Uncapacitated Single Allocation Hub Location Research Articles

Oracle-based algorithms for binary two-stage robust optimization

In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

A single allocation hub location and pricing problem

This study introduces a new problem for uncapacitated single allocation hub location in which pricing is taken into account. The objective is profit maximization by choosing the best hub and spoke topology and applying the optimal pricing, in the case of price-dependent demand. It is assumed that the source determining the number of hubs is endogenous. Two variants of the considered problem are addressed: deterministic and robust. For the initial non-linear model, we show how the deterministic variant can be reformulated as a mixed-integer linear program, excluding the price variables. In the robust counterpart case, the quantity of commodity flows between the pairs of customers is of stochastic nature. The goal of the robust variant is to design a hub and spoke network, together with the pricing structure, that would be immune to small perturbations of demand. Starting from the original model for the robust case, we have shown how to formulate an equivalent mixed-integer conic-quadratic program. In addition, we have proposed a 2-phase matheuristic approach for the robust variant. A computational study was conducted on the set of hub instances from the literature using the commercial state-of-the-art solver. The obtained computational results are thoroughly discussed, location patterns are analyzed and some managerial insights are provided. The experimental study also showed that the proposed matheuristic approach for the robust variant performs better compared to the commercial solver.

Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem

The hub location problem (HLP) is a special type of the facility location problem with numerous applications in the airline industry, postal services, and computer and telecommunications networks. This paper addresses two basic variants of the HLP, namely the uncapacitated single allocation hub location problem (USAHLP) and the uncapacitated single allocation p-hub median problem (USAp HMP). Exact solution procedures based on Benders decomposition algorithm are proposed to tackle large sized instances of these problems. The standard Benders decomposition algorithm is enhanced through implementation of several algorithmic refinements such as using a new cut disaggregation scheme, generating strong optimality cuts, and an efficient algorithm to solve the dual subproblems. Furthermore, a modern implementation of the algorithm is used where a single search tree is established for the problem and Benders cuts are successively added within a branch-and-cut framework. Extensive computational experiments are conducted to examine the efficiency of the proposed algorithms. We have been able to solve all the instances of the problems from all three main data sets of the HLP to optimality in reasonable computational times.

A multi-start iterated local search algorithm for the uncapacitated single allocation hub location problem

The uncapacitated single allocation hub location problem (USAHLP) is a particular variant of the hub location problem, which has broad applications in the transportation network. The objective of USAHLP is to minimize the sum of transportation cost and fixed cost. In this paper, a multi-start iterated local search algorithm (MSLSA) is proposed for solving the USAHLP. Firstly, a randomized greedy construction procedure is built to generate initial solutions with good quality. Then, solutions are improved by an iterated local search, which consists of promising solutions selection and improvement on nodes reallocation. Meanwhile, a perturbation mechanism helps the search to escape from local optima and explore new promising regions. Our proposed algorithm is evaluated on four USAHLP data sets and compared with two state-of-the-art algorithms. The experimental results demonstrate the high competitiveness of our proposed MSLSA in terms of both solution quality and computational efficiency. MSLSA achieves the same solutions for multiple runs on each instance, which highlights the advantage of MSLSA in terms of solution robustness and stability. With the high solution quality and the rapid running speed, the proposed algorithm could be a promising tool for other hub location problems.

A learning-based probabilistic tabu search for the uncapacitated single allocation hub location problem

In this paper, we develop a learning-based probabilistic tabu search to solve the uncapacitated single allocation hub location problem (USAHLP). In the proposed algorithm, a novel integer representation of solution is presented to maintain the feasibility of solution throughout the search and to simplify the calculation of the objective function value. Two randomized greedy construction procedures are adopted to obtain good initial solutions. Location improvement and allocation improvement procedures are utilized to enhance the exploitation ability. Furthermore, a new learning-based probabilistic tabu strategy is proposed to prevent the location improvement procedure from visiting the inferior solutions previously investigated. In the allocation improvement procedure, the difference between the value of the initial solution and its neighbor is applied to obtain the value of the neighbor for the purpose of reducing the running time. To verify the efficiency of the proposed algorithm, computational experiments are conducted on the benchmark instances for the USAHLP. Of all 76 instances, our algorithm is capable of attaining all the previous best known results and improving the best known results for five large instances in a reasonable time. The obtained results reveal that the proposed algorithm is competitive with the state-of-the-art heuristics.

