Assume constant cash flow rate during the activity duration, i.e., cash flow required per week for an activity = activity budget / activity duration.
(a) Draw the Gantt chart to display the early start schedule. Paste image/capture screenshot below.
(b) Develop the time-constrained project network displaying the early start schedule and late start schedule. Paste image/capture screenshot below.
(c) Identify the critical activities, critical path(s) and the project duration in (b).
(d) Develop the cash flow diagram for the early start schedule and the late start schedule, respectively, on the same graph. Paste image/capture screenshot below.
(e) Formulate the problem to determine the earliest start schedule for all activities by a linear program (LP).
(f) Implement the LP model in part (e) on Excel to determine an optimal schedule for part (e). Save Excel file with the executable model as “Q1_LP.xlsx” for submission.
(g) If there is more than one schedule with the earliest project completion time as in part (f), display one with the minimum cash flow required in any week during the project. Choose a Gantt chart to display the start time, finish time of each activity and include the weekly cash flow required. What is the peak weekly requirement of cash?
A project consists of the following eight activities and only three workers are available at any time. Please fill in your Duration:
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Activity
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Predecessors
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Duration (days)
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Workers (units)
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1
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-
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max{1st digit of your student ID, 1}
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2
|
|
2
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1
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max{2nd digit of your student ID, 1}
|
2
|
|
3
|
1
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max{3rd digit of your student ID, 1}
|
2
|
|
4
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2, 3
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max{4th digit of your student ID, 1}
|
2
|
|
5
|
4
|
max{5th digit of your student ID, 1}
|
2
|
|
6
|
4
|
max{6th digit of your student ID, 1}
|
1
|
|
7
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5
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max{7th digit of your student ID, 1}
|
2
|
|
8
|
6
|
max{8th digit of your student ID, 1}
|
2
|
Enter “Q2 Project” as a summary activity in the first row to represent the entire project. Set the project start date to be 5 August 2024. Enter the activity names, durations and the predecessors in Microsoft Project.
(a) Capture the screen showing the Task view of the task names, durations, start date, finish date and the predecessors. What is the project completion date and project duration?
(b) Capture the screen of the Gantt chart showing the critical activities in red and the slack of non-critical activities indicated in the Gantt chart.
(c) Capture the screen of the network diagram showing the critical activities in red. The format of each activity node should display the start date, finish date, latest start, latest finish, and duration.
(d) Enter the “workers” resource in the Resource Sheet. Only three workers are available. Display a worker in “unit”. The standard rate of the workers is $100/hour. The availability of all the three workers is from today to 31 October, 2024. Then enter the required workers of each activity as shown in the table above. Capture the screen of the Resource Sheet.
(e) Use resource leveling and the option “Level only within available slack” to solve the resource conflicts, if any. Apply the “Level All” function. If some resource(s) is still over-allocated, deselect the option “Level only within available slack” and re-apply the “Level All” function. Capture the screen of the Leveling results in the Task view, including the Resource Names and Gantt chart (right). What is the new project completion date? How much longer (in workdays) is the project duration?
(f) In the Resource Usage view, Add New Column to display Cost. In column “Details”, display the fields of Work and Cost. After adjusting the time scale appropriately, capture the screen to show the weekly hours and costs incurred throughout the entire project.
(g) Suppose there is a bonus of $B for completing the project earlier than the date in part (e) by at least 1 day. Overtime work is allowed at a rate of $120/hour for those already assigned to each activity. Is it worthwhile? Explore. What would be the minimum value of $B for this option to be worth considering? Capture the screen of a new schedule in the Task view.
Save Microsoft Project file as “Q2_Project.mpp” for submission.
Question 3
Consider the following project requiring three resources W, X, and Y. Each resource represents one person, therefore; the maximum unit is 1 for each resource. Please fill in your Duration:
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Activity
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Predecessors
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Duration (days)
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Resource(s) used
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A
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-
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max{2nd digit of your student ID, 1}
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X, Y
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B
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A
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max{3rd digit of your student ID, 1}
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X
|
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C
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A
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max{4th digit of your student ID, 1}
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X
|
|
D
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B, C
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max{5th digit of your student ID, 1}
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X, Y
|
|
E
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D
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max{6th digit of your student ID, 1}
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W
|
|
F
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D
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max{7th digit of your student ID, 1}
|
W, X, Y
|
|
G
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E, F
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max{8th digit of your student ID, 1}
|
X, Y
|
Enter “Q3 Project” as a summary activity in the first row to represent the entire project. Set the project start date to be 29 July 2024. Enter the activity names, durations and the predecessors in Microsoft Project.
(a) Capture the screen showing the Task view of the task names, durations, start date, finish date and the predecessors.
(b) Capture the screen of the Gantt chart showing the critical activities in red and the slack of non-critical activities indicated in the Gantt chart.
(c) Enter the resources with the available dates of X and Y start from 26 July 2024 and W from 5 August 2024 onwards. The maximum availability is 1 unit each. Then enter the required resource(s) of each activity as shown in the table above. Capture the screen of the Resource Sheet.
(d) Use resource leveling and the option “Level only within available slack” to solve the resource conflict, if any. Apply the “Level All” function. If some resource(s) is still over-allocated, deselect the option “Level only within available slack” and re-apply the “Level All” function. Capture the screen of the Leveling results in the Task view, including the Gantt chart (right).
(e) When resource is taken into consideration (part (d)), how much more time (workdays) is needed? What is the new project completion date?
(f) If activity E can start 1 day after activity D has been started, modify the dependency type of activity D and activity E. Resolve resource conflicts, if any, using the “Level All” function. Capture the screen of the Leveling results in the Task view, including the Gantt chart (right). Can the project be completed earlier than the date in part (e)? If yes, by how many workdays?
(g) (This part is independent from (f).)
Does any resource by working overtime for not more than 125% daily on some selected activity can enable the project to complete earlier than the date in part (e)? Avoid the heavily used resource. Capture the screen of the Task view indicating the identified resource, selected activity and new project completion date.
Save Microsoft Project file as “Q3_Project.mpp” for submission.
Topic 4 Critical chain project management
Question 4
Suppose the activity duration in Question 2 has been estimated with safety time. Develop a critical chain project schedule. Display the schedule in a Gantt chart indicating the duration of activities, project and feeding buffer(s). Paste image/capture screenshot below. Identify the critical chain of activities. What is the expected project duration as compared with the CPM approach (Q2(e))?
Save this Word file with your student ID (e.g., “56789876.docx”) for submission.