An extended bilevel programming model and its kth-best algorithm for dynamic decision making in emergency situations

Linear bilevel programming has been studied for many years and applied in different domains such as transportation, economics, engineering, environment, and telecommunications. However, there is lack of attention of the impacts on dynamic decision making with abrupt or unusual events caused by unpredictable natural environment or human activities (e.g. Tsunami, earthquake, and malicious or terrorist attacks). In reality these events could happens more often and have more significant impacts on decision making in an increasingly complex and dynamic world. This paper addresses this unique problem by introducing a concept of Virtual Follower (VF). An extended model of bilevel multi-follower programming with a virtual follower (BLMFP-VF) is defined and the kth-best algorithm for solving this problem is proposed. An example is given to illustrate the working of the extended model and approach.