Bilevel Programming: Applications

Bilevel programming (see Bilevel programming: Introduction, history and overview; Bilevel programming) is ideally suited to model situations where the decision maker does not have full control over all decision variables. Five such situations are described in this article.

EXAMPLE 1

The first example involves the improvement of a road network through either capacity expansion, traffic signals synchronization, vehicle guidance systems, etc. While management may be assumed to control the design variables, it can only affect indirectly the travel choices of the network users. Let x denote the design vector, y the flow vector, X the set of feasible design variables and c _i (x, y) the travel delay along link i. One wishes to minimize over the set X the system travel cost ∑ _i y _i c _i (x, y), where the vector y is required to be an equilibrium traffic assignment corresponding to the design vector x. Neglecting the latter equilibrium requirement could lead to suboptimal policies. However, as...