Computational Experience with an M-Salesman Traveling Salesman Algorithm

Abstract

A formulation of the traveling salesman problem with more than one salesman is offered. The particular formulation has computational advantages over other formulations. Experience is obtained with an exact branch and bound algorithm employing both upper and lower bounds (mean run time for 55 city problems is one minute). Due to the special formulation, certain subtours may satisfy the constraints, thus reducing the search. A very good initial tour and upper bound are employed. The determination of these as well as the pathology of the formulation and the algorithm are discussed. No increase in computation time over the one-salesman case is experienced.

Traveling Salesman Problem: an Overview of Applications, Formulations, and Solution Approaches

“…iii. Crew scheduling problem: An application for deposit carrying between different branch banks is reported by (Svestka & Huckfeldt, 1973). Here, deposits need to be picked up at branch banks and returned to the central office by a crew of messengers.…”

Implementing vehicle routing algorithms

“…Multiple Traveling Salesmen Problems arise in many sorts of scheduling and sequencing applications. For example, the framework could be used to develop the basic route structure for a pickup or delivery service (perhaps a schoolbus or rural bus service); it has proved to be an appropriate model for the problem of bank messen6 r scheduling, where a crew of messengers picks up deposits at branch banks and returns them to the central office for processing [65].…”

Optimization of a Transportation System Planning Problem.

“…This problem requires each of n points to be serviced once by only one of the m vehid e s provided in the system ; vehicles must collectively execute their itinerancy at minim um total cost. This problem may be expressed mathematically (see Taha (1971, Svestka (1973, and Miller , et al (1960) 15] through [7]. The approach has apparently not been further refined by more recent research.…”