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We describe two optimization methods for vehicle routing problems with time windows. These are a K-Tree relaxation with time windows added as side constraints and a Lagrangian decomposition in which variable splitting is used to divide the problem into two subproblems—a semi-assignment problem and a series of shortest path problems with time windows and capacity constraints. We present optimal solutions to problems with up to 100 customers.
Fisher et al. (Sun,) studied this question.