A constraint programming approach to the Chinese postman problem with time windows

The Chinese postman problem with time windows is modelled as a constraint program and results are reported for a set of test problems with up to 69 edges. Two different formulations are proposed. The first formulation approaches the problem directly and the second transforms the problem to an equivalent vehicle routing problem with time windows. The results demonstrate that optimal solutions can be obtained quickly when the time windows are tight. However, the results also show that as the time windows are made wider and the number of feasible solutions increases, these constraint programming formulations take significantly longer to find a provably optimal solution. The results also demonstrate how the size and density of the graph affects the computing time needed to find an optimal solution.