Single- and multi-objective defensive location problems on a network

This paper considers a new optimal location problem, called defensive location problem (DLP). In the DLPs, a decision maker locates defensive facilities in order to prevent her/his enemies from reaching an important site, called a core; for example, “a government of a country locates self-defense bases in order to prevent her/his aggressors from reaching the capital of the country.” It is assumed that the region where the decision maker locates her/his defensive facilities is represented as a network and the core is a vertex in the network, and that the facility locater and her/his enemy are an upper and a lower level of decision maker, respectively. Then the DLPs are formulated as bilevel 0-1 programming problems to find Stackelberg solutions. In order to solve the DLPs efficiently, a solving algorithm for the DLPs based upon tabu search methods is proposed. The efficiency of the proposed solving methods is shown by applying to examples of the DLPs. Moreover, the DLPs are extended to multi-objective DLPs that the decision maker needs to defend several cores simultaneously. Such DLPs are formulated as multi-objective programming problems. In order to find a satisfying solution of the decision maker for the multi-objective DLP, an interactive fuzzy satisfying method is proposed, and the results of applying the method to examples of the multi-objective DLPs are shown.