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In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The strategy of releasing nonbasic variables from their bounds, combined with the 'active constraint' method and the notion of superbasics, has been developed for efficiently requirements; this strategy is used to force the appropriate non-integer basic variables to move to their neighborhood integer points. A study of criteria for choosing a nonbasic variable to work with in the integerizing strategy has also been made. [ABSTRACT FROM AUTHOR]