The document outlines a project proposal for upgrading airport infrastructure, detailing financial objectives, cost structures, and anticipated income from various sources. Key stages of the project include parking space leasing and runway extensions, with a projected total expenditure of approximately €1,274,450 over various phases. The financial model aims to minimize municipal allocations while navigating constraints on bank financing and sustainability metrics.

1. Francisco Lemosa and Pedro Martinsb,c
(a) Master in Information Systems and Management
(b) Polytechnic Institute of Coimbra – ISCAC, Portugal
(c) Operations Research Center (CIO), Faculty of Sciences, University of Lisbon,
Portugal

3. Functional structure
 Pilot School - Aero
Clube de Coimbra
 Aeronautic maintenance –
Industrias Aeronáuticas de Coimbra

4. Functional structure
 Fire prevention
squadron
 Functional runway –
landing of Brazil’s
President, Dilma Roussef

5. Financial envelope
 Cost structure:
 Anual current expense aprox. 150.000,00 € (Financial +
HR)
 No income, no landing, parking or fuel supply fees

6. What’s the problem’s objective?
Minimize the yearly Municipal financial
allocation
300,000
250,000
200,000
150,000
100,000
50,000
000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Q
Objective Min. Q

7. Formulation
Financial Income = Financial outcome  C -> cost of building
25 years to pay the project
 Q -> Municipal
allocation
 P -> Bank financing
 l -> European Union
funding
 q -> Income from
investments being
made
infrastructure
 D -> financial cost
center and HR cost
 P -> bank debt
 J -> debt interest
15 years to execute the project’s
infrastructure

8. Formulation – Data – Project stages
The infrastructures are built
according to the time sequence
defined for the 5 stages
푖 =
푌푡
1 푖푓 푡ℎ푒 푖푛푓푟푎푠푡푟푢푐푡푢푟푒 푖푠 푏푢푖푙푡 푎푡 푦푒푎푟 푡
0 case otherwise
, i=1,…,9 ; t=1,…,15
i (Stage) Infras.
Expected
income
value when
concluded
1
Parking
space lease 12.179,20
5
Parking
space lease 8.752,76
6
Parking
space
lesase 16.814,38
9
Hangars
space lease 5.376,22
Total 43.122,56
1
Parkin
g space
3
Runwa
y
exten.
2
Fuel
supply 4
Transf.
of
safeho.
5
Parkin
g space
6
Parkin
g space
7
Access
to
runway
8
Hangar
Altern.
access
9
Hangar
layout

9. Architecture project for development – 5
stages with a total of 9 infrastructures
1st stage: Parking space and fuel
supply (174.000,00 €)
2nd stage: runway extension and
transfer of safe house
(156.000,00 €)
3rd stage: Parking space
(30.300,00 €)
4th stage: Parking space and
access to runway
(114.700,00 €)
5th stage: Hangar alternative
access and hangar layout
(137.450,00 €)

10. Bank financing constraints
t
[year
]
풇풕[€] (Min.
Loan
amount)
푭풕 [€] (Max.
Loan
amount)
휸풕 [%]
(interest
rate)
푴풕 [year]
(maturity)
1 0 60000,00 8 10
2 0 60000,00 8 10
3 0 60000,00 8 10
4 0 60000,00 8 10
5 0 60000,00 8 10
6 0 60000,00 8 10
7 0 60000,00 8 10
8 0 60000,00 8 10
9 0 60000,00 8 10
10 0 60000,00 8 10
11 0 60000,00 8 10
12 0 60000,00 8 10
13 0 60000,00 8 10
14 0 60000,00 8 10
15 0 60000,00 8 10
(sum of debt payment
equals the loan’s
amount)
10
푗=1
푗 = 푃푡 푡 = 1, 2, … 15
푋푡

11. Scenario results - Initial scenario(5.1.1)
Income side
Income
Infrastructure
Year 1 2 3 4 5 6 7 8 9
1 Pt + Q 1 1 0 0 0 0 0 0 0
2 Pt + 24/52xQ l +q l 1 1 1 1 0 0
3 23/25 x Q q l l l +q l +q 1 0 1
4 22/25 x Q q q q l 0 l +q
5 21/25 x Q q q q 0 q
6 to 14 … q q q 0 q
15 11/25 x Q q q q 1 q
16 10/25 x Q q q q l
17 to 24 … q q q q
25 1/25 x Q q q q q

