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An optimal algorithm for the mixed Chinese postman problem
Author(s) -
Nobert Yves,
Picard JeanClaude
Publication year - 1996
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/(sici)1097-0037(199603)27:2<97::aid-net1>3.0.co;2-8
Subject(s) - integer programming , simplex algorithm , mathematics , mathematical optimization , simplex , set (abstract data type) , mixed graph , graph , integer (computer science) , linear programming , algorithm , combinatorics , computer science , voltage graph , line graph , programming language
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. © 1996 John Wiley & Sons, Inc.