We describe two optimization methods for vehicle routing problems with
time windows. These are a K-Tree relaxation with time windows added a
s side constraints and a Lagrangian decomposition in which variable sp
litting is used to divide the problem into two subproblems-a semi-assi
gnment problem and a series of shortest path problems with time window
s and capacity constraints. We present optimal solutions to problems w
ith up to 100 customers.