An extension of the Christofides heuristic for the generalized multiple depot multiple traveling salesmen problem

• Main Authors: XU, Zhou, RODRIGUES, Brian Charles
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2017
• Subjects: Approximation algorithm; Multiple depots; Traveling salesman problem; Operations and Supply Chain Management; Operations Research, Systems Engineering and Industrial Engineering
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/4999
• Institution: Singapore Management University

We study a generalization of the classical traveling salesman problem, where multiple salesmen are positioned at different depots, of which only a limited number (k) can be selected to service customers. For this problem, only two 2-approximation algorithms are available in the literature. Here, we improve on these algorithms by showing that a non-trivial extension of the well-known Christofides heuristic has a tight approximation ratio of 2 -1/(2k). In doing so, we develop a body of analysis which can be used to build new approximation algorithms for other vehicle routing problems.