10:30 AM - 10:55 AM
Dynamic programming approach for bidding problems on day-ahead markets
In several markets, such as the electricity market, spot prices are determined via a bidding system involving an oligopoly of producers and a system operator. We consider a profit-maximizing producer, whose bids depend on the behaviour of the system operator, as well as the stochastic nature of final demand, and that can be cast within the framework of stochastic bilevel programming. A dynamic programming approach is applied to tackle this problem.
10:55 AM - 11:20 AM
Arc-based MILP reformulation of a traffic control bi-level program
We discuss a traffic control application where a transportation network manager allocates traffic flow controlling resources. Traffic flows can be antagonistic or cooperative. We present a bi-level programming formulation with an arc-based random utility model that we reformulate in a mixed integer linear program.
11:20 AM - 11:45 AM
A branch-and-bound algorithm for a bilevel location model involving competition and queueing
We consider a competitive environment in which users patronize the facility minimizing the sum of travel time and queueing delay. This situation can be modeled as a bilevel program that involves discrete and continuous variables, as well as linear and nonlinear functions. We propose an exact branch-and-bound framework for determining the optimal locations and service levels associated with facilities. A valid upper bound for this maximization problem is obtained via linearization of the lower level nonlinear terms. Whenever an integer solution is achieved, a lower bound is computed by solving the follower's mathematical program. Numerical results will be presented and discussed.
11:45 AM - 12:10 PM
A transportation network pricing problem
I will present a transportation network pricing problem where the leader wants to maximize its revenue by considering the network’s equilibrium. This profit depends on the tolls that we impose on a subset of roads. Thereafter, I will introduce different reformulations for this bilevel program and the methods that we used to solve them.