Proprietor and customer costs in the incomplete hub location-routing network topology

The hub location problem finds the location of hubs and allocates the other nodes to them. It is widely supposed the network created with the hub nodes is complete in the extensive literature. Relaxation of this basic supposition forms the present work. The model minimizes the cost of the proprietor, including the fixed costs of hubs, hub links and spoke links. Costs of hub and spoke links are contemplated as fixed cost or maintenance cost. Moreover, the model considers routing costs of customers who want to travel from origins to destinations. In this study, we offer a model to the multiple allocations of the hub location problems, under the incomplete hub location-routing network design. This model is easily transformed to other hub location problems using one or more constraints. No network format is dictated on the hub network. We suggest a set of valid inequalities for the formulation. Some lower bounds are developed using a Lagrangian relaxation approach and the valid inequalities. Computational analyses evaluate the performances of the lower bounding implementations and valid inequalities. Furthermore, we explore the effects of several factors on the design and solution time of the problem formulation.     

基于线路“异质性”假设的轴辐式公共交通网络优化研究

特大城市公共交通局部静态拥堵问题日益成为制约公共交通网络运行效率提高的关键。针对这一问题改变线路“同质性”假设,在线路“异质性”假设的基础上,提出了将轴辐式网络设计运用到公共交通领域中来,综合考虑居民采用公共交通方式出行的单位运输可变成本、不变成本、枢纽换乘成本等要素,将枢纽间大型客车干线运输所带来的规模经济效应进行量化,构建了基于单分配、多枢纽、混合式网络结构特征的轴辐式公共交通网络优化模型,旨在多重约束下通过枢纽布局降低网络运输成本,提高公共交通网络站点的可达性。最后根据模拟退火算法对模型进行求解,并通过算例分析与讨论的方式验证了模型的有效性。     

A fuzzy programming approach for dynamic virtual hub location problem

Hub location problem has been used in transportation network to exploit economies of scale. For example, a controversial issue in the planning of air transportation networks is inclement weather or emergency conditions. In this situation, hub facilities would not be able to provide a good service to their spoke nodes temporarily. Thus, some other kinds of predetermined underutilized facilities in the network are used as virtual hubs to host some or all connections of original hubs to recover the incurred incapacitation and increase network flexibility and demand flow. In such an unexpected situation, it is not unreasonable to expect that some information be imprecise or vague. To deal with this issue, fuzzy concept is used to pose a more realistic problem. Here, we present a fuzzy integer liner programming approach to propose a dynamic virtual hub location problem with the aim of minimizing transportation cost in the network. We examine the effectiveness of our model using the well-known CAB data set.     

Modeling fuzzy capacitated p-hub center problem and a genetic algorithm solution

Hub and spoke networks are used to switch and transfer commodities between terminal nodes in distribution systems at minimum cost and/or time. The p-hub center allocation problem is to minimize maximum travel time in networks by locating p hubs from a set of candidate hub locations and allocating demand and supply nodes to hubs. The capacities of the hubs are given. In previous studies, authors usually considered only quantitative parameters such as cost and time to find the optimum location. But it seems not to be sufficient and often the critical role of qualitative parameters like quality of service, zone traffic, environmental issues, capability for development in the future and etc. that are critical for decision makers (DMs), have not been incorporated into models. In many real world situations qualitative parameters are as much important as quantitative ones. We present a hybrid approach to the p-hub center problem in which the location of hub facilities is determined by both parameters simultaneously. Dealing with qualitative and uncertain data, Fuzzy systems are used to cope with these conditions and they are used as the basis of this work. We use fuzzy VIKOR to model a hybrid solution to the hub location problem. Results are used by a genetic algorithm solution to successfully solve a number of problem instances. Furthermore, this method can be used to take into account more desired quantitative variables other than cost and time, like future market and potential customers easily.     

The hub covering flow problem

The hub covering flow problem (HCFP) seeks to find the minimal cost hub-and-spoke network by optimally locating hub nodes and assigning non-hub nodes to the hub nodes subject to a coverage constraint. The cost of establishing such a hub network is based on a fixed cost of opening hubs and the cost of transporting demand flow through the network. We also present an extension called the multi-aircraft HCFP. The results from computational experiments are presented and discussed.     

