New Tighter Polynomial Length Formulations For The

trading operations Research Letters 33 (2005) 62 70

Operations Research Letters
www.elsevier.com/locate/dsw

New tighter polynomial length formulations for the irregular locomotion salesman trouble with and without precedence constraints
Subhash C. Sarin, Hanif D. Sherali? , Ajay Bhootra
Grado Department of Industrial and Systems Engineering, Virginia polytechnic institute Institute and State University, 250 Durham Hall, Blacksburg, VA 24061, USA Received 18 February 2003; accepted 16 March 2004

Abstract We propose a new formulation for the asymmetric traveling salesman problem, with and without precedence relationships, which employs a polynomial number of subtour liquidation constraints that imply an exponential subset of real relaxed DantzigFulkersonJohnson subtour constraints. Promising computational results are presented, particularly in the front of precedence constraints. c 2004 Elsevier B.V. All rights reserved.
Keywords: Asymmetric traveling salesman problem; Precedence constraints; Subtour elimination constraints

1. Introduction The traveling salesman problem (TSP) is possibly the most widely researched combinatorial optimization problem.



The TSP can be stated as follows: Given a ÿnite set of cities N = {1; 2; : : : ; n} and the cost of travel cij betwixt each pair of cities i; j ? N , ÿnd a tour that visits each city exactly once, piece minimizing the total cost of travel. In this paper, we address the asymmetric traveling salesman problem (ATSP) for which cij and cji might di er for any pair i; j ? N . Mathematical programming formulations for the ATSP involve the duty assignment constraints along with subtour elimination constraints (SECs), besides the binary restrictions on the ratiocination variables
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Corresponding author. E-mail address: hanifs@vt.edu (H.D. Sherali).

(see [5,1012]). In this paper, we present a new formulation for ATSP based on modeling the subtour elimination constraints using a polynomial number of restrictions that imply an...If you expect to get a full essay, order it on our website: Orderessay



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