An Additive Branch-and-Bound Algorithm for the Pickup and Delivery Traveling Salesman Problem with LIFO or FIFO Loading

Carrabs, Francesco; Cerulli, Raffaele; Cordeau, Jean‐François

doi:10.3138/infor.45.4.223

Cited by 44 publications

(54 citation statements)

References 19 publications

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“…We call the new model the row precedence model. Here, the y variables are replaced by a set of variables that additionally reflect the row assignment and is thereby sparser: The model consists of the original objective function (1) and constraints (2), (3), (8) and (9), along with the following:…”

Section: Variation: the Row Precedence Modelmentioning

confidence: 99%

“…These instances, with the exception of the two largest sizes, were adapted by Ref. [1] to test the TSPPDL. These instances provide node coordinates, as well as a division of the set of customers into pickup and delivery customers, and a 1-to-1 matching of the pickup and delivery customers.…”

Section: Instances From the Literaturementioning

confidence: 99%

“…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. Additionally, the TSPPDL is treated using exact methods by Carrabs et al [1], which uses a branchand-bound approach based on additive lower bounds, and heuristically by Carrabs et al [2], using variable neighborhood search with a collection of old and new operators. A closely related problem is also the TSPPD with First In First Out (FIFO) loading studied in [1,3,5].…”

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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Section: Variation: the Row Precedence Modelmentioning

confidence: 99%

Section: Instances From the Literaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact solutions to the double travelling salesman problem with multiple stacks

2010

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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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“…Carrabs et al in Ref. [2], propose an additive branchand-bound algorithm that is capable of consistently solving instances with up to 35 nodes. Cordeau et al in Ref.…”

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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An Additive Branch-and-Bound Algorithm for the Pickup and Delivery Traveling Salesman Problem with LIFO or FIFO Loading

Cited by 44 publications

References 19 publications

Exact solutions to the double travelling salesman problem with multiple stacks

Exact solutions to the double travelling salesman problem with multiple stacks

An exact method for the double TSP with multiple stacks

Improved exact method for the double TSP with multiple stacks

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