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A B C D E F G H I J K L M
Union Airways Personnel Scheduling Problem
6am-2pm 8am-4pm Noon-8pm
4pm-midnight
10pm-6am Range Name Cells
Shift Shift Shift Shift Shift CostPerShift C5:G5
Cost per Shift $173.40 $163.20 $178.50 $183.60 $198.90 MinimumNeeded J8:J17
Total Minimum NumberWorking C21:G21
Time Period Shift Works Time Period? (1=yes, 0=no) Working Needed ShiftWorksTimePeriod C8:G17
6am-8am 1 0 0 0 0 48 >= 48 TotalCost J21
8am-10am 1 1 0 0 0 79 >= 79 TotalWorking H8:H17
10am- 12pm 1 1 0 0 0 79 >= 65
12pm-2pm 1 1 1 0 0 118 >= 87
2pm-4pm 0 1 1 0 0 70 >= 64
4pm-6pm 0 0 1 1 0 82 >= 73
6pm-8pm 0 0 1 1 0 82 >= 82
8pm-10pm 0 0 0 1 0 43 >= 43
10pm-12am 0 0 0 1 1 58 >= 52
12am-6am 0 0 0 0 1 15 >= 15
6am-2pm 8am-4pm Noon-8pm
4pm-midnight
10pm-6am
Shift Shift Shift Shift Shift Total Cost
Number Working 48 31 39 43 15 $31,222
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost
Coefficient
Increase Decrease
$C$21 Number Working Shift 48 0170 1E+30 10
$D$21 Number Working Shift 31 0160 10 160
$E$21 Number Working Shift 39 0175 5175
$F$21 Number Working Shift 43 0180 1E+30 5
$G$21 Number Working Shift 15 0195 1E+30 195
Constraints
Final Shadow
Constraint
Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$H$8 6am-8am Working 48 10 48 648
$H$9 8am-10am Working 79 160 79 1E+30 6
$H$10 10am- 12pm Working 79 065 14 1E+30
$H$11 12pm-2pm Working 118 087 31 1E+30
$H$12 2pm-4pm Working 70 064 6 1E+30
$H$13 4pm-6pm Working 82 073 9 1E+30
$H$14 6pm-8pm Working 82 175 82 1E+30 6
$H$15 8pm-10pm Working 43 543 6 6
$H$16 10pm-12am Working 58 052 6 1E+30
$H$17 12am-6am Working 15 195 15 1E+30 6
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18
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20
21
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38
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40
41
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A B C D E F G H I J K L M
Union Airways Personnel Scheduling Problem
6am-2pm 8am-4pm Noon-8pm
4pm-midnight
10pm-6am Range Name Cells
Shift Shift Shift Shift Shift CostPerShift C5:G5
Cost per Shift $170 $160 $175 $180 $195 MinimumNeeded J8:J17
Total Minimum NumberWorking C21:G21
Time Period Shift Works Time Period? (1=yes, 0=no) Working Needed ShiftWorksTimePeriod C8:G17
6am-8am 1 0 0 0 0 48 >= 48 TotalCost J21
8am-10am 1 1 0 0 0 79 >= 79 TotalWorking H8:H17
10am- 12pm 1 1 0 0 0 79 >= 65
12pm-2pm 1 1 1 0 0 118 >= 87
2pm-4pm 0 1 1 0 0 70 >= 64
4pm-6pm 0 0 1 1 0 82 >= 73
6pm-8pm 0 0 1 1 0 82 >= 82
8pm-10pm 0 0 0 1 0 43 >= 43
10pm-12am 0 0 0 1 1 58 >= 52
12am-6am 0 0 0 0 1 15 >= 15
6am-2pm 8am-4pm Noon-8pm
4pm-midnight
10pm-6am
Shift Shift Shift Shift Shift Total Cost
Number Working 48 31 39 43 15 $30,610
Cost per Shift 6am-2pm 8am-4pm Noon-8pm
4pm-midnight
10pm-6am Total
6am-2pm Shift Shift Shift Shift Shift Cost
48 31 39 43 15 $30,610
$155 54 25 39 43 15 $29,860
$158 54 25 39 43 15 $30,022
$161 48 31 39 43 15 $30,178
$164 48 31 39 43 15 $30,322
$167 48 31 39 43 15 $30,466
$170 48 31 39 43 15 $30,610
$173 48 31 39 43 15 $30,754
$176 48 31 39 43 15 $30,898
$179 48 31 39 43 15 $31,042
$182 48 31 39 43 15 $31,186
$185 48 31 39 43 15 $31,330
Cost per Shift 6am-2pm 8am-4pm Noon-8pm
4pm-midnight
10pm-6am Total
8am-4pm Shift Shift Shift Shift Shift Cost
48 31 39 43 15 $30,610
43
44
45
46
47
48
49
50
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52
53
54
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61
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80
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82
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A B C D E F G H I J K L M
$145 48 31 39 43 15 $30,145
$148 48 31 39 43 15 $30,238