A capacitated hub location problem in freight logistics multimodal networks

In this paper we deal with a capacitated hub location problem arising in a freight logistics context; in particular, we have the need of locating logistics platforms for containers travelling via road and rail. The problem is modelled on a weighed multimodal network. We give a mixed integer linear programming model for the problem, having the goal of minimizing the location and shipping costs. The proposed formulation presents some novel features for modelling capacity bounds that are given both for the candidate hub nodes and the arcs incident to them; further, the containerised origin-destination (\(o-d)\) demand can be split among several platforms and different travelling modes. Note that here the network is not fully connected and only one hub for each \(o-d\) pair is used, serving both to consolidate consignments on less transport connections and as reloading point for a modal change. Results of an extensive computational experimentation performed with randomly generated instances of different size and capacity values are reported. In the test bed designed to validate the proposed model all the instances up to 135 nodes and 20 candidate hubs are optimally solved in few seconds by the commercial solver CPLEX 12.5.     

A branch and cut algorithm for hub location problems with single assignment

The hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. The aim of this paper is to investigate polyhedral properties of these problems and to develop a branch and cut algorithm based on these results.Acknowledgement The research of the first author was partially supported by the Banque Nationale de Belgique. The research of the second author was supported by France Telecom R&D under contract no. 99 1B 774. Their support is gratefully acknowledged.     

A hub covering network design problem for cargo applications in Turkey

Hub location problems involve locating hub facilities and allocating demand nodes to hubs in order to provide service between origin–destination pairs. In this study, we focus on cargo applications of the hub location problem. Through observations from the Turkish cargo sector, we propose a new mathematical model for the hub location problem that relaxes the complete hub network assumption. Our model minimizes the cost of establishing hubs and hub links, while designing a network that services each origin–destination pair within a time bound. We formulate a single-allocation hub covering model that permits visiting at most three hubs on a route. The model is then applied to the realistic instances of the Turkish network and to the Civil Aeronautics Board data set.     

基于正交试验的乘用车运输网络优化方法

在交通部治理公路超限运输的背景下,本文研究了乘用车物流企业多式联运模式下的网络优化问题,以运输网络总成本最小为目标,考虑物流时效、枢纽节点容量及规模经济效应等因素,构建了基于轴辐式理论的运输网络优化模型,提出了混合智能优化算法。针对多参数多水平的寻优问题,对模型的三个关键输入参数,即枢纽节点数量、枢纽节点容量和规模效应折扣系数,引入正交试验方法,降低求解多参数多水平寻优问题的工作量,为确定各参数合理取值提供了新的途径。研究结果表明:枢纽节点容量、折扣系数与枢纽数量三个输入参数对优化结果的影响具有主次顺序,影响程度依次减弱,而且只有枢纽节点容量与折扣系数对乘用车运输网络总效益的影响起显著作用。采用混合轴辐式的网络结构与多式联运的运输组织模式进行优化后的运输网络,相对于原有“点对点”公路运输网络总成本减少10%,从运营管理与成本控制两方面均可有效应对公路治超带来的风险。     

A biased random-key genetic algorithm for the tree of hubs location problem

Hubs are facilities used to treat and dispatch resources in a transportation network. The objective of Hub Location Problems (HLP) is to locate a set of hubs in a network and route resources from origins to destinations such that the total cost of attending all demands is minimized. In this paper, we investigate a particular HLP, called the Tree of Hubs Location Problem in which hubs are connected by means of a tree and the overall network infrastructure relies on a spanning tree. This problem is particularly interesting when the total cost of building the hub backbone is high. We propose a biased random key genetic algorithm for solving the tree of hubs location problem. Computational results show that the proposed heuristic is robust and effective to this problem. The method was able to improve best known solutions of two benchmark instances used in the experiments.     

