Time‐dependent traveling salesman problem–the deliveryman case

Abstract

We consider a scheme to derive lower bounds for the time-dependent traveling salesman problem. It involves splitting lower bounds into a number of components and optimizing each of these components. The lower bounds thus derived are shown to be at least as sharp as the ones previously suggested for the problem. We describe a branch-andbound algorithm based on our lower bounding scheme and computationally test it for an instance of the problem known as the traveling deliveryman problem.

The time dependent traveling salesman problem: polyhedra and algorithm

“…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]. This paper is organized as follows.…”

Cumulative Vehicle Routing Problems

“…The Time-Dependent Traveling Salesman Problem (TDTSP) is a generalization of the standard Traveling Salesman Problem in which the cost of traveling from one node to another depends not only on the two locations, but also on their positions in the tour (Picard & Queyranne (1978), Lucena (1990), Gouviea & VoB (1995)). When the objective of the TDTSP is to minimize the sum of distances traveled from the depot to all nodes, the problem is known as the Traveling Salesman Problem with Cumulative Cost or the Cumulative Traveling Salesman Problem (CTSP), as defined by Bianco et al(1993).…”

Natural and extended formulations for the Time-Dependent Traveling Salesman Problem

“…Exact methods for solving the CTSP are described, among others, in Lucena (1990), Fischetti et al (1992), Bianco at al (1993) and, more recently, in Bigras et al (2008), Méndez-Dias et al (2008) and Abeledo et al (2010). Lucena (1990) proposes an algorithm based on a non-linear integer programming formulation by Picard and Queyranne in which lower bounds are obtained from a Lagrangean relaxation and presents computational results for problems up to 30 nodes.…”

“…Lucena (1990) proposes an algorithm based on a non-linear integer programming formulation by Picard and Queyranne in which lower bounds are obtained from a Lagrangean relaxation and presents computational results for problems up to 30 nodes. A similar approach was followed by Bianco at al.…”