$151 48 31 39 43 15 $30,331
$154 48 31 39 43 15 $30,424
$157 48 31 39 43 15 $30,517
$160 48 31 39 43 15 $30,610
$163 48 31 39 43 15 $30,703
$166 48 31 39 43 15 $30,796
$169 48 31 39 43 15 $30,889
$172 54 25 39 43 15 $30,970
$175 54 25 39 43 15 $31,045
Cost per Shift 6am-2pm 8am-4pm Noon-8pm
4pm-midnight
10pm-6am Total
Noon-8pm Shift Shift Shift Shift Shift Cost
48 31 39 43 15 $30,610
$160 48 31 39 43 15 $30,025
$163 48 31 39 43 15 $30,142
$166 48 31 39 43 15 $30,259
$169 48 31 39 43 15 $30,376
$172 48 31 39 43 15 $30,493
$175 48 31 39 43 15 $30,610
$178 48 31 39 43 15 $30,727
$181 48 31 33 49 15 $30,838
$184 48 31 33 49 15 $30,937
$187 48 31 33 49 15 $31,036
$190 48 31 33 49 15 $31,135
Cost per Shift 6am-2pm 8am-4pm Noon-8pm
4pm-midnight
10pm-6am Total
4pm-midnight Shift Shift Shift Shift Shift Cost
48 31 39 43 15 $30,610
$165 48 31 33 49 15 $29,905
$168 48 31 33 49 15 $30,052
$171 48 31 33 49 15 $30,199
$174 48 31 33 49 15 $30,346
$177 48 31 39 43 15 $30,481
$180 48 31 39 43 15 $30,610
$183 48 31 39 43 15 $30,739
$186 48 31 39 43 15 $30,868
$189 48 31 39 43 15 $30,997
$192 48 31 39 43 15 $31,126
$195 48 31 39 43 15 $31,255
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101
A B C D E F G H I J K L M
Cost per Shift 6am-2pm 8am-4pm Noon-8pm
4pm-midnight
10pm-6am Total
10pm-6am Shift Shift Shift Shift Shift Cost
48 31 39 43 15 $30,610
$180 48 31 39 43 15 $30,385
$183 48 31 39 43 15 $30,430
$186 48 31 39 43 15 $30,475
$189 48 31 39 43 15 $30,520
$192 48 31 39 43 15 $30,565
$195 48 31 39 43 15 $30,610
$198 48 31 39 43 15 $30,655
$201 48 31 39 43 15 $30,700
$204 48 31 39 43 15 $30,745
$207 48 31 39 43 15 $30,790
$210 48 31 39 43 15 $30,835
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A B C D E F G H I J K
Think-Big Development Co. Capital Budgeting Problem
Office Shopping
Building Hotel Center Range Name Cells
Net Present Value 45 70 50 CapitalAvailable H9:H12
($millions) Cumulative Cumulative CapitalRequired C9:E12
Capital Capital CapitalSpent F9:F12
Cumulative Capital Required ($millions) Spent Available ParticipationShare C16:E16
Now 40 80 90 25 <= 25 NetPresentValue C5:E5
End of Year 1 100 160 140 44.757 <= 45 TotalNPV H16
End of Year 2 190 240 160 60.583 <= 65
End of Year 3 200 310 220 80 <= 80
Office Shopping Total NPV
Building Hotel Center ($millions)
Participation Share 0.00% 16.50% 13.11% 18.11
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A B C D E F G H I J K
Think-Big Development Co. Capital Budgeting Problem
Office Shopping
Building Hotel Center Range Name Cells
Net Present Value 45.2 70 50 CapitalAvailable H9:H12
($millions) Cumulative Cumulative CapitalRequired C9:E12
Capital Capital CapitalSpent F9:F12
Cumulative Capital Required ($millions) Spent Available ParticipationShare C16:E16
Now 40 80 90 24.299 <= 25 NetPresentValue C5:E5
End of Year 1 100 160 140 45.000 <= 45 TotalNPV H16
End of Year 2 190 240 160 65.000 <= 65
End of Year 3 200 310 220 80 <= 80
Office Shopping Total NPV
Building Hotel Center ($millions)
Participation Share 13.31% 6.12% 15.65% 18.12
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A B C D E F G H I J K
Think-Big Development Co. Capital Budgeting Problem
Office Shopping
Building Hotel Center Range Name Cells
Net Present Value 45 70.2 50 CapitalAvailable H9:H12
($millions) Cumulative Cumulative CapitalRequired C9:E12
Capital Capital CapitalSpent F9:F12
Cumulative Capital Required ($millions) Spent Available ParticipationShare C16:E16
Now 40 80 90 25 <= 25 NetPresentValue C5:E5
End of Year 1 100 160 140 44.757 <= 45 TotalNPV H16
End of Year 2 190 240 160 60.583 <= 65
End of Year 3 200 310 220 80 <= 80
Office Shopping Total NPV
Building Hotel Center ($millions)
Participation Share 0.00% 16.50% 13.11% 18.14
