The increasing threat of terrorism makes security at major locations of economic or political importance a major concern. Limited security resources prevent complete security coverage, allowing adversaries to observe and exploit patterns in patrolling or monitoring, and enabling them to plan attacks that avoid existing patrols. The use of randomized security policies that are more difficult for adversaries to predict and exploit can counter their surveillance capabilities. We describe two applications, ARMOR and IRIS, that assist security forces in randomizing their operations. These applications are based on fast algorithms for solving large instances of Bayesian Stackelberg games. Police at the Los Angeles International Airport deploy ARMOR to randomize the placement of checkpoints on roads entering the airport and the routes of canine unit patrols within the airport terminals. The Federal Air Marshal Service has deployed IRIS in a pilot program to randomize the schedules of air marshals on international flights. This paper examines the design choices, information, and evaluation criteria that were critical to developing these applications.
We consider the Courier Delivery Problem, a variant of the Vehicle Routing Problem with time windows in which customers appear probabilistically and their service times are uncertain. We use scenario-based stochastic programming with recourse to model the uncertainty in customers and robust optimization for the uncertainty in service times. Our proposed model generates a master plan and daily schedules by maximizing the coverage of customers and the similarity of routes in each scenario while minimizing the total time spent by the couriers and the total earliness and lateness penalty. The computational results show that our heuristic improves the similarity of routes and the lateness penalty at the expense of increased total time spent when compared to a solution by independently scheduling each day. Our experimental results also show improvements over current industry practice on two real-world data sets.
This paper presents a robust optimization model for n-person finite state/action discounted stochastic games with incomplete information. We consider n-player, non-zero sum discounted stochastic games in which none of the players knows the true data of the game and each player considers a distribution-free incomplete information stochastic game to be played using robust optimization. We call such games "discounted robust stochastic games". Discounted robust stochastic games allow us to use simple uncertainty sets for the unknown data of the game, and eliminate the need to have an a-priori probability distribution over a set of games. We prove the existence of equilibrium points and propose an explicit mathematical programming formulation for an equilibrium calculation. We illustrate the use of discounted robust stochastic games in a single server queueing control problem.
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