) A 7 5 500 900 B 4 2 400 600 C 5 5 500 500 D 6 4 800 1000 E 7 4 700 1000 F 5 2 800 1400 G 6 4 800 1600 The following are all the paths in the project from start to end and the durations of each: A-B-E-G : 24 days A-C-E-G : 25 days A-C-F-G : 23 days A-D-F-G : 24 days Develop a crashing schedule to show which activities should be crashed to crash the project by 4 days and the lowest cost of doing so.arrow_forwardconsider the following project represented by the table of activities and predecessors. Illustrate how this project can be crashed stagewise. What is the minimum time and cost for the crashed project? Hint: you need to crash it to the minimum time you can.arrow_forward
- Use the following network and the data to perform the following: a) Prepare the manpower loaded Gantt chart with total floats of this project using early start and late times. Plot the manpower resource profile that shows the total number of laborers per day over the course of the project. Prepare the Gantt chart and the resource profile using the early start and finish dates of activities (not necessary to produce the late start and finish charts). b) Level the manpower resource given the constraint that the owner has only 14 workers to allocate to this project per day. Please try to do in excel. Thannksarrow_forward“The shortest total length of a project is determined by the longest path through the network.” Explain the concept behind this statement. Why does the longest path determine the shortest project length?arrow_forward. True/False Statements (Tick the correct option) Selection of the critical path in network activity diagram for any project, is always focused onresult of the minimum time duration of the critical activities [ True / False ] Suppose, we have total 03 activities in the project “X”; namely L, M and N respectively. An activity “M” is the immediate successor of the activity “L”, while the activity “M” is the immediate predecessor for the activity “N”. According to this scenario, an activity “M” will be the last activity of the project “X” in the network activity diagram [True / False ] The dummy activity consumes both time and resources [True / False ] Towards the optimal solution through stepping stone method, when degeneracy problem is occurred, the next step is to focus on searching lowest value on the independent position in a non-allocated cells [True / False ] Hungarian algorithm, first convert any given assignment matrix into row reduction matrix [True / Falsearrow_forward
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