A new formulation and an exact approach for the many-to-many hub location-routing problem

An important problem of the freight industry is the parcel delivery network design, where several facilities are responsible for assembling flows from several origins, re-routing them to other facilities where the flows are disassembled and the packages delivered to their final destinations. In order to provide this service, local tours are established for the vehicles assigned to each of the processing facilities, which are then responsible for the pickup and delivery tasks. This application gives rise to the many-to-many hub location routing problem that is the combination of two well known problems: the vehicle routing problem and the single assignment hub location problem. In this work, a new formulation for this important problem is proposed and solved by a specially tailored Benders decomposition algorithm. The proposed method is robust enough to solve instances up to 100 nodes having 4 million integer variables.     

Locating landfills—Optimization vs. reality

This paper examines the locations of landfills and garbage transfer stations in New Brunswick, one of Canada’s Maritime Provinces. The locations of the existing facilities are then compared to a system of optimized locations. The model used for the optimization is similar to those employed in the analysis of standard hub location models.     

General network design: A unified view of combined location and network design problems

This paper presents a unified framework for the general network design problem which encompasses several classical problems involving combined location and network design decisions. In some of these problems the service demand relates users and facilities, whereas in other cases the service demand relates pairs of users between them, and facilities are used to consolidate and re-route flows between users. Problems of this type arise in the design of transportation and telecommunication systems and include well-known problems such as location-network design problems, hub location problems, extensive facility location problems, tree-star location problems and cycle-star location problems, among others. Relevant modeling aspects, alternative formulations and possible algorithmic strategies are presented and analyzed.     

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.     

A specialized branch & bound & cut for Single-Allocation Ordered Median Hub Location problems

The Single-Allocation Ordered Median Hub Location problem is a recent hub model introduced by Puerto et al. (2011) [32] that provides a unifying analysis of the class of hub location models. Indeed, considering ordered objective functions in hub location models is a powerful tool in modeling classic and alternative location paradigms, that can be applied with success to a large variety of problems providing new distribution patterns induced by the different users’ roles within the supply chain network. In this paper, we present a new formulation for the Single-Allocation Ordered Median Hub Location problem and a branch-and-bound-and-cut (B&B&Cut) based algorithm to solve optimally this model. A simple illustrative example is discussed to demonstrate the technique, and then a battery of test problems with data taken from the AP library are solved. The paper concludes that the proposed B&B&Cut approach performs well for small to medium sized problems.     

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.     

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.     

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.     

航线联盟下航空货运网络枢纽点选址问题研究

本文研究航空联盟下航空货运网络的枢纽点选址问题(HLP),基于枢纽点的数量及位置随机与容量的限制。首先引入航线联盟选择概率函数,确定不同航段上的航线自营运输或外包运输的概率;其次根据选址中心法则,以网络总成本最小化为目标,建立枢纽点选址模型;再次采用改进的免疫混沌遗传算法求解模型;最后,以顺丰航空公司案例进行实例分析。结果表明:1)本文改进的算法较免疫混沌遗传算法并与免疫遗传算法及CPLEX结果对比,发现本文设计的算法有较强的收敛性和计算速度,且计算结果与CPLEX求解器求解结果相差不大;2)枢纽点数量不确定时,枢纽点的位置多集中在东部城市;3)航空公司选择联盟环境可以大大降低运营成本,航空公司为提高自身利润,应考虑加入联盟,从而降低自身成本。     

Reliability problems in multiple path-shaped facility location on networks

In this paper we study a location problem on networks that combines three important issues: (1) it considers that facilities are extensive, (2) it handles simultaneously the location of more than one facility, and (3) it incorporates reliability aspects related to the fact that facilities may fail. The problem consists of locating two path-shaped facilities minimizing the expected service cost in the long run, assuming that paths may become unavailable and their failure probabilities are known in advance. We discuss several aspects of the computational complexity of problems of locating two or more reliable paths on graphs, showing that multifacility path location–with and without reliability issues–is a difficult problem even for 2 facilities and on very special classes of graphs. In view of this, we focus on trees and provide a polynomial time algorithm that solves the 2 unreliable path location problem on tree networks in $O\left(n^2\right)$ time, where $n$ is the number of vertices.     

The p-hub center allocation problem

The p-hub center problem is to locate p hubs and to allocate non-hub nodes to hub nodes such that the maximum travel time (or distance) between any origin–destination pair is minimized. We address the p-hub center allocation problem, a subproblem of the location problem, where hub locations are given. We present complexity results and IP formulations for several versions of the problem. We establish that some special cases are polynomially solvable.     

A generalized Weiszfeld method for the multi-facility location problem

An iterative method is proposed for the K facilities location problem. The problem is relaxed using probabilistic assignments, depending on the distances to the facilities. The probabilities, that decompose the problem into K single-facility location problems, are updated at each iteration together with the facility locations. The proposed method is a natural generalization of the Weiszfeld method to several facilities.     

离散设施选址问题研究综述

本文首先回顾了设施选址问题百年发展历史,认为其研究经历了零散研究、系统研究、不确定性研究三个阶段.离散选址问题包括中值问题、覆盖问题、中心问题、多产品问题、动态问题、多目标问题、路径选址问题、网络中心选址问题8个子问题.最后作者讨论了选址问题研究中存在的问题以及今后发展的趋势.     

Stochastic air freight hub location and flight routes planning

This paper introduced a stochastic programming model to address the air freight hub location and flight routes planning under seasonal demand variations. Most existing approaches to airline network design problems are restricted to a deterministic environment. However, the demand in the air freight market usually varies seasonally. The model is separated into two decision stages. The first stage, which is the decision not affected by randomness, determines the number and the location of hubs. The second stage, which is the decision affected by randomness, determines the flight routes to transport flows from origins to destinations based upon the hub location and realized uncertain scenario. Finally, the real data based on the air freight market in Taiwan and China is used to test the proposed model.     

连续设施选址:模型、方法与应用

给定度量空间和该空间中的若干顾客,设施选址为在该度量空间中确定新设施的位置使得某种目标达到最优。连续设施选址是设施选址中的一类重要问题,其中的设施可在度量空间的某连续区域上进行选址。本文对连续设施选址的模型、算法和应用方面的工作进行了综述。文章首先讨论了连续设施选址中几个重要元素,包括新设施个数、距离度量函数、目标函数;然后介绍了连续选址中的几种经典模型和拓展模型;接着概述了求解连续选址问题的常用优化方法和技术,包括共轭对偶、全局优化、不确定优化、变分不等式方法、维诺图;最后介绍了连续设施选址的重要应用并给出了研究展望。     

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.     

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.     

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.     

A competitive hub location and pricing problem

We formulate and solve a new hub location and pricing problem, describing a situation in which an existing transportation company operates a hub and spoke network, and a new company wants to enter into the same market, using an incomplete hub and spoke network. The entrant maximizes its profit by choosing the best hub locations and network topology and applying optimal pricing, considering that the existing company applies mill pricing. Customers’ behavior is modeled using a logit discrete choice model. We solve instances derived from the CAB dataset using a genetic algorithm and a closed expression for the optimal pricing. Our model confirms that, in competitive settings, seeking the largest market share is dominated by profit maximization. We also describe some conditions under which it is not convenient for the entrant to enter the market.     

On the convergence of a modified algorithm for the spherical facility location problem

We study the spherical facility location problem which is a more realistic model than the Euclidean facilities location. We present a modified algorithm for this problem, which has the following good properties: (a) It is very easy to initialize the algorithm with an arbitrary point as its starting point; (b) Under suitable assumptions, it is proved that the algorithm globally converges to a global minimizer of the problem.