Column Generation Based Heuristics for a Generalized Location Routing Problem with Profits Arising in Space Exploration Jaemyung Ahn (jaemyung@mit.edu) Olivier de Weck (deweck@mit.edu) Department of Aeronautics and Astronautics Massachusetts Institute of Technology Yue Geng (yue-geng@northwestern.edu) Diego Klabjan (d-klabjan@northwestern.edu) Department of Industrial Engineering and Management Sciences Northwestern University January 15, 2012 Abstract The generalized location routing problem with profits is a new routing problem class that combines the vehicle routing problem with profits, depot or base selection, and the notion of strategies and route tactics to be employed at selected bases. The problem simultaneously determines base locations, strategies to use at the bases, sites to visit, and routes to carry out the visits, to maximize the sum of profits that can be obtained by visiting sites, un- der resource consumption constraints. The problem arises in exploration of planetary bodies where strategies correspond to different technologies. A description of the generalized location routing problem with profits and its mathematical formulation as an integer program are pro- vided. Two solution methodologies to solve the problem - branch-and-price and a three-phase heuristic method combined with a generalized randomized adaptive search procedure - are proposed. Numerical experiments for the two solution methodologies are carried out. Their performance in terms of computation time and optimality gap are analyzed and compared to establish the problem characteristics, indicating which method is more advantageous. 1 Introduction During exploration of planetary bodies, NASA first identifies a set of potential surface locations to serve as exploration bases. At each base various strategies can be used. Among all strategies, exactly one has to be employed at each selected base. Each base can have its own strategies and they do not have to be the same for all bases. For example, the standard strategy might imply that once an exploration vehicle leaves the base, the route length must not exceed its fuel capacity. On the other hand, under the orbiting depot strategy, a depot might orbit around the planetary body and it can provide additional fuel to the exploration vehicles. If this strategy is employed at a base, routes can be longer. The selected strategy at a base implies a set of resource constraints on the routes originating at the base. Exploration sites are potential locations on the surface to be explored by NASA scientists and astronauts. All sites are not required to be visited, however, exploring a site yields a given 1