1. Introduction of new service, Part II Summary
Important facility location problem
Modeling of uncertainty and dynamic decisions
robust decision under uncertainty has a structure which can not be recovered from consideration of individual scenarios
Interplay between decisions of different scale: tactical and operational decisions;
Profit and pricing
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

2. Case study:Introduction of new service
Service: internet access through phone line
Features: geographical regions, demand is uncertain, costs are uncertain, fixed costs, variable costs, time, competition and substitution between services, relations between different market actors, e.g. network providers and service providers
Decisions: Locations of servers, pricing, number of servers in Phase 1 and Phase 2;
Strategies:
Phase 1 deployment now, look for user response, Phase 2 deployment later;
real options: option to expand, option to abandon
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

3. Universita’ degli Studi di Bergamo Corso di dottorato di ricerca
Description of demand uncertainty: scenarios
value of demand under scenario r
probability (frequency) of scenario r
Time structure of decisions:
now: placement of servers tactical decision
future correction: assignment of demand to servers when demand scenario r will be known
operational
decision
now
future
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

4. Two Phase service deployment
Find Phase 1 server placement and current demand assignment which minimize current deployment cost and average Phase 2 expansion and demand service cost
costs
first stage constraints
second stage constraints
for scenario r
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

5. Modeling of price and profit: unique service
How demand depend on price?
Simplest case: linear dependence
- reference price
h incremental price
- demand which corresponds to reference price
w demand elasticity
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

6. Universita’ degli Studi di Bergamo Corso di dottorato di ricerca
Demand vs price
demand
f(h) d0
price h h0
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

7. Universita’ degli Studi di Bergamo Corso di dottorato di ricerca
Description of demand uncertainty: scenarios
base value of demand under scenario r
base price under scenario r
demand elasticity under scenario r
probability (frequency) of scenario r
Time structure of decisions:
Phase 1
Phase 2
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

8. Two Phase service deployment
Find Phase 1 server placement and current demand assignment which maximize expected profit
revenue
costs
first stage constraints
second stage
constraints
for scenario r
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

9. Universita’ degli Studi di Bergamo Corso di dottorato di ricerca
where
revenue
first stage
second stage
averaged among
scenarios
costs
first stage
second stage
averaged among
scenarios
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

10. Universita’ degli Studi di Bergamo Corso di dottorato di ricerca
Features
Quadratic with respect to continuous variables
Binary variables
Straightforward linear MIP is not applicable
Solution techniques:
Benders decomposition
Genetic algorithms
Iterative fixed point techniques
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

11. Iterative fixed point techniques
Idea: substitute one difficult problem with a sequence of simpler ones
a.Fix binary location variables y, resulting problem is quadratic programming problem in continuous variables, solve it with XPRESS or other solver
b. Fix continuous variables to the values just obtained, resulting problem is IP in binary variables, solve it again with XPRESS
c. Repeat steps a-b several times
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

12. Universita’ degli Studi di Bergamo Corso di dottorato di ricerca
Dependence of profit on price
Profit
Price
Blue graph: fixed costs doubled
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca

13. Competition with other providers
Classical efficient market: just charge market price and improve your own efficiency
Our situation: we provide service which is different, but not quite
Reference service provided by competitors for reference price h0
Our decision: amount h by which our price differs from reference price
Scenarios about future prices of competitors
We are back to monopoly case, BUT, more difficult to get scenario data
Alexei A.Gaivoronski
June 2001
Universita’ degli Studi di Bergamo
Corso di dottorato di ricerca