A classification of formulations for the (time-dependent) traveling salesman problem

The time dependent traveling salesman problem: polyhedra and algorithm

“…Let I(S, p) be an alternating independent set and (i, j, t) ∈ A with 1 ≤ t ≤ n − 2. Then the facet defined by inequality (10) for I(S, p) and the facet defined by inequality (4) for (i, j, t) are not the same.…”

“…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].…”

Exact algorithms for different classes of vehicle routing problems

“…The first formulation (therein P1) has 4n constraints, whereas the second formulation (hereafter P1b) has 3n constraints and is obtained from the first one by dropping a set of n constraints. Thus, the LP relaxation of the first formulation is stronger than that of the second one; Gouveia and Voß [1995] showed that the LP relaxations of both formulations are stronger than that of GG. The third formulation proposed by Fox et al (therein P2) has n + 1 constraints and is obtained from the first formulation by surrogating the first 3n constraints.…”

A Survey of Different Integer Programming Formulations of the Travelling Salesman Problem

“…Some of the time staged formulations have also been compared by Gouveia and Voss (1995) and discussed by Picard and Queyranne (1978). The sequential formulation has also been improved by Gouveia and Pires (2001).…”