Technical Note—An <i>n</i>-Constraint Formulation of the (Time-Dependent) Traveling Salesman Problem

Fox, Kenneth R.; Gavish, Bezalel; Graves, Stephen C.

doi:10.1287/opre.28.4.1018

Cited by 117 publications

(56 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Either way, we can pick i, j ∈ {3, 5} with i = j such that i / ∈ S ′ , j ∈ S ′ . So pick an s-path that goes through vertices (1, 1), (2, 2), (4, 3), (i, 4), (j, 5), (7,6). Such an s-path satisfies (10) for S at equality and for S ′ as a strict inequality since it cannot use any arcs of A(S ′ , t) for any t.…”

Section: Theorem 12 If N ≥ 7 Then (10) Defines a Distinct Facet Of Pmentioning

confidence: 99%

See 1 more Smart Citation

The time dependent traveling salesman problem: polyhedra and algorithm

et al. 2012

View full text Add to dashboard Cite

The Time Dependent Traveling Salesman Problem (TDTSP) is a generalization of the classical Traveling Salesman Problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very challenging TDTSP instances with less than 100 vertices. In this work, we study the polytope associated to the TDTSP formulation by Picard and Queyranne, which can be viewed as an extended formulation of the TSP. We determine the dimension of the TDTSP polytope and identify several families of facet-defining cuts. We obtain good computational results with a branch-cut-and-price algorithm using the new cuts, solving almost all instances from the TSPLIB with up to 107 vertices.

show abstract

Section: Theorem 12 If N ≥ 7 Then (10) Defines a Distinct Facet Of Pmentioning

confidence: 99%

“…Results for the STSP are surveyed in [13] and for the ATSP in [3]. Formulations for the TDTSP have been proposed or studied in [23,20,7,10,29,9]. Exact algorithms for the TDTSP are presented in [20,4,29] and, for the special case of the TDP, in [6,17,18].…”

Section: Introductionmentioning

confidence: 99%

The time dependent traveling salesman problem: polyhedra and algorithm

et al. 2012

View full text Add to dashboard Cite

show abstract

“…Langevin et al [1990] showed that the LP relaxation of GG is equivalent to that of the two-commodity flow formulation proposed by Finke et al [1984] -hereafter FCG. Fox et al [1980] proposed three formulations for the time-dependent traveling salesman problem that are valid for the ATSP, as well. These formulations present n 3 binary variables, r ijk , that are equal to 1 if and only if arc (i, j) ∈ A is in position k in the optimal tour.…”

Section: Review Of Polynomial Formulationsmentioning

confidence: 99%

Exact algorithms for different classes of vehicle routing problems

Roberti¹

2012

4OR-Q J Oper Res

View full text Add to dashboard Cite

“…FISCHETTI, LA-PORTE, and MARTELLO (1993) presented an algorithm based upon dual ascent and gave computational results for the (optimal) solution of problems involving up to 60 cities. For earlier work on this problem, see PICARD and QUEYRANNE (1978), FOX et al (1980).…”

Section: Previous Workmentioning

confidence: 99%

Scheduling Aircraft Landings—The Static Case

Beasley

Krishnamoorthy

Sharaiha

et al. 2000

Transportation Science

355

309

View full text Add to dashboard Cite

In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a planeInthispaper,weconsidertheproblemofscheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time on a runway for each plane in a given set of planes such that each plane lands within a predetermined time window, and that separation criteria between the landing of a plane, and the landing of all successive planes, are respected.This paper is organized as follows. In Section 1, we set the problem in context. In Section 2, we present a mixed-integer zero-one formulation of the problem for the single runway case. We then discuss previous work on the problem in Section 3. In Section 4, we extend the formulation to the multiple runway case, and, in Section 5, we strengthen the linear programming (LP) relaxations of these formulations by introducing additional constraints. These formulations can be solved using LP-based tree search. An effective heuristic for the problem (for any number of runways) is presented in Section 6. Computational results for both the heuristic and the optimal algorithm for a number of test problems involving up to 50 planes and four runways are presented in Section 7.It is important to note here that, although throughout this paper we shall typically refer to planes landing, the models presented in this paper are applicable to problems involving just takeoffs only and to problems involving a mix of landings and takeoffs on the same runway. We should also stress here that we are dealing only with the static case. In other words, we are dealing with the off-line case where we have complete knowledge of the set of planes that are going to land. The dynamic, or on-line, case, where decisions about the landing times for planes must be made as time passes and the situation changes (planes land, new planes appear, etc.) is the subject of a separate paper (BEASLEY et al., 1995).

show abstract

Technical Note—An n-Constraint Formulation of the (Time-Dependent) Traveling Salesman Problem

Abstract: A new formulation of the time-dependent salesman problem is presented which uses n3 variables and only n constraints.

Cited by 117 publications

References 4 publications

The time dependent traveling salesman problem: polyhedra and algorithm

The time dependent traveling salesman problem: polyhedra and algorithm

Exact algorithms for different classes of vehicle routing problems

Scheduling Aircraft Landings—The Static Case

Contact Info

Product

Resources

About