Networks and Spatial Economics

, Volume 16, Issue 3, pp 743–768 | Cite as

An Algorithm for the One Commodity Pickup and Delivery Traveling Salesman Problem with Restricted Depot

  • Lanshan Han
  • Binh T. Luong
  • Satish UkkusuriEmail author


In this paper we study the one commodity pickup-and-delivery traveling salesman problem with restricted depot (1-PDTSP-RD), which is a generalization of the classical traveling salesman problem (TSP). We first introduce a polynomial size integer programming formulation for the problem and then study the feasibility issue which is shown to be \(\mathcal {NP}\)-complete by itself. In particular, we prove sufficient conditions for the feasibility of the problem and provide a polynomial algorithm to find a feasible solution. We also develop a bound on the cost of the 1-PDTSP-RD solution in terms of the cost of the TSP solution. Based on this bound, we provide a heuristic algorithm to solve the 1PDTSP-RD. Extensive numerical experiments are performed to evaluate the efficiency of both the exact and approximation algorithms.


Traveling salesman Pickup and delivery Capacitated vehicle 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Civil EngineeringPurdue UniversityWest LafayetteUSA

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