This article presents a new framework for the geographic profiling problem which assesses and integrates the travel environment of road networks; beliefs and assumptions formed through the investigation process about the perpetrator; and information derived from the analysis of evidence. Each piece of information is evaluated in conjunction with functions which gather real-time travel information, including both time and distance of likely perpetrator travel, and is then used to update prior beliefs about the potential base of operation of the perpetrator. A novel approach was developed to generate geographic profiles given different amounts of information about the perpetrator: a centrographic strategy for when only the victim dump sites are known; a perpetrator trek strategy for instances where both victim encounter and dump sites are available; and a formal evidence-driven model which leverages and integrates available information and evidence relevant to the case for the development of a geographic profile. A follow-up article will evaluate these models through a comprehensive application to the Yorkshire Ripper investigation (see Part II).