Solving Single Allocation Hub Location Problems on Euclidean Data

If shipments have to be transported between many sources and sinks, direct connections from each source to each sink are often too expensive. Instead, a small number of nodes are upgraded to hubs that serve as transshipment points. All sources and sinks are connected to these hubs, so that only a few, strongly consolidated transport relations exist. While hubs and detours lead to additional costs, the savings from bundling shipments—i.e., economies of scale—usually outweigh these costs. Typical applications for hub networks are in cargo, air freight, and postal and parcel transport services. In this paper, we consider three classical and two recent formulations of single allocation hub location problems—i.e., hub location problems in which every source and sink is connected to exactly one hub. Solving larger instances of these problems to optimality is difficult because the inherent quadratic structure of the problem has to be linearized: This leads to a sharp rise in the number of variables. Our new approach relies on the fact that many instances—including the Civil Aeronautics Board and Australian Post data sets—have a Euclidean structure: The distances between the possible hub locations are Euclidean. This enables us to construct a new linearization together with a row generation procedure that solves instances of up to 200 nodes to optimality. For problems like the uncapacitated single allocation p-hub median problem and the uncapacitated single allocation hub location problem, we present the first optimal results for instances of this size.

Landscape analysis and scatter search metaheuristic for solving the uncapacitated single allocation hub location problem

In this paper, solution space landscapes of the uncapacitated single allocation hub location problem (USAHLP) for the well-known CAB and AP benchmark datasets are investigated and analysed through several statistical criteria. The analyses show that both datasets have rugged landscapes, and the optimal solutions are concentrated in the search space of the CAB dataset while they are uniformly distributed in the search space of the AP dataset. It follows that in order for a method to find good solutions to the USAHLP, it should perform both proper exploitation and exploration of the workspace. Based on the landscape analysis, an efficient scatter search-based heuristic method called SSUHLP is tailored for solving the USAHLP. The performance of the SSUHLP is evaluated by solving all problems of the CAB and AP datasets and comparing them with some existing algorithms in the literature.

A parallel heuristics for the single allocation hub location problem

This paper introduces a cooperative parallel heuristic for the uncapacitated single allocation hub location problem. The proposed heuristic consists in combining multiple parallel ILS-RVND local search and Path-Relinking, cooperating through asynchronously exchaging solutions in a shared pool. This method as devised to tackle large scale instances up to 3038 nodes. Generally, papers in the literature solve problems up to 400 nodes. The combination of efficient methods of search allowed the proposed heuristic to explore efficiently the space of search, and outperformed four well known heuristics of the literature for the select instances.

An efficient tabu search for solving the uncapacitated single allocation hub location problem

We here propose an efficient tabu search (TS) for solving the uncapacitated single allocation hub location problem. To decrease the computational time, in the proposed tabu search, some new tabu rules are considered. Also, to compute the changes in the objective function’s value in each move, some new results are given. The performance of the proposed tabu search is compared with a recently proposed tabu search (Silva & Cunha, 2009) on all standard ORLIB instances (CAB and AP data sets), modified AP data set and finally on four large instances with 300 and 400 nodes proposed by Silva and Cunha. The numerical experiments show that the proposed tabu search can find all optimal solutions of CAB data and the best known solution of other standard test problems in less computational time than Silva and Cunha’s tabu search. Also, the proposed tabu search can improve the best known solutions for some standard test problems.

A threshold accepting algorithm for the uncapacitated single allocation hub location problem

Hub location problem simultaneously determines the number and locations of hubs, and customer allocations. In this study, we tackle the uncapacitated single allocation hub location problem (USAHLP) that has no capacity constraint on hubs and all non-hub nodes must be allocated to a single hub so that the total flow cost is minimized. Since USAHLP is NP-hard, we propose a threshold accepting (TA) algorithm to solve the problem. Our algorithm was tested on two sets of benchmark instances, Civil Aeronautics Board and Australia Post (AP), and two sets of new larger and modified AP instances from the literature. The computational experiments and comparisons with other metaheuristics are reported. The results show that TA is competitive with other well-known algorithms and able to update numerous new best solutions.

An efficient memetic algorithm for the uncapacitated single allocation hub location problem

In this paper, we present a memetic algorithm (MA) for solving the uncapacitated single allocation hub location problem (USAHLP). Two efficient local search heuristics are designed and implemented in the frame of an evolutionary algorithm in order to improve both the location and allocation part of the problem. Computational experiments, conducted on standard CAB/AP hub data sets (Beasley in J Global Optim 8:429---433, 1996) and modified AP data set with reduced fixed costs (Silva and Cunha in Computer Oper Res 36:3152---3165, 2009), show that the MA approach is superior over existing heuristic approaches for the USAHLP. For several large-scale AP instances up to 200 nodes, the MA improved the best-known solutions from the literature until now. Numerical results on instances with 300 and 400 nodes introduced in Silva and Cunha (Computer Oper Res 36:3152---3165, 2009) show significant improvements in the sense of both solution quality and CPU time. The robustness of the MA was additionally tested on a challenging set of newly generated large-scale instances with 520---900 nodes. To the best of our knowledge, these are the largest USAHLP problem dimensions solved in the literature until now. In addition, in this paper, we report for the first time optimal solutions for 30 AP and modified AP instances.

