An optimal algorithm for the mixed Chinese postman problem

The Chinese Postman Problem is well solved when the original graph contains only arcs or only edges. The mixed Chinese Postman Problem (MCPP) is, however, NP-complete, and very few papers have been devoted to this problem. In this paper, we present a new integer programming model and a new optimal algorithm for the MCPP. The simplex method is used iteratively to obtain sharp lower bounds by solving successive relaxations of this model. Optimality is achieved by using Gomory cuts, blossom inequalities and balanced set constraints. Detailed computational results are presented.