Abstract: We consider a model of competition process organized as a Stackelberg game. Two parties open their facilities with the aim to maximize profit from serving the customers which behave in accordance to a binary rule. The set of customers is unknown for the party opening its facilities first but reveals itself before the second party makes own decision. A finite set of scenarios specifying all the customer’s parameters is provided to the first party, and one of the scenarios would be realized in the future. The scenarios have a known probability of realization, and the first party, beside maximizing the profit, aims to increase the probability to get a certain profit value. We formulate a problem of the first party as a bi-objective bi-level mathematical program incorporating the second party’s problem at the lower-level. To approximate the set of effective solutions, we develop an ε-constraint method solving a sequence of bi-level problems with a single objective. A subset of weakly efficient solutions obtained by the method allows to analyze trade-offs caused by uncertainties in demand specification.

Cite: Melʹnikov A.A. , Beresnev V.L.
ε-Constraint method for bi-objective competitive facility location problem with uncertain demand scenari
2nd international workshop on Bilevel Programming 18-22 Jun 2018