Design of intermodal logistics networks with hub delays

In an intermodal hub network, cost benefits can be achieved through the use of intermodal shipments and the economies of scale due to consolidation of flows at the hubs. However, due to limited resources at the logistics hubs, shipment delays may affect the service performance. In this research hub operations are modeled as a GI/G/1 queuing network and the shipments as multiple job classes with deterministic routings. By integrating the hub operation queuing model and the hub location-allocation model, the effect of limited hub resources on the design of intermodal logistics networks under service time requirements is investigated. The managerial insights gained from a study of 25-city road-rail intermodal logistics network show that the level of available hub resources significantly affects the logistics network structure in terms of number and location of hubs, total network costs, choice of single-hub and inter-hub shipments and service performance.     

A linear program for the two-hub location problem

This paper considers the discrete two-hub location problem. We need to choose two hubs from a set of nodes. The remaining nodes are to be connected to one of the two hubs which act as switching points for internodal flows. A configuration which minimizes the total flow cost needs to be found. We show that the problem can be solved in polynomial time when the hub locations are fixed. Since there are at most ways to choose the hub locations, the two-hub location problem can be solved in polynomial time. We transform the quadratic 0–1 integer program of the single allocation problem in the fixed two-hub system into a linear program and show that all extreme points of the polytope defined by the LP are integral. Also, the problem can be transformed into a minimum cut problem which can be solved efficiently by any polynomial time algorithm.     

The planar hub location problem: a probabilistic clustering approach

Given the demand between each origin-destination pair on a network, the planar hub location problem is to locate the multiple hubs anywhere on the plane and to assign the traffic to them so as to minimize the total travelling cost. The trips between any two points can be nonstop (no hubs used) or started by visiting any of the hubs. The travel cost between hubs is discounted with a factor. It is assumed that each point can be served by multiple hubs. We propose a probabilistic clustering method for the planar hub-location problem which is analogous to the method of Iyigun and Ben-Israel (in Operations Research Letters 38, 207–214, 2010; Computational Optmization and Applications, 2013) for the solution of the multi-facility location problem. The proposed method is an iterative probabilistic approach assuming that all trips can be taken with probabilities that depend on the travel costs based on the hub locations. Each hub location is the convex combination of all data points and other hubs. The probabilities are updated at each iteration together with the hub locations. Computations stop when the hub locations stop moving. Fermat-Weber problem and multi-facility location problem are the special cases of the proposed approach.     

The Tree of Hubs Location Problem

This paper presents the Tree of Hubs Location Problem. It is a network hub location problem with single assignment where a fixed number of hubs have to be located, with the particularity that it is required that the hubs are connected by means of a tree. The problem combines several aspects of location, network design and routing problems. Potential applications appear in telecommunications and transportation systems, when set-up costs for links between hubs are so high that full interconnection between hub nodes is prohibitive. We propose an integer programming formulation for the problem. Furthermore, we present some families of valid inequalities that reinforce the formulation and we give an exact separation procedure for them. Finally, we present computational results using the well-known AP and CAB data sets.     

轴辐式枢纽网络系统的关键枢纽设施识别问题研究

作为轴辐式枢纽网络关键因素的节点,尤其是起到中转作用的枢纽节点是网络稳定运行的重要环节。当这些节点被中断时,将对整个网络产生严重的影响。最直接的表现方式即是网络运行成本的急剧上升。因此本文研究如何识别对网络成本具有决定性影响的关键节点。首先,提出枢纽功能性中断问题和模型,并通过禁忌搜索算法进行求解。最后通过中国航空实例验证模型和算法在实际应用中的有效性。结果显示模型和算法能够有效识别出中国航空网络较重要的关键城市以及相对影响较弱的城市。可以为资源有限情况下,中国航空网络中各城市防御设施的合理分级和部署,为重点保护城市的鉴别提供依据和帮助。     

The hub location and network design problem with fixed and variable arc costs: formulation and dual-based solution heuristic

Many air, less-than-truck load and intermodal transportation and telecommunication networks incorporate hubs in an effort to reduce total cost. These hubs function as make bulk/break bulk or consolidation/deconsolidation centres. In this paper, a new hub location and network design formulation is presented that considers the fixed costs of establishing the hubs and the arcs in the network, and the variable costs associated with the demands on the arcs. The problem is formulated as a mixed integer programming problem embedding a multi-commodity flow model. The formulation can be transformed into some previously modelled hub network design problems. We develop a dual-based heuristic that exploits the multi-commodity flow problem structure embedded in the formulation. The test results indicate that the heuristic is an effective way to solve this computationally complex problem.     

