An exact method for the double TSP with multiple stacks

Abstract

The double travelling salesman problem with multiple stacks (DTSPMS) is a pickup and delivery problem in which all pickups must be completed before any deliveries can be made. The problem originates from a real-life application where a 40 foot container (configured as 3 columns of 11 rows) is used to transport up to 33 pallets from a set of pickup customers to a set of delivery customers. The pickups and deliveries are performed in two separate trips, where each trip starts and ends at a depot and visits a number of customers. The aim of the problem is to produce a stacking plan for the pallets that minimizes the total transportation cost (ignoring the cost of transporting the container between the depots of the two trips) given that the container cannot be repacked at any stage. In this paper we present an exact solution method based on matching k-best TSP solutions for each of the separate pickup and delivery TSP problems and show that previously unsolved instances can be solved within seconds using this approach.

Improved exact method for the double TSP with multiple stacks

“…[10] on the same instances as Ref. [9] show larger optimality gaps in general. Although a much shorter computing time limit is observed in Ref.…”

“…Results in Ref. [9] suggest that containers with dimensions (6 × 3) and (7 × 2) are the current limit for this approach. Although such instances are shown to be solved within a few percent of optimality, less than 30% of the considered instances are actually solved to optimality.…”

“…Motivated by the need to identify better lower bounds, as well as the need to push the boundary on what can be solved to optimality, this article focuses on improving the exact method of Ref. [9]. This article is organized as follows.…”

“…[9] and [10] method described in Ref. [9] uses k-best TSP methodology. It proceeds by iteratively constructing the set of k-best tours to each of the pickup and delivery TSP problems and then considers every possible pickup and delivery tour pair in attempting to identify a feasible packing of the container.…”

The Uncapacitated Asymmetric Traveling Salesman Problem with Multiple Stacks

“…It strongly relies on the specific structure with two stacks and does not extend straightforwardly to the general case. A different approach was adopted by Lusby et al in [8], where they check whether there are k-consistent hamiltonian circuits within the t best ones, for some t. Despite the variety of available approaches, the largest instances solved to optimality roughly have 25 items.…”