Modeling of Competition and Collaboration Networks under Uncertainty: Stochastic Programs with Resource and Bilevel

Gaivoronski, A.A. & Werner, A. (2007). Modeling of Competition and Collaboration Networks under Uncertainty: Stochastic Programs with Resource and Bilevel. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-07-041

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Abstract

We analyze stochastic programming problems with recourse characterized by a bilevel structure. Part of the uncertainty in such problems is due to actions of other actors such that the considered decision maker needs to develop a model to estimate their response to his decisions. Often, the resulting model exhibits connecting constraints in the leaders (upper-level) subproblem. It is shown that this problem can be formulated as a new class of stochastic programming problems with equilibrium constraints (SMPEC). Sufficient optimality conditions are stated. A solution algorithm utilizing a stochastic quasi-gradient method is proposed, and its applicability extensively explained by practical numerical examples.

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