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16
A B C D E F G H I J K
Think-Big Development Co. Capital Budgeting Problem
Office Shopping
Building Hotel Center Range Name Cells
Net Present Value 40 70 50 CapitalAvailable H9:H12
($millions) Cumulative Cumulative CapitalRequired C9:E12
Capital Capital CapitalSpent F9:F12
Cumulative Capital Required ($millions) Spent Available ParticipationShare C16:E16
Now 40 80 90 25 <= 25 NetPresentValue C5:E5
End of Year 1 100 160 140 44.757 <= 45 TotalNPV H16
End of Year 2 190 240 160 60.583 <= 65
End of Year 3 200 310 220 80 <= 80
Office Shopping Total NPV
Building Hotel Center ($millions)
Participation Share 0.00% 16.50% 13.11% 18.11
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A B C D E F G H I J K
Think-Big Development Co. Capital Budgeting Problem
Office Shopping
Building Hotel Center Range Name Cells
Net Present Value 45 70 49.8 CapitalAvailable H9:H12
($millions) Cumulative Cumulative CapitalRequired C9:E12
Capital Capital CapitalSpent F9:F12
Cumulative Capital Required ($millions) Spent Available ParticipationShare C16:E16
Now 40 80 90 25 <= 25 NetPresentValue C5:E5
End of Year 1 100 160 140 44.757 <= 45 TotalNPV H16
End of Year 2 190 240 160 60.583 <= 65
End of Year 3 200 310 220 80 <= 80
Office Shopping Total NPV
Building Hotel Center ($millions)
Participation Share 0.00% 16.50% 13.11% 18.08
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A B C D E F G H I J K
Think-Big Development Co. Capital Budgeting Problem
Office Shopping
Building Hotel Center Range Name Cells
Net Present Value 40 70.2 49.8 CapitalAvailable H9:H12
($millions) Cumulative Cumulative CapitalRequired C9:E12
Capital Capital CapitalSpent F9:F12
Cumulative Capital Required ($millions) Spent Available ParticipationShare C16:E16
Now 40 80 90 20.645 <= 25 NetPresentValue C5:E5
End of Year 1 100 160 140 41.290 <= 45 TotalNPV H16
End of Year 2 190 240 160 61.935 <= 65
End of Year 3 200 310 220 80 <= 80
Office Shopping Total NPV
Building Hotel Center ($millions)
Participation Share 0.00% 25.81% 0.00% 18.12
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A B C D E F G H I J K
Think-Big Development Co. Capital Budgeting Problem
Office Shopping
Building Hotel Center Range Name Cells
Net Present Value 46 69 49 CapitalAvailable H9:H12
($millions) Cumulative Cumulative CapitalRequired C9:E12
Capital Capital CapitalSpent F9:F12
Cumulative Capital Required ($millions) Spent Available ParticipationShare C16:E16
Now 40 80 90 24.299 <= 25 NetPresentValue C5:E5
End of Year 1 100 160 140 45.000 <= 45 TotalNPV H16
End of Year 2 190 240 160 65.000 <= 65
End of Year 3 200 310 220 80 <= 80
Office Shopping Total NPV
Building Hotel Center ($millions)
Participation Share 13.31% 6.12% 15.65% 18.01
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A B C D E F G H I J K
Think-Big Development Co. Capital Budgeting Problem
Office Shopping
Building Hotel Center Range Name Cells
Net Present Value 54 84 60 CapitalAvailable H9:H12
($millions) Cumulative Cumulative CapitalRequired C9:E12
Capital Capital CapitalSpent F9:F12
Cumulative Capital Required ($millions) Spent Available ParticipationShare C16:E16
Now 40 80 90 25.000 <= 25 NetPresentValue C5:E5
End of Year 1 100 160 140 44.757 <= 45 TotalNPV H16
End of Year 2 190 240 160 60.583 <= 65
End of Year 3 200 310 220 80 <= 80
Office Shopping Total NPV
Building Hotel Center ($millions)
Participation Share 0.00% 16.50% 13.11% 21.73
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$C$16 Participation Share Building 0.00% -4.85% 45 0.0485 1E+30
$D$16 Participation Share Hotel 16.50% 0.00% 70 0.4545 0.0543
$E$16 Participation Share Center 13.11% 0.00% 50 0.1389 0.3226
