Physical Sciences and Mathematics Commons^™

Submodularity And Local Search Approaches For Maximum Capture Problems Under Generalized Extreme Value Models, Tien Thanh Dam, Thuy Anh Ta, Tien Mai

Research Collection School Of Computing and Information Systems

We study the maximum capture problem in facility location under random utility models, i.e., the problem of seeking to locate new facilities in a competitive market such that the captured user demand is maximized, assuming that each customer chooses among all available facilities according to a random utility maximization model. We employ the generalized extreme value (GEV) family of discrete choice models and show that the objective function in this context is monotonic and submodular. This finding implies that a simple greedy heuristic can always guarantee a (1−1/e) approximation solution. We further develop a new algorithm combining a greedy heuristic, …