期刊
NETWORKS
卷 59, 期 1, 页码 107-116出版社
WILEY-BLACKWELL
DOI: 10.1002/net.20482
关键词
bilevel; stochastic; optimization; networks; pricing
资金
- France/HongKong Joint Research Scheme [PROCORE F-HK09/07T]
- GRF (Hong Kong Research Grants Council) [414608]
In this article, a mixed integer bilevel problem having a probabilistic knapsack constraint in the first level is proposed. The problem formulation is mainly motivated by practical pricing and service provision problems as it can be interpreted as a model for the interaction between a service provider and customers. A discrete probability space is assumed which allows a reformulation of the problem as an equivalent deterministic bilevel problem. The problem is further transformed into a linear bilevel problem, which in turn yields a quadratic optimization problem, namely the global linear complementarity problem. Based on this quadratic problem, a procedure to compute upper bounds on the initial problem by using a Lagrangian relaxation and an iterative linear minmax scheme is proposed. Numerical experiments confirm that the scheme practically converges. (C) 2011 Wiley Periodicals, Inc. NETWORKS, Vol. 59(1), 107-116 2012
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