A branch‐and‐cut algorithm for the pickup and delivery traveling salesman problem with LIFO loading

Cordeau, Jean‐François; Iori, Manuel; Laporte, Gilbert; González, Juan Manuel

doi:10.1002/net.20312

Cited by 82 publications

(91 citation statements)

References 21 publications

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“…The values for the TSPPDL for N > 8 have been found by using the formula given in Ref. [4]. We denote by DTSPxS the DTSPMS with x rows.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…The most closely related earlier work on exact solutions to the TSPPDL has been done by Cordeau et al [4], which presents three different models for the TSPPDL and a branch-and-cut approach. The two first models use continuous variables to represent the load of the vehicle, while the last model solves the problem without adding extra variables, and instead imposes additional constraints on subsets of the existing variables.…”

Section: Introductionmentioning

confidence: 99%

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Exact solutions to the double travelling salesman problem with multiple stacks

2010

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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.

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“…The values for the TSPPDL for N > 8 have been found by using the formula given in Ref. [4]. We denote by DTSPxS the DTSPMS with x rows.…”

Section: Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact solutions to the double travelling salesman problem with multiple stacks

2010

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show abstract

“…One can further observe that pallets 3, 1, and 8 are delivered in the reverse order to that in which they are picked up, all pallets are picked up before pallet 9 and, furthermore, all are delivered before pallet 9. Hence, these can only be packed in a single column in positions (2,1), (3,1), and (4,1).…”

Section: Theorem 322 Let L Denote the Length Of The Lcs Satisfyinmentioning

confidence: 99%

“…Cordeau et al in Ref. [3], converseley, present three integer programming formulations and propose a branch-and-cut solution approach. Violated sub tour elimination constraints, precedence constraints, and LIFO constraints are separated exactly, while other families of valid inequalities are separated heuristically.…”

Section: Introductionmentioning

confidence: 99%

Improved exact method for the double TSP with multiple stacks

Lusby

Larsen

2011

Networks

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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.

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“…Exact approaches to the regular PDP with one vehicle and a single column based on a LIFO ordering can be found in [1,3]. Another related problem is the routing problems with backhauls (most closely related to the TSP with backhauls).…”

Section: Introductionmentioning

confidence: 99%

An exact method for the double TSP with multiple stacks

Lusby¹,

Larsen²,

Ehrgott

et al. 2010

Int Trans Operational Res

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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.

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A branch‐and‐cut algorithm for the pickup and delivery traveling salesman problem with LIFO loading

Cited by 82 publications

References 21 publications

Exact solutions to the double travelling salesman problem with multiple stacks

Exact solutions to the double travelling salesman problem with multiple stacks

Improved exact method for the double TSP with multiple stacks

An exact method for the double TSP with multiple stacks

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