Jorge Cortés


Robust optimal investment policies for servicing targets in acyclic digraphs
C. Nowzari, J. Cortés
Proceedings of the IEEE Conference on Decision and Control, Maui, Hawaii, 2012, pp. 136-141


This paper considers a class of scenarios where targets emerge from some known location and move towards some (unknown) destinations in a network of roads modeled as a weighted acyclic digraph. A decision maker with knowledge about the target positions must decide when preparations should be made for the arrival of a target at different possible goals. The trade-off the decision maker faces is that making early decisions means more time for preparation at the cost of higher uncertainty in the target's destination, while late decisions means less uncertainty at the cost of having less time to prepare. We show how this problem can be formulated as an Optimal Stopping problem on a Markov chain. This sets the basis for the introduction of the best investment algorithm. This strategy prescribes when investments must be made conditioned on where the target has been. We establish the optimality of the proposed strategy and examine the robustness of the optimal solution against changing conditions of the problem. Finally, we develop the recomputation decision algorithm that is capable of determining whether the solution computed by the best investment algorithm remains optimal under changes in the problem data or must be recomputed. Several simulations illustrate our results.

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