Network hub location problems: The state of the art

Hubs are special facilities that serve as switching, transshipment and sorting points in many-to-many distribution systems. The hub location problem is concerned with locating hub facilities and allocating demand nodes to hubs in order to route the traffic between origin–destination pairs. In this paper we classify and survey network hub location models. We also include some recent trends on hub location and provide a synthesis of the literature.     

Allocation strategies in hub networks

In this paper, we study allocation strategies and their effects on total routing costs in hub networks. Given a set of nodes with pairwise traffic demands, the p-hub median problem is the problem of choosing p nodes as hub locations and routing traffic through these hubs at minimum cost. This problem has two versions; in single allocation problems, each node can send and receive traffic through a single hub, whereas in multiple allocation problems, there is no such restriction and a node may send and receive its traffic through all p hubs. This results in high fixed costs and complicated networks. In this study, we introduce the r-allocation p-hub median problem, where each node can be connected to at most r hubs. This new problem generalizes the two versions of the p-hub median problem. We derive mixed-integer programming formulations for this problem and perform a computational study using well-known datasets. For these datasets, we conclude that single allocation solutions are considerably more expensive than multiple allocation solutions, but significant savings can be achieved by allowing nodes to be allocated to two or three hubs rather than one. We also present models for variations of this problem with service quality considerations, flow thresholds, and non-stop service.     

Designing Least-Cost Survivable Wireless Backhaul Networks

This paper presents a new heuristic algorithm for designing least-cost telecommunications networks to carry cell site traffic to wireless switches while meeting survivability, capacity, and technical compatibility constraints. This requires solving the following combinatorial optimization problems simultaneously: (1) Select a least-cost subset of locations (network nodes) as hubs where traffic is to be aggregated and switched, and choose the type of hub (high-capacity DS3 vs. lower-capacity DS1 hub) for each location; (2) Optimally assign traffic from other nodes to these hubs, so that the traffic entering the network at these nodes is routed to the assigned hubs while respecting capacity constraints on the links and routing-diversity constraints on the hubs to assure survivability; and (3) Optimally choose the types of links to be used in interconnecting the nodes and hubs based on the capacities and costs associated with each link type. Each of these optimization problems must be solved while accounting for its impacts on the other two. This paper introduces a short term Tabu Search (STTS) meta-heuristic, with embedded knapsack and network flow sub-problems, that has proved highly effective in designing such backhaul networks for carrying personal communications services (PCS) traffic. It solves problems that are challenging for conventional branch-and-bound solvers in minutes instead of hours and finds lower-cost solutions. Applied to real-world network design problems, the heuristic has successfully identified designs that save over 20% compared to the best previously known designs.     

Reducing costs of backhaul networks for PCS networks using genetic algorithms

Designing cost-effective telecommunications networks often involves solving several challenging, interdependent combinatorial optimization problems simultaneously. For example, it may be necessary to select a least-cost subset of locations (network nodes) to serve as hubs where traffic is to be aggregated and switched; optimally assign other nodes to these hubs, meaning that the traffic entering the network at these nodes will be routed to the assigned hubs while respecting capacity constraints on the links; and optimally choose the types of links to be used in interconnecting the nodes and hubs based on the capacities and costs associated with each link type. Each of these three combinatorial optimization problems must be solved while taking into account its impacts on the other two. This paper introduces a genetic algorithm (GA) approach that has proved effective in designing networks for carrying personal communications services (PCS) traffic. The key innovation is to represent information about hub locations and their interconnections as two parts of a chromosome, so that solutions to both aspects of the problem evolve in parallel toward a globally optimal solution. This approach allows realistic problems that take 4–10 hours to solve via a more conventional branch-and-bound heuristic to be solved in 30–35 seconds. Applied to a real network design problem provided as a test case by Cox California PCS, the heuristics successfully identified a design 10% less expensive than the best previously known design. Cox California PCS has adopted the heuristic results and plans to incorporate network optimization in its future network designs and requests for proposals.