12. Scenario results - Initial scenario(5.1.1)
Cost side
퐷푡 =
4
푘=1
퐷푘푡 (1 + Ω푖 )푡−푡푘푖
푘 = 1, 2 … , 4 푡푘푖
k Human
resource
expenses
≤ 푡 ≤ 푡푘푖
푫풌풕[€]
(initial
value)
풕풌풊
+ Δ푡푘 −1
[year]
(starting
year of
expense)
Δ풕풌[year]
(ending year
of expense)
Ω풌[%]
(increase
rate)
1 Air trafic
controller
26.200,00 1 25 1,5
2 Air trafic
controller being
retired in five
years
8.610,00 1 5 1,5
3 Airfield director
(one year
contract)
9.804,00 1 1 0
4 Financial costs 110.192,82 1 25 1,5
Cost
Infrastructure
Year 1 2 3 4 5 6 7 8 9
1 푫풕 + 푪풕 1 1
2
푫풕 + 푪풕 +
DEBT+
INTEREST 1 1 1 1
3
푫풕 + 푪풕
+DEBT+
INTEREST 1 1
4 푫풕
5 푫풕
6 to 14
푫풕
15 푫풕 + 푪풕 1
16 푫풕
17 to 24 푫풕
25 푫풕
(debt payment)
푗−1
푡=1
(interests)
푗 푗 = 2, … 25 훾푡 푃푡 −
푋푡
푡+1
푗−푡≤10
푗 푡 = 1, 2, … 15
푋푡

13. Formulation – Sustainability constraint
Sustainability constraint at the end of the planning horizon (t = 25) adds up to: the
sum of every income plus Z must be larger than the expenses:
9
푖 =1
15
푗=1
푖 + 푍 ≥ 퐷25
휃푖푌푗
Z being positive is commonly known as deficit .

14. Scenario results Initial scenario(5.1.1)
Income
Infrastructure
Year 1 2 3 4 5 6 7 8 9
1 Pt + Q 1 1 0 0 0 0 0 0 0
2 Pt +
24/52xQ
l +q l 1 1 1 1 0 0
3 23/25 x Q q l l l +q l +q 1 0 1
4 22/25 x Q q q q l 0 l +q
5 21/25 x Q q q q 0 q
6 to 14 … q q q 0 q
15 11/25 x Q q q q 1 q
16 10/25 x Q q q q l
17 to 24 … q q q q
25 1/25 x Q q q q q
Cost
Infrastructure
Year 1 2 3 4 5 6 7 8 9
1
푫풕 + 푪풕 1 1
2
푫풕 + 푪풕 +
DEBT+
INTEREST 1 1 1 1
3
푫풕 + 푪풕
+DEBT+
INTEREST 1 1
4 푫풕
5 푫풕
6 to 14
푫풕
15 푫풕 + 푪풕 1
16 푫풕
17 to 24 푫풕
25 푫풕

15. Scenario results
Initial scenario(5.1.1)
Q [€] SQ[€] (Total
allocation)
SRI [€] (Total
income from
investment)
NPV [€] SD [€] (Total of
expenses)
SP [€] (Total
loans)
SJ [€] (Total
interest paid)
Z [€]
(Deficit)
250.744,37 3.259.676,78 998.621,86 121.234,73 4.154.545,59 113.562,45 11.023,52 151.851,36
194973.920
300000.000
250000.000
200000.000
150000.000
100000.000
50000.000
.000
-50000.000
-100000.000
-150000.000
-200000.000
Financial evolution
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Cash flow operacional RI Despesa

16. Scenario evolution
Cost decrease(5.1.2)
k Human
resource
expenses
푫풌풕[€] (initial value) 풕풌풊
[year] (starting year
of expense)
Δ풕풌[year]
(ending year
of expense)
Ω풌[%]
(increase
rate)
1 Air trafic
controller
26.200,00 1 25 1,5
2 Air trafic
controller being
retired in five
years
8.610,00 1 5 1,5
3 Airfield director
(one year
contract)
9.804,00 1 1 0
4 Financial costs 110.192,82 1 25 -10

