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Observing mobile or static targets in the ground using flying drones is a common task for civilian and military applications. We introduce the minimum cost drone location problem and its solutions for this task in a two-dimensional terrain. The number of drones and the total energy consumption are the two cost metrics considered. We assume that each drone has a minimum and a maximum observation altitude. Moreover, the drone's energy consumption is related to this altitude. Indeed, the higher the altitude, the larger the observed area but the higher the energy consumption. The aim is to find drone locations that minimize the cost while ensuring the surveillance of all the targets. The problem is mathematically solved by defining an integer linear and a mixed integer non-linear optimization models. We also provide some centralized and localized heuristics to approximate the solution for static and mobile targets. A computational study and extensive simulations are carried out to assess the behavior of the proposed solutions.

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This article surveys the main contributions that have appeared in the scientific literature addressing resource constrained shortest path problems. The aim of this work is twofold: to give a structured survey of the literature on this topic; to provide a starting point for researchers who want to address the problems at hand. The study is focused on the relevant contributions dealing with exact solution approaches.

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