Improved exact method for the double TSP with multiple stacks

Abstract

The Double TSP with Multiple Stacks is a logistics problem where one must, using a container, transport a given number of orders from a set of pickup customers to a set of delivery customers at minimum cost. Each order corresponds to the movement of one pallet, all pickups must be completed before the first delivery, and the container cannot be repacked once packed. In this paper we improve the previously proposed exact method of Lusby et al. (Int Trans Oper Res 17 (2010), 637-652) through an additional preprocessing technique that uses the longest common subsequence between the respective pickup and delivery problems. The results suggest an impressive improvement, and we report, for the first time, optimal solutions to several unsolved instances from the literature containing 18 customers. Instances with 28 customers are also shown to be solvable within a few percent of optimality.

A metaheuristic for the double traveling salesman problem with partial last‐in‐first‐out loading constraints

“…Lusby et al (2010) presented an exact method based on matching k-best tours for each region separately and was able to solve to optimality up to 18 customers. Lusby and Larsen (2011) then refined the above exact method through an additional preprocessing technique that uses the longest common subsequence between the respective areas. The enhanced approach was able to solve to optimality up to 24 customers.…”

The Double Traveling Salesman Problem with Multiple Stacks and a Choice of Container Types

“…Several mathematical formulations of the double traveling salesman problem with multiple stacks with corresponding solution strategies were presented by Petersen et al [5]. A specialized algorithm was given by [6] and improved by Lusby and Larsen [6], based on combining separate traveling salesman problems for the pickup region and the delivery region. Branch-and-cut was used by Alba Martínez et al [7], whereas Carrabs et al [8] presented a branch-and-bound algorithm for the problem with only two stacks.…”

Loading constraints in vehicle routing problems: a focus on axle weight limits

“…The solution of the TSPIP with a decomposition approach turned out to be the most successful approach in which the problem is solved exactly for instances with up to 25 requests. Lusby and Larsen (2011) improve the exact method developed by Lusby et al (2010) by including an additional preprocessing technique: the longest common subsequence between the pickup and the delivery tour. This preprocessing technique significantly decreases the number of matching problems that need to be solved.…”