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$F$9 Now Spent 25 0.0097 25 0.3049 4.3548
$F$10 End of Year 1 Spent 44.757 0.0000 45 1E+30 0.2427
$F$11 End of Year 2 Spent 60.583 0.0000 65 1E+30 4.4175
$F$12 End of Year 3 Spent 80 0.2233 80 0.7812 18.8889
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A B C D E F G H I J K
Think-Big Development Co. Capital Budgeting Problem
Office Shopping
Building Hotel Center Range Name Cells
Net Present Value 45 70 50 CapitalAvailable H9:H12
($millions) Cumulative Cumulative CapitalRequired C9:E12
Capital Capital CapitalSpent F9:F12
Cumulative Capital Required ($millions) Spent Available ParticipationShare C16:E16
Now 40 80 90 25 <= 25 NetPresentValue C5:E5
End of Year 1 100 160 140 44.757 <= 45 TotalNPV H16
End of Year 2 190 240 160 60.583 <= 65
End of Year 3 200 310 220 80 <= 80
Office Shopping Total NPV
Building Hotel Center ($millions)
Participation Share 0.00% 16.50% 13.11% 18.11
Net Present Value Participation
Project 1 (Office) Office Shopping Total NPV
($millions) Building Hotel Center ($millions)
0.00% 16.50% 13.11% 18.11
40 0.00% 16.50% 13.11% 18.11
41 0.00% 16.50% 13.11% 18.11
42 0.00% 16.50% 13.11% 18.11
43 0.00% 16.50% 13.11% 18.11
44 0.00% 16.50% 13.11% 18.11
45 0.00% 16.50% 13.11% 18.11
46 13.31% 6.12% 15.65% 18.23
47 13.31% 6.12% 15.65% 18.36
48 13.31% 6.12% 15.65% 18.49
49 13.31% 6.12% 15.65% 18.63
50 13.31% 6.12% 15.65% 18.76
Net Present Value Participation
Project 2 (Hotel) Office Shopping Total NPV
38
39
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42
43
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45
46
47
48
49
50
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58
59
60
61
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63
64
65
66
67
A B C D E F G H I J K
($millions) Building Hotel Center ($millions)
0.00% 16.50% 13.11% 18.11
65 13.31% 6.12% 15.65% 17.79
66 13.31% 6.12% 15.65% 17.85
67 13.31% 6.12% 15.65% 17.91
68 13.31% 6.12% 15.65% 17.97
69 13.31% 6.12% 15.65% 18.03
70 0.00% 16.50% 13.11% 18.11
71 0.00% 25.81% 0.00% 18.32
72 0.00% 25.81% 0.00% 18.58
73 0.00% 25.81% 0.00% 18.84
74 0.00% 25.81% 0.00% 19.10
75 0.00% 25.81% 0.00% 19.35
Net Present Value Participation
Project 3 (Shopping C.)
Office Shopping Total NPV
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A B C D E F
Grandfather Wall
Clock Clock
Unit Profit $300 $200
Hours Hours
Used Available
Assembly (David) 6 4 33 <= 40
Carving (LaDeana) 8 4 40 <= 40
Shipping (Lydia) 3 3 20 <= 20
Grandfather Wall
Clock Clock Total Profit
Production 3.33 3.33 $1,667
Time Required
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2
3
4
5
6
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8
9
10
11
12
A B C D E F
Grandfather Wall
Clock Clock
Unit Profit $375 $200
Hours Hours
Used Available
Assembly (David) 6 4 33 <= 40
Carving (LaDeana) 8 4 40 <= 40
Shipping (Lydia) 3 3 20 <= 20
Grandfather Wall
Clock Clock Total Profit
Production 3.33 3.33 $1,917
Time Required
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10
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12
A B C D E F
Grandfather Wall
Clock Clock
Unit Profit $375 $175
Hours Hours
Used Available
Assembly (David) 6 4 30 <= 40
Carving (LaDeana) 8 4 40 <= 40
Shipping (Lydia) 3 3 15 <= 20
Grandfather Wall
Clock Clock Total Profit
Production 5 0 $1,875
Time Required
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3
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5
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49
50
A B C D E F
Grandfather Wall
Clock Clock
Unit Profit $300 $200
Hours Hours
Used Available
Assembly (David) 6 4 33 <= 40
Carving (LaDeana)
8 4 40 <= 40
Shipping (Lydia) 3 3 20 <= 20
Grandfather Wall
Clock Clock Total Profit
Production 3.33 3.33 $1,667
Time Required