On Searching for Large Objects with Small Probes: A Search Model for Exploration

We propose a model for optimal allocation of effort when searching for large objects with small probes. Because of the size of the objects, search activities at different locations can be physically and statistically dependent, and consequently classical search models are inappropriate. The difficulties resulting from such statistical dependence can be overcome by using original data or Monte-Carlo derived scenarios in an integer linear programming model. The proposed optimization model should be of moderate size in typical applications, and by exploiting its special structure it can be solved optimally by standard methods. When this is uneconomical it may be solved approximately by efficient heuristics. Applications of these ideas have already been made to the detection of glaucoma. This paper focuses on possible applications in exploratory drilling for petroleum.