  We present two models of perpetrators' decision-making in extracting
resources from a protected area. It is assumed that the authorities conduct
surveillance to counter the extraction activities, and that perpetrators choose
their post-extraction paths to balance the time/hardship of travel against the
expected losses from a possible detection. In our first model, the authorities
are assumed to use ground patrols and the protected resources are confiscated
as soon as the extractor is observed with them. The perpetrators' path-planning
is modeled using the optimal control of randomly-terminated process. In our
second model, the authorities use aerial patrols, with the apprehension of
perpetrators and confiscation of resources delayed until their exit from the
protected area. In this case the path-planning is based on multi-objective
dynamic programming. Our efficient numerical methods are illustrated on several
examples with complicated geometry and terrain of protected areas, non-uniform
distribution of protected resources, and spatially non-uniform detection rates
due to aerial or ground patrols.
