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

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Abstract

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.

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Authors and Affiliations

  1. School of Civil Engineering, Purdue University, West Lafayette, IN, 47906, USA

    Lanshan Han, Binh T. Luong & Satish Ukkusuri

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  1. Lanshan Han
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  2. Binh T. Luong
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  3. Satish Ukkusuri
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Correspondence to Satish Ukkusuri.

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Han, L., Luong, B.T. & Ukkusuri, S. An Algorithm for the One Commodity Pickup and Delivery Traveling Salesman Problem with Restricted Depot. Netw Spat Econ 16, 743–768 (2016). https://doi.org/10.1007/s11067-015-9297-3

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