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APPENDIX ONE

Solutions to Selected Exercises

Chapter 2

2. 

   A lower payback is better. Project Alpha has the lower payback and so has the better payback.

5. 

   For Dust Devils Project using the NPV equation:

   

For Dust Devils Project using Excel:

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The expected ROI is entered in cell C1 and that will be referenced in the worksheets for the next two projects. Cells E6 to E10 repeat the calculations shown in the previous equations, only using Excel. Cells E7 to E9 perform the three discounting calculations. The equation used is shown in cell F7. The dollar signs in “$C$1” keep that cell from changing when this formula is copied up or down. In Excel, this is called an absolute reference.

Cell E12 performs the NPV calculations as shown in the textbook. Excel gives the same answer either way. Cell F12 shows the formula for the direct NPV calculations.

For Osprey Project using the NPV equation:

For Osprey Project using Excel:

For Voyagers Project using the NPV equation:

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For Voyagers Project using Excel:

The only project SIMSOX should consider is Voyagers. Each of the other two projects would not satisfy the high rate of return SIMSOX expects from its projects.

Chapter 6

3. 

Activity C is a burst activity. Activity G is a merge activity.

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11. 

Early start, late start, early finish, late finish, and slack are shown on the diagram above. The completion time is 150 days. The critical path is A-C-E-G-J.

13. 

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Early start, late start, early finish, late finish, and slack are shown on the diagram above. The Gantt chart is shown below.

The critical path is A-B (finish only)-C-D-F.

Chapter 8

7. Log of Parallel Method of Scheduling: Exercise 8-7

   Period		Activity		Changes
   0–1		B		Schedule Activity B (first by minimum slack rule)
   		A		Schedule Activity A
   1–2		-		No changes
   2–3		-		No changes
   3–4		-		No changes
   4–5		C		Delay ES of Activity C to 5. Reduce slack to 1
   5–6		D		Schedule Activity D (minimum slack rule)
   		C		Schedule Activity C
   		E		Delay ES of Activity E to 6. Reduce slack to 1
   6–7		E		Delay ES of Activity E to 7. Reduce slack to 0
   7–8		E		Delay ES of Activity E to 8. Reduce slack to −1
   		F		Delay ES of Activity F to 11. Reduce slack to −1
   8–9		E		Delay ES of Activity E to 9. Reduce slack to −2
   		F		Delay ES of Activity F to 12. Reduce slack to −2
   9–10		E		Schedule Activity E
   10–11		-		No changes
   11–12		-		No changes
   12–13		F		Schedule Activity F

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10. You should not spend time planning how you are going to spend your bonus. The schedule will take 16 days.

    

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13. 

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Chapter 9

2. Use the information contained below to compress one time unit per move using the least cost method. Reduce the schedule until you reach the crash point of the network. For each move identify what activity(ies) was crashed and the adjusted total cost.

   Note: Choose B instead of C and E (equal costs) because it is usually smarter to crash early rather than late AND one activity instead of two activities.

   

   

Project duration is reduced from 13 time periods to 10. Total direct cost goes up from 1,000 to 1,240. The steps are shown below:

The project has two paths, A-B-C-F, which takes 12 time periods, and A-B-D-E-F, which takes 13 time periods. This gives the project a duration of 13 time periods. The total direct cost is $1,000.

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The cheapest activity to reduce is D at a cost of $40 for one time period. That makes both paths critical. That means that further reductions will require either reducing the same time from an activity on both paths or finding an activity shared by both paths and reducing that activity. Total direct cost goes up from $1,000 to $1,040.

Activity B is on both paths and can be reduced by one time period at a cost of $100.¹ That lowers the completion time to 11 time periods and raises total direct cost to $1,140.

Finally, we can reduce C on the first path at a cost of $50 and E on the second path at a cost of $50. That reduces the completion time to 10 time units and raises total direct cost to $1,240. No further reductions are possible.

8. 

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Duration		Direct Cost		Indirect Cost		Total Cost
17		2,000		1,500		3,500
16		2,040		1,450		3,490
15		2,100		1,400		3,500
14		2,160		1,350		3,560
13		2,260		1,300		3,660
12		2,460		1,250		3,860

The optimum time-cost schedule would be 16 weeks at a cost of $3,490.

Chapter 13

8. 

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With two-thirds of the project completed the forecast is that the project will be $105,000 over budget at completion.

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¹ Activities C on the first path and E on the second path also have a combined cost of $100. We select B first since it is usually smarter to crash earlier activities first and it is usually smarter to crash one activity rather than two.