Exact solutions to the double travelling salesman problem with multiple stacks

Abstract

In this article we present mathematical programming formulations and solution approaches for the optimal solution of the Double Travelling Salesman Problem with Multiple Stacks (DTSPMS). A set of orders is given, each one requiring transportation of one item from a customer in a pickup region to a customer in a delivery region. The vehicle available for the transportation in each region carries a container. The container is organized in rows of given length. Each row is handled independently from the others according to a Last In First Out stack policy. The DTSPMS problem consists of determining the pickup tour, the loading plan of the container and the delivery tour in such a way that the total length of the two tours is minimized. The formulations are based on different modeling ideas and each formulation gives rise to a specific solution approach. We present computational results on a set of benchmark instances that compare the different approaches and show that the most successful one is a decomposition approach applied to a new model.

Vehicle routing problems with loading constraints: state-of-the-art and future directions

“…Only the k-best delivery and pickup tours in terms of length are considered. Petersen et al (2010) propose several different modeling approaches for an exact solution of the DTSPMS. First, a branch-and-cut approach is used on the mathematical programming formulation of the problem introduced in Petersen and Madsen (2009) which is called the 'precedence' model.…”

Routing problems with loading constraints

“…Lusby et al (2010) presented an exact algorithm, which generates the k best solutions for each of the two separate routes, and looks for the lowest cost pair (if any) that allows a feasible stacking plan. Petersen et al (2010) proposed several branch-and-cut algorithms, one of which, based on the separation of infeasible path constraints, clearly outperforms the others.…”

Combining vehicle routing and packing for optimal delivery schedules of water tanks

“… pickup and delivery problems: VRPs where a set of transportation requests is satisfied by a given fleet of vehicles (Cordeau et al, 2007b); each request is characterised by its pickup location (origin), its delivery location (destination) and the size of the load that has to be transported from the origin to the destination; in the variant with time windows, for each pickup and delivery location, a time window and loading and unloading times are specified; the load capacity, the maximum length of its operating interval, a start location and an end location are given for each vehicle; in order to fulfil the requests, a set of routes has to be planned such that each request is transported from its origin to its destination by exactly one vehicle (Pankratz, 2005); a variant with separate pickup and delivery tours and goods to be stacked in a container on a truck is described in (Petersen et al, 2010); in another variant intermediate storage facilities are used (Angelelli and Speranza, 2002).…”