17. Scenario results Reduction of expenses(5.1.2)
Income
Infrastructure
Year 1 2 3 4 5 6 7 8 9
1 Pt + Q 0 0 0 0 0 0 0 0 0
2 Pt +24/25 x Q 1 0 0 0 0 0 0 0 0
3 Pt + 23/25 x Q l +q 0 0 0 0 0 0 0 0
4 Pt + 22/25 x Q q 1 0 0 0 0 0 0 0
5 Pt + 21/25 x Q q l 1 0 0 0 0 0 0
6 Pt + 20/25 x Q q l 1 1 0 1 0 0
7 Pt + 19/25 x Q q l l +q 1 l 0 1
8 Pt +18/25 x Q q q l +q 0 l +q
9
Pt +18/25 x Q
q q q 0 q
10 to 14 Pt + (…) q q q 0 q
15 Pt + 11/25 x Q q q q 1 q
16 10/25 x Q q q q l
17 9/25 x Q q q q q
18 to 24 (…) q q q q
25 1/25 x Q q q q q
Cost
Infrastructure
Year 1 2 3 4 5 6 7 8 9
1 푫풕 0 0 0 0 0 0 0 0 0
2 푫풕 + 푪풕+ INTEREST 1 0 0 0 0 0 0 0 0
3 푫풕 + 푪풕+ INTEREST 0 0 0 0 0 0 0 0
4 푫풕+ 푪풕+ INTEREST 1 0 0 0 0 0 0 0
5 푫풕+ 푪풕 + DEBT+ INTEREST 1 0 0 0 0 0 0
6 푫풕+ 푪풕 + DEBT+ INTEREST 1 1 0 1 0 0
7 푫풕+ 푪풕+ INTEREST 1 0 1
8 푫풕+DEBT+ INTEREST 0
9 푫풕 + DEBT+ INTEREST 0
10 to 14 푫풕 + DEBT+ INTEREST 0
15 푫풕+ 푪풕 + DEBT+ INTEREST 1
16 푫풕 + DEBT+ INTEREST
17 푫풕 + DEBT+ INTEREST
18 to 24 푫풕 + DEBT+ INTEREST
25 푫풕 + DEBT+ INTEREST

18. Scenario results
Reduction of expenses(5.1.2)
Q [€] SQ[€] (Total
allocation)
SRI [€] (Total
income from
investment)
NPV [€] SD [€] (Total of
expenses)
SP [€] (Total
loans)
SJ [€] (Total
interest
paid)
Z [€]
(Deficit)
107.220,96 1.393.872,42 845.854,84 189.979,72 1.864.637,23 617.193,30 282.360,40 3.120,10
46242.663
200000.000
150000.000
100000.000
50000.000
.000
-50000.000
-100000.000
-150000.000
Financial evolution
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Cash flow operacional RI Despesa

19. Scenario evolution
3 years of re-adjustment + 10 years no cost
increase + 12 cost increase (5.1.3)
k Human resource
expenses
푫풌풕[€] (initial
value)
풕풌풊[year] (starting
year of expense)
Δ풕풌[year]
(ending year
of expense)
Ω풌[%]
(increase
rate)
1ATIA 26200 1 3 -0,015
2ATIA to be retired 8610 1 3 -0,015
3BBMA director 9804 1 3 -0,015
4 Financial cost center 110192,8 1 3 -0,1
5ATIA 25038,6 4 10 0
6ATIA to be retired 8228,33 4 2 0
7BBMA director 9369,4 4 10 0
Financial cost center 80330,56 4 10 0
8
9ATIA 25038,6 14 12 0,01
10BBMA director 9369,4 14 12 0,01
11 Financial cost center 80330,56 14 12 0,01

