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.     

Stochastic uncapacitated hub location

We study stochastic uncapacitated hub location problems in which uncertainty is associated to demands and transportation costs. We show that the stochastic problems with uncertain demands or dependent transportation costs are equivalent to their associated deterministic expected value problem (EVP), in which random variables are replaced by their expectations. In the case of uncertain independent transportation costs, the corresponding stochastic problem is not equivalent to its EVP and specific solution methods need to be developed. We describe a Monte-Carlo simulation-based algorithm that integrates a sample average approximation scheme with a Benders decomposition algorithm to solve problems having stochastic independent transportation costs. Numerical results on a set of instances with up to 50 nodes are reported.     

The capacitated single-allocation hub location problem revisited: A note on a classical formulation

In this paper a well-known formulation for the capacitated single-allocation hub location problem is revisited. An example is presented showing that for some instances this formulation is incomplete. The reasons for the incompleteness are identified leading to the inclusion of an additional set of constraints. Computational experiments are performed showing that the new constraints also help to decrease the computational time required to solve the problem optimally.     

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.     

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.     

An exact solution procedure for a cluster hub location problem

This paper proposes a new (MIP) model formulation and a new solution procedure for the hub network design problem under a non-restrictive policy introduced by Sung and Jin [Sung, C.S., Jin, H.W., 2001. Dual-based approach for a hub network design problem under non-restrictive policy. European Journal of Operational Research 132 (1), 88–105]. The model formulation contains significantly fewer variables so that optimal solutions for the LP-relaxation of the model can be determined for large instances using standard procedures for LP-models. Furthermore, the LP-relaxation provides very tight lower bounds. Computational results are given, which demonstrate that the new model formulation allows for solving much larger instances. It turned out that the new (exact) solution procedure, which utilises the new model formulation, is faster than the heuristic proposed by Sung and Jin (2001). It is also shown that the problem is np-hard.     

Solving the uncapacitated multiple allocation hub location problem by means of a dual-ascent technique

This paper deals with the uncapacitated multiple allocation hub location problem. The dual problem of a four-indexed formulation is considered and a heuristic method, based on a dual-ascent technique, is designed. This heuristic, which is reinforced with several specifical subroutines and does not require any external linear problem solver, is the core tool embedded in an exact branch-and-bound framework. Besides, the heuristic provides the branch-and-bound algorithm with good lower bounds for the nodes of the branching tree. The results of the computational experience (with the classical CAB and AP data sets) are included, showing the great effectiveness of this approach: instances with up to 120 nodes are solved.     

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.     

Solving a capacitated hub location problem

In this paper we address a problem consisting of determining the routes and the hubs to be used in order to send, at minimum cost, a set of commodities from sources to destinations in a given capacitated network. The capacities and costs of the arcs and hubs are given, and the arcs connecting the hubs are not assumed to create a complete graph. We present a mixed integer linear programming formulation and describe two branch-and-cut algorithms based on decomposition techniques. We evaluate and compare these algorithms on instances with up to 25 commodities and 10 potential hubs. One of the contributions of this paper is to show that a Double Benders’ Decomposition approach outperforms the standard Benders’ Decomposition, which has been widely used in recent articles on similar problems. For larger instances we propose a heuristic approach based on a linear programming relaxation of the mixed integer model. The heuristic turns out to be very effective and the results of our computational experiments show that near-optimal solutions can be derived rapidly.     

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 co-opetitive framework for the hub location problems in transportation networks

In this paper, we present the first model of co-opetition for a Hub Location Problem between two logistics service provider (LSPs) companies where the mother company is the owner of infrastructure. The LSPs would like to cooperate with each other by establishing joint edges with limited capacities connecting their service networks. Such services are in form of pendulum services (a direct service between two points) between nodes of different networks. Additional market can be generated as a result of joining the two networks. At the same time, a competition is taking place between the two operators to increase their share from the additional market generated. In order to solve this problem, we propose a matheuristic approach combining a local search algorithm and a Lagrangian relaxation-based approach. In our matheuristic algorithm, the neighbourhood solutions are evaluated using a Lagrangian relaxation-based approach. Numerical results of applying the proposed algorithm on a real case study of the problem are presented.     

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 transfer point location problem

In this paper, we introduce the transfer point location problem. Demand for emergency service is generated at a set of demand points who need the services of a central facility (such as a hospital). Patients are transferred to a helicopter pad (transfer point) at normal speed, and from there they are transferred to the facility at increased speed. The general model involves the location of p helicopter pads and one facility. In this paper, we solve the special case where the location of the facility is known and the best location of one transfer point that serves a set of demand points is sought. Both minisum and minimax versions of the models are investigated. In follow up papers we investigate the general model using the results obtained in this paper.     

Improved algorithms for several network location problems with equality measures

We consider single facility location problems with equity measures, defined on networks. The models discussed are, the variance, the sum of weighted absolute deviations, the maximum weighted absolute deviation, the sum of absolute weighted differences, the range, and the Lorenz measure. We review the known algorithmic results and present improved algorithms for some of these models.     

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 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.     

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 computational evaluation of a general branch-and-price framework for capacitated network location problems

The purpose of this paper is to illustrate a general framework for network location problems, based on column generation and branch-and-price. In particular we consider capacitated network location problems with single-source constraints. We consider several different network location models, by combining cardinality constraints, fixed costs, concentrator restrictions and regional constraints. Our general branch-and-price-based approach can be seen as a natural counterpart of the branch-and-cut-based commercial ILP solvers, with the advantage of exploiting the tightness of the lower bound provided by the set partitioning reformulation of network location problems. Branch-and-price and branch-and-cut are compared through an extensive set of experimental tests.     

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.