Jorge Cortés
Professor
Cymer Corporation Endowed Chair
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
Abstract
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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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo