Mathematical formulations for a 1-full-truckload pickup-and-delivery problem

Gendreau, Michel; Nossack, Jenny; Pesch, Erwin

doi:10.1016/j.ejor.2014.10.053

Cited by 19 publications

(11 citation statements)

References 44 publications

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“…, f s − 1 and each station s ∈ S. For each vehicle the depot's starting node 0 has to have one outgoing arc (15), and similarly, the depot's target node 0 has to have one incoming arc (16). The arc selection variables are linked with the assignment variables as follows: Equalities (17) ensure that every node u ∈ V has one outgoing arc iff it is assigned to vehicle l, that is, x ul = 1, while Equalities (18) guarantee that each node v ∈ V which is assigned to vehicle l ∈ L has to have one corresponding ingoing arc. Equalities (19) express that the number of ingoing arcs has to be equal to the number of outgoing arcs for each node v ∈ V , l ∈ L. We eliminate subtours with Inequalities (20) by computing an ordering of the nodes in variables a v .…”

Section: Compact Mixed Integer Linear Programming Modelmentioning

confidence: 99%

“…Another problem related to the one introduced here is the one-commodity full-truckload pickup and delivery problem (1-FTPDP) proposed by Gendreau et al [18]. This is a variant of the well-known pickup and delivery problem where a truck has to alternatively visit pickup as well as delivery customers all demanding a unit-capacity pickup, respectively, delivery.…”

Section: Other Related Problems and Approachesmentioning

confidence: 99%

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Full‐load route planning for balancing bike sharing systems by logic‐based benders decomposition

Kloimüllner

Raidl

2017

Networks

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Public bike sharing systems require some kind of rebalancing to avoid too many rental stations of running empty or entirely full, which would make the system ineffective and annoy customers. Most frequently, a fleet of vehicles with trailers is used for this purpose, moving bikes among the stations. Previous works considered different objectives and modeled the underlying routing problem in different ways, but they all allow an arbitrary number of bikes to be picked up at some stations and delivered to other stations, just limited by the vehicles' capacities. Observations in practice, however, indicate that in larger well-working bike sharing systems drivers almost never pickup or deliver only few bikes, but essentially always approximately full vehicle loads. Many stations even require several visits with full loads. Due to budgetary reasons, typically only just enough drivers and vehicles are employed to achieve a reasonable balance most of the time, but basically never an ideal one where single bikes play a substantial role. Consequently, we investigate here a simplified problem model, in which only full vehicle loads are considered for movement among the rental stations. This restriction appears to have only a minor impact on the achieved quality of the rebalancing in practice but eases the modeling substantially. More specifically, we formulate the rebalancing problem as a selective unit-capacity pickup and delivery problem with time budgets on a bipartite graph and present a compact mixed integer linear programming model, a logic-based Benders decomposition and a variant thereof, namely branch-and-check for it. For the general case, instances with up to 70 stations, and for the single-vehicle case instances with up to 120 stations are solved to proven optimality. A comparison to leading metaheuristic approaches considering flexible vehicle loads indicates that indeed the restriction to full loads has only a very small impact on the finally achieved balance in typical scenarios of Citybike Wien.

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Section: Compact Mixed Integer Linear Programming Modelmentioning

confidence: 99%

Section: Other Related Problems and Approachesmentioning

confidence: 99%

Full‐load route planning for balancing bike sharing systems by logic‐based benders decomposition

Kloimüllner

Raidl

2017

Networks

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“…The version of the STSP in which distances satisfy the triangle inequality (

c (v_{i}, v_{j}) + c (v_{j}, v_{k}) \geq c (v_{i}, v_{k})

for all distinct

v_{i}, v_{j}, v_{k} \in V

) is the most studied special case of the problem, notably including the particular instance where

V

is a set of points in a two‐dimensional (2D) plane and

c (v_{i}, v_{j})

is the Euclidian distance between

v_{i}

and

v_{j} .

The ATSP is more general than the STSP and likewise embraces a wide range of applications particularly arising in scheduling optimization in manufacturing and in vehicle routing in distribution and transportation networks . These basic applications are significantly expanded by the variety of complex real‐world vehicle routing problems (encompassing time‐windows and other hard constraints and multiple vehicles) that can be solved by first recasting them as an ATSP using polynomial‐time transformations .…”

Section: Introductionmentioning

confidence: 99%

Doubly‐rooted stem‐and‐cycle ejection chain algorithm for the asymmetric traveling salesman problem

2016

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Ejection chain methods, which include the classical Lin-Kernighan (LK) procedure and the Stem-and-Cycle (S&C) reference structure, have been the source of the currently leading algorithms for large scale symmetric traveling salesman problems (STSP). Although these methods proved highly effective in generating large neighborhoods for symmetric instances, their potential application to the asymmetric setting of the problem (ATSP) introduces new challenges that require special consideration. This article extends our studies on the single-rooted S&C to examine the more advanced doublyrooted (DR) reference structure. The DR structure, which is allied both to metaheuristics and network optimization, allows more complex network-related (alternating) paths to transition from one tour to another, and offers special advantages for the ATSP. Computational experiments on an extensive testbed exhibits superior performance for the DR neighborhood over its LK counterpart for the ATSP. We additionally show that a straightforward implementation of a DR ejection chain algorithm outperforms the best local search algorithms and obtains solutions comparable to those obtained by the currently most advanced special-purpose algorithms for the ATSP, while requiring dramatically reduced computation time.

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“…In the literature this problem class has been rst referred to as VRP with simultaneous delivery and pickup points by Min (1989), the Traveling Salesman Problem (TSP) with Pickup and Delivery by Gendreau et al (1999), multivehicle case as VRP with simultaneous pickup and delivery by Angelelli and Mansini (2002), simultaneous VRP with Pickup and Delivery by Nagy and Salhi (2005) Table 2 summarizes recent articles related to PDP published since the past 5 years. All the problems dealing with a vehicle eet; TSP with Pickup and Delivery such as Li et al (2011), Ting andLiao (2013) or Gendreau et al (2015) are not included. The rst column shows the references.…”

Section: State Of the Artmentioning

confidence: 99%

The inventory-routing problem of returnable transport items with time windows and simultaneous pickup and delivery in closed-loop supply chains

Iassinovskaia

Limbourg

Riane³

2017

International Journal of Production Economics

105

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Reducing environmental impact, related regulations and potential for operational benets are the main reasons why companies share their returnable transport items (RTIs) among the dierent partners of a closed-loop supply chain. In this paper, we consider a producer, located at a depot, who has to distribute his products packed in RTIs to a set of customers. Customers dene a time window wherein the service can begin. The producer is also in charge of the collection of empty RTIs for reuse in the next production cycle. Each partner has a storage area composed of both empty and loaded RTI stock, as characterized by initial levels and maximum storage capacity. As deliveries and returns are performed by a homogeneous eet of vehicles that can carry simultaneously empty and loaded RTIs, this research addresses a pickup and delivery inventory-routing problem within time windows (PDIRPTW) over a planning horizon.A mixed-integer linear program is developed and tested on small-scale instances. To handle more realistic large-scale problems, a cluster rst-route second matheuristic is proposed.

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Mathematical formulations for a 1-full-truckload pickup-and-delivery problem

Cited by 19 publications

References 44 publications

Full‐load route planning for balancing bike sharing systems by logic‐based benders decomposition

Full‐load route planning for balancing bike sharing systems by logic‐based benders decomposition

Doubly‐rooted stem‐and‐cycle ejection chain algorithm for the asymmetric traveling salesman problem

The inventory-routing problem of returnable transport items with time windows and simultaneous pickup and delivery in closed-loop supply chains

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