On a stochastic bilevel programming problem

✍ Scribed by Stefanie Kosuch; Pierre Le Bodic; Janny Leung; Abdel Lisser

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 160 KB
• Volume: 59
• Category: Article
• ISSN: 0028-3045
• DOI: 10.1002/net.20482

✦ Synopsis

Abstract

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.© 2011 Wiley Periodicals, Inc. NETWORKS, 2012