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

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

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

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

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

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

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

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

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

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

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

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

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