20. Scenario evolution
Bank financing constraints(5.1.3)
t [year]
풇풕[€] (Min. Loan
amount)
푭풕 [€] (Max. Loan
amount)
휸풕 [%] (interest
rate)
푴풕 [year]
(maturity)
1 0 60000 0,08 10
2 0 60000 0,08 10
3 0 60000 0,08 10
4 0 60000 0,07 10
5 0 80000 0,06 10
6 0 80000 0,055 10
7 0 80000 0,055 10
8 0 90000 0,05 10
9 0 80000 0,055 10
10 0 80000 0,055 10
11 0 100000 0,05 10
12 0 80000 0,06 10
13 0 80000 0,055 10
14 0 60000 0,07 10
15 0 60000 0,075 10

21. Scenario results
(5.1.3)
Income
Infrastructure
Year 1 2 3 4 5 6 7 8 9
1 Pt + Q 1 0 0 0 0 0 0 0 0
2 Pt +24/25 x Q l +q 1 0 1 0 0 0 0 0
3 Pt + 23/25 x Q q l 1 l 1 1 0 0 0
4
Pt + 22/25 x Q
q l l +q l +q 1 0 1
5
21/25 x Q
q q q l 0 l +q
6 20/25 x Q q q q 0 q
7 19/25 x Q q q q 0 q
8 18/25 x Q q q q 0 q
9
18/25 x Q
q q q 0 q
10 to 14 (…) q q q 0 q
15 11/25 x Q q q q 1 q
16 10/25 x Q q q q l q
17 9/25 x Q q q q q
18 to 24 (…) q q q q
25 1/25 x Q q q q q
Cost
Infrastructure
Year 1 2 3 4 5 6 7 8 9
1 푫풕 + 푪풕 1 0 0 0 0 0 0 0 0
2 푫풕 + 푪풕+ INTEREST 1 0 1 0 0 0 0 0
3 푫풕 + 푪풕+ INTEREST 1 1 1 0 0 0
4
푫풕 + 푪풕+ DEBT+
INTEREST 1 0 1
5
푫풕 +DEBT +
INTEREST 0
6 푫풕 0
7 푫풕 0
8 푫풕 0
9 푫풕 0
10 to 14 푫풕 0
15 푫풕 + 푪풕 1
16 푫풕
17 푫풕
18 to 24 푫풕
25 푫풕

22. Scenario results
(5.1.3)
Q [€] SQ[€] (Total
allocation)
SRI [€] (Total
income from
investment)
NPV [€] SD [€] (Total of
expenses)
SP [€]
(Total
loans)
SJ [€] (Total
interest
paid)
Z [€]
(Deficit)
169.824,55 2.207.719,10 963.028,51 58.890,48 3.049.481,34 193.314,95 28.536,23 84.887,62
200000.00
150000.00
100000.00
50000.00
0.00
-50000.00
-100000.00
-150000.00
Financial evolution
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Cash flow operacional RI Despesa

23. Scenarios
Q [€] SQ[€] (Total
allocation)
SRI [€] (Total
income from
investment)
NPV [€] SD [€] (Total of
expenses)
SP [€] (Total
loans)
SJ [€] (Total
interest paid)
Z [€]
(Deficit)
250.744,37 3.259.676,78 998.621,86 121.234,73 4.154.545,59 113.562,45 11.023,52 151.851,36
107.220,96 1.393.872,42 845.854,84 189.979,72 1.864.637,23 617.193,30 282.360,40 3.120,10
169.824,55 2.207.719,10 963.028,51 58.890,48 3.049.481,34 193.314,95 28.536,23 84.887,62

24. Sustainability study conclusions
 Unconstrained costs leads to earlier infrastructure
construction with short span.
 Strong costs reduction leads to decrease in liquity.
 More need of bank loans.
 Wider time span for infrastructure construction

25. Model conclusions
 What’s left to explore?
 Other applications:
 Highways, hospital, stadiums?
 Production of pharmaceuticals?
 Software development?

26. References
J. Nocedal e S. J. Wright, Numerical Optimization, 2nd Edition, Springer,
Berlim, 2006
Cornuejols, G., & Tütüncü, R. (2007). Optimization Methods in Finance.
Cambridge University Press, New York

27. The End
Thank you