New simple and efficient heuristics for the uncapacitated single allocation hub location problem

Hub-and-spoke networks are widely studied in the area of location theory. They arise in several contexts, including passenger airlines, postal and parcel delivery, and computer and telecommunication networks. Hub location problems usually involve three simultaneous decisions to be made: the optimal number of hub nodes, their locations and the allocation of the non-hub nodes to the hubs. In the uncapacitated single allocation hub location problem (USAHLP) hub nodes have no capacity constraints and non-hub nodes must be assigned to only one hub. In this paper, we propose three variants of a simple and efficient multi-start tabu search heuristic as well as a two-stage integrated tabu search heuristic to solve this problem. With multi-start heuristics, several different initial solutions are constructed and then improved by tabu search, while in the two-stage integrated heuristic tabu search is applied to improve both the locational and allocational part of the problem. Computational experiments using typical benchmark problems (Civil Aeronautics Board (CAB) and Australian Post (AP) data sets) as well as new and modified instances show that our approaches consistently return the optimal or best-known results in very short CPU times, thus allowing the possibility of efficiently solving larger instances of the USAHLP than those found in the literature. We also report the integer optimal solutions for all 80 CAB data set instances and the 12 AP instances up to 100 nodes, as well as for the corresponding new generated AP instances with reduced fixed costs.

A note on solution of the capacitated single allocation hub location problem

Hub-and-spoke designs are frequently used in many types of transportation and communication networks. The challenge to academics is to develop effective solution procedures for determining the number of hubs, locating hub facilities and allocating the non-hubs to the hubs. In this note, we deal with the capacitated single allocation hub location problem (CSAHLP) in which each non-hub can only be allocated to a single hub, each hub has its capacity constraint, and the objective function includes fixed costs for establishing hubs. A problem closely related to the CSAHLP is the uncapacitated single allocation hub location problem (USAHLP). We have proposed a hybrid heuristic for solving the USAHLP with competitive results obtained. In this note, an effective procedure to allocate the non-hubs to the capacitated hubs is developed to be embedded in the previous hybrid heuristic to solve the CSAHLP. Computational results show the presented heuristic is capable of obtaining optimal solutions for almost all small-scale problems and outperforms a simulated annealing algorithm from the literature in solving the large-scale CSAHLP. It is expected that this note can provide distribution managers an effective heuristic to design hub-and-spoke networks where the volume of traffic that a hub can collect is restricted.

A hybrid heuristic for the uncapacitated single allocation hub location problem

The uncapacitated single allocation hub location problem (USAHLP), with the hub-and-spoke network structure, is a decision problem in regard to the number of hubs and location–allocation. In a pure hub-and-spoke network, all hubs, which act as switching points for internodal flows, are interconnected and none of the non-hubs (i.e., spokes) are directly connected. The key factors for designing a successful hub-and-spoke network are to determine the optimal number of hubs, to properly locate hubs, and to allocate the non-hubs to the hubs. In this paper two approaches to determine the upper bound for the number of hubs along with a hybrid heuristic based on the simulated annealing method, tabu list, and improvement procedures are proposed to resolve the USAHLP. Computational experiences indicate that by applying the derived upper bound for the number of hubs the proposed heuristic is capable of obtaining optimal solutions for all small-scaled problems very efficiently. Computational results also demonstrate that the proposed hybrid heuristic outperforms a genetic algorithm and a simulated annealing method in solving USAHLP.

Solving the uncapacitated hub location problem using genetic algorithms

Hub location problems are widely studied in the area of location theory, where they involve locating the hub facilities and designing the hub networks. In this paper, we present a new and robust solution based on a genetic search framework for the uncapacitated single allocation hub location problem (USAHLP). To present its effectiveness, we compare the solutions of our GA-based method with the best solutions presented in the literature by considering various problem sizes of the CAB data set and the AP data set. The experimental work demonstrates that even for larger problems the results of our method significantly surpass those of the related work with respect to both solution quality and the CPU time to obtain a solution. Specifically, the results from our method match the optimal solutions found in the literature for all test cases generated from the CAB data set with significantly less running time than the related work. For the AP data set, our solutions match the best solutions of the reference study with an average of 8 times less running time than the reference study. Its performance, robustness and substantially low computational effort justify the potential of our method for solving larger problem sizes.