2018 Optimization Days

HEC Montréal, Québec, Canada, May 7 — 9, 2018

Schedule Authors My Schedule
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TA11 Bilevel optimization

May 8, 2018 10:30 AM – 12:10 PM

Location: Xerox Canada (48)

Chaired by Teodora Dan

4 Presentations

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    10:30 AM - 10:55 AM

    Dynamic programming approach for bidding problems on day-ahead markets

    • Jérôme De Boeck, presenter, Université Libre de Bruxelles
    • Martine Labbé, GOM, Université Libre de Bruxelles and INRIA
    • Patrice Marcotte, Université de Montréal
    • Étienne Marcotte, Engie
    • Gilles Savard, Polytechnique Montréal

    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.

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    10:55 AM - 11:20 AM

    Arc-based MILP reformulation of a traffic control bi-level program

    • Léonard Ryo Morin, presenter, UdeM
    • Emma Frejinger, DIRO and CIRRELT
    • Bernard Gendron, Université de Montréal, CIRRELT

    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.

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    11:20 AM - 11:45 AM

    A branch-and-bound algorithm for a bilevel location model involving competition and queueing

    • Teodora Dan, presenter, Université de Montréal
    • Lodi Andrea, Polytechnique Montreal
    • Patrice Marcotte, Université de Montréal

    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.

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    11:45 AM - 12:10 PM

    A transportation network pricing problem

    • Julie Kienzle, presenter, Université de Montréal
    • Patrice Marcotte, Université de Montréal
    • Gilles Savard, Polytechnique Montréal

    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.

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