Leasing Policies of a Satellite Operator: Comparison of two Methodologies

1
Leasing Policies of a Satellite Operator
Comparison of two Methodologies
5th International Conference on Communication
Systems, Networks and Digital Signal Processing,
CSNDSP 2006

• Elena Sarri
• George P. Papavassilopoulos

Department of Electrical and Computer
Engineering, National Technical University of
Athens
2
Description of framework

• evaluation of different decisions of a Satellite
  Operator leasing capacity to different customers
  requesting different services
• real situation (Hellas-Sat the Greek satellite
  operator)
• Data concerning demands of several customers were
  collected using those available in particular
  organizations
• These data was first classified and statistically
  treated.
• A decision tree has been created
• derive optimal leasing policies/scenarios and
  characterize them in terms of both profit and
  risk.
• the final outcome is a decision making tool
  which can be used by a Satellite Operator in
  order to evaluate possible states, profits and
  associated risks.
• we included the stochastic discrete
  optimization approach to the methodology,
  developing a second model, in order to verify the
  preceding work

3
Statistical treatment of gathered Data

• The first stage of this study involved the
  recording and the evaluation of the pricing data
  coming from the international market of leasing
  satellite capacity as well as their statistical
  treatment.

4
Statistical treatment of gathered Data
5
Second stage- Formulation of the model

• The goal of the proposed model, is to enable the
  decision maker to determine the best possible
  scenario for the satellite operator, which is the
  scenario with the larger amount of income.

Input Parameters
6
Second stage- Formulation of the model
Possible Combinations
All Possible Combinations
Total Possible Combinations

• Description of Combination

All combinations (Possible, Not Possible,
Negotiable Combination)
Possible Combinations
Possible Combinations with the highest maximum
occupied capacity
7
CONCEPT OF THE MODEL
Max Profits ProfitsReal Revenues Additional
Expected future profits
Profits from leasing C Remaining
Additional Expected future profits
Profits from leasing C Empty

• Real Revenues revenues that an operator will
  gain from the hire of capacity to the customers
  of each combination.

Each combination has different maximum requested
time of hiring the capacity. Therefore in order
to be able to properly compare the scenarios it
is necessary to reduce both of them to the same
period of time i.e. at the same maximum month of
hiring, and then to calculate the additional
possible income that we can acquire from this
left over free capacity that is called Remaining
Capacity (C Remaining)
It is also possible that at specific months not
all the available capacity of the transponder of
the satellite will be occupied with each
combination. This leads to the undesirable fact
of not having maximum occupancy of the
transponder of the satellite in each month. So
the satellite operator could probably hire this
available capacity to another possible future
customer that is not included to the combination
and gain more revenues. This is called Empty
Capacity (C Empty)
8
Case Scenario
MHz
Scenario 1
36
C Empty
Customer 1
Customer 2
20
Customer 3
15
1
1
2
15
10
20
month
Scenario 2
MHz
36
30
Customer 4
C Remaining
Customer 5
20
Customer 6
15
5
1
2
15
20
10
1
month
9
Calculation of revenues from C Remaining

• Expected Value from the Remaining Capacity

Probability of appearance of a customer asking
for satellite services Probability of
appearance of a customer (in 1 month) asking
for each service Number of months Mean
value Price/36 MHz/month
PB
PA
Broadcast
Theoretical Revenues Broadcast
?
?
Corporate
Leasing of C Remaining
Theoretical Revenues Corporate
Government
Theoretical Revenues Government
IP Gateway
Theoretical Revenues IP Gateway
Media Company
Scenario i
Theoretical Revenues Media Company
Telephony
Theoretical Revenues Telephony
Video Contribution
Theoretical Revenues Video Contribution
VSAT
Theoretical Revenues VSAT
Not leasing of C Remaining
Theoretical Revenues
10
Calculation of revenues from C Empty

• Expected Value from the Remaining Capacity

Probability of appearance of a customer (in 1
month) asking for each bandwidth
Probability of appearance of a customer asking
for satellite services number of
MHz of Empty C number of
months Mean value
Price/MHz/month
PC
PA
0-1,3 MHz
Theoretical Revenues
?
C
4 MHZ
Leasing of C Empty
Theoretical Revenues
6 MHZ
Theoretical Revenues
10MHz
Theoretical Revenues
18MHZ
Scenario i
Theoretical Revenues
33 MHz
Theoretical Revenues
36 MHz
Theoretical Revenues
Not leasing of C Empty
Theoretical Revenues
11
Output of the model Decision Tree
Standard Deviation Theoretical Revenues
Standard Deviation Expected Value
Expected Value
Theoretical Revenues
PB
PA
Broadcast
Corporate
?
?
Government
Leasing C Remaining
IP Gateway
Media Company
Telephony
Video Contribution
VSAT
Not leasing C Remaining
Scenario i
Real Revenues
1,3 MHz
PC
PA
4 MHz
C
6 MHz
Leasing C Empty
10 MHz
18 MHz
33 MHz
36 MHz
Not leasing C Empty
12
Comparison criteria

• Total Expected Revenues
• Real Revenues
• (Expected Value from C Empty
• Standard Deviation Expected Value
  C Empty)
• (Expected Value Revenues
  from C Remaining
• Standard
  Deviation Expected Value C Remaining)
• The real amount of money that will possibly
  result to the satellite operator is
• Total Revenues
• Real Revenues
• (Theoretical Revenues from C Empty
• Standard Deviation Theoretical
  Revenues C Empty)
• (Theoretical Revenues from
  C Remaining
• Standard Deviation
  Theoretical Revenues C Remaining)
• The decision depends on the attitude toward risk
  of the decision maker

13
Best-Worst Case Scenario

• Risk loving-Risk averse Attitude of the Decision
  Maker

Real Revenues Expected Value from C Empty
s Expected Value C Empty) (Expected Value
Revenues from C Remaining s Expected Value C
Remaining)
Real Revenues Expected Value from C Empty
- s Expected Value C Empty) (Expected Value
Revenues from C Remaining - s Expected Value C
Remaining)
14
Dynamic Programming Formulation

• state of the system xk and summarizes past
  information that is relevant for future
  optimization,
• the control uk which is the decision variable to
  be selected at each time k,
• and the disturbance wk which is the unknown noise
  parameter.

xk the sum of the capacity of all of the
customers of each combination, from the time k
and forward. uk the control of selling the
Empty Capacity or not. So uk could take the
values 1 or 0. wk is less or equal to the
Empty Capacity, and it is the amount of the Empty
Capacity that the operator decides to lease at
each time period.
15
Dynamic Programming Formulation
The system has the form
The closed loop optimization model has the form
of minimization of the expected cost function
including future costs
Total Expected Revenues for the satellite
operator
The dynamic programming formulation takes the
form of
16
Conclusion

• Addresses a real case
• Both heuristic and the dynamic programming, has
  shown similar results
• The modelling and analysis could also be useful
  to related types of activities where leasing for
  specific volumes to customers is the essence of
  the business enterprise.
• A more extended version of the work presented
  here with all the mathematical details (discrete
  time stochastic dynamic programming formulation
  and solution) is under development and will be
  presented in future publications

17
Thank you very much