Ordered median hub location problems with capacity constraints

Puerto, Justo; Ramos, Aline Sharlon Maciel Batista; Rodríguez‐Chía, Antonio M.; Sánchez-Gil, M. Carmen

doi:10.1016/j.trc.2015.05.012

Cited by 36 publications

(17 citation statements)

References 42 publications

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“…This new approach can be used to start new avenues of research by applying tools from continuous optimization to approximate or numerically solve some other hard discrete location problems, as for instance single allocation hub location problems and ordered median hub location problems with and without capacities, see e.g. Fernández et al (2013); Puerto et al (2011Puerto et al ( , 2016, to mention a few.…”

Section: Discussionmentioning

confidence: 99%

An exact completely positive programming formulation for the discrete ordered median problem: an extended version

Puerto

2019

J Glob Optim

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This paper presents a first continuous, linear, conic formulation for the Discrete Ordered Median Problem (DOMP). Starting from a binary, quadratic formulation in the original space of location and allocation variables that are common in Location Analysis (L.A.), we prove that there exists a transformation of that formulation, using the same space of variables, that allows us to cast DOMP as a continuous linear problem in the space of completely positive matrices. This is the first positive result that states equivalence between the family of continuous convex problems and some hard problems in L.A. The result is of theoretical interest because it allows us to share the tools from continuous optimization to shed new light into the difficult combinatorial structure of the class of ordered median problems.

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Section: Discussionmentioning

confidence: 99%

An exact completely positive programming formulation for the discrete ordered median problem: an extended version

Puerto

2019

J Glob Optim

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“…e capacity of links is another essential feature of the HLPs. Capacity constraints on flows are usually applied on hubs [25,[48][49][50][51][52], links [53,54], or both [55], as exogenous constraints. Some studies also treat hub capacities as decision variables to select the optimal hub capacity from a list set of predefined capacity levels, each of which is associated with a fixed setup cost [56][57][58].…”

Section: Literature Review: Hub Location Problemsmentioning

confidence: 99%

A Multimodal Passenger-and-Package Sharing Network for Urban Logistics

Zheng

Zhao

et al. 2020

Journal of Advanced Transportation

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This paper envisions a multimodal passenger-and-package sharing (PPS) network for urban logistics integrating metro, taxi, and truck. A hub-and-spoke structure is designed including hubs located at metro stations and service stores connected to the hubs. Packages are transported by metro on backbone links between the hubs and are carried by taxis or trucks between service stores and hubs, depending on the unit costs of these two modes and capacity constraint of the taxi. A mixed integer linear programming model for hub location problems—fusing the multiassignment p-hub median problem without capacity constraints and the capacitated multiassignment p-hub covering problem—is formulated to optimize the multimodal PPS network. The model is implemented based on the real-world data in Shanghai (China) under a series of scenarios to evaluate the network performance from two perspectives: the number of hubs and the proportion of taxi drivers who are willing to carry packages. The scenarios show that with increased number of hubs, the spatial distribution of hubs disperses from the city center to peripheral areas and more areas can be serviced by taxis. There is, however, a trade-off between the operation cost saved by taxis and the establishment cost of an extra hub. The analysis also presents that if the proportion of taxis willing to carry packages associates with the incentive payments to taxi drivers, an optimal value of incentives exists, by balancing the operation costs of taxis and trucks.

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“…Recently, another feature, namely weighted averaging objective functions, has also been incorporated to the analysis of HLPs (Puerto et al 2011;Ramos 2012;Puerto et al 2013Puerto et al , 2016. It has been recognized as a powerful tool from a modeling point of view because it allows to distinguish the roles played by the different entities participating in a hub-and-spoke network inducing new type of distribution patterns, see Rodríguez-Martín and Salazar-González (2008), Fonseca et al (2010), Kalcsics et al (2010a) and Kalcsics et al (2010b).…”

Section: Introductionmentioning

confidence: 99%

The ordered median tree of hubs location problem

Pozo

Puerto

Rodríguez‐Chía

2020

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In this paper, we propose the Ordered Median Tree of Hub Location Problem (OMTHL). The OMTHL is a single-allocation hub location problem where p hubs must be placed on a network and connected by a non-directed tree. Each non-hub node is assigned to a single hub and all the flow between origin-destination pairs must cross at least one hub. The objective is to minimize the sum of the ordered weighted averaged collection and distribution costs plus the sum of the interhub flow costs. We present different MILP formulations for the OMTHL based on the properties of the Minimum Spanning Tree Problem, the ordered median optimization and on the different ways of modeling flow within the network. Given that ordered median hub location problems are rather difficult to solve, we have improved the OMTHL solution performance by introducing covering variables in two valid reformulations. In addition, we have developed two pre-processing phases to reduce the size of these formulations. We establish an empirical comparison between these new formulations and we also provide enhancements that together with a proper formulation allow to solve medium-size instances on general random graphs.

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Ordered median hub location problems with capacity constraints

Cited by 36 publications

References 42 publications

An exact completely positive programming formulation for the discrete ordered median problem: an extended version

An exact completely positive programming formulation for the discrete ordered median problem: an extended version

A Multimodal Passenger-and-Package Sharing Network for Urban Logistics

The ordered median tree of hubs location problem

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