Capacitated Single Allocation Hub Location Research Articles

A heuristic approach to the stochastic capacitated single allocation hub location problem with Bernoulli demands

Hubs are critical components of transportation and distribution systems, and hub networks play a special role in freight and passenger transportation services worldwide. This paper studies a capacitated single allocation hub location problem with Bernoulli demands. Since the origin-destination (OD) demands are stochastic in nature, and the nodes are allocated to hubs before knowing their realized values, the actual total demand allocated to each hub is uncertain. Therefore, demand can exceed the capacity of hubs, rendering a need for outsourcing. The problem is studied under two distinct outsourcing policies, namely the facility and customer outsourcing. Mathematical models are developed for each case as two-stage stochastic programs. Deterministic equivalent formulations are obtained for problems, assuming a homogeneous demand distribution for all OD pairs. A Tabu Search-based algorithm is presented as a solution approach to deal with large problem instances. Extensive computational tests demonstrate the outstanding performance of the developed models and the metaheuristic procedure in terms of solution quality and computational time. The relevance of using stochastic programming approach for the problems is demonstrated via computational results. This study also reports solutions for problems with 200 nodes for the first time.

Branch-and-price-and-cut algorithm for the capacitated single allocation hub location routeing problem

The paper focuses on a variant of hub location routeing problem arising in the design of intra-city express service networks, named as capacitated single allocation hub location routeing problem, in which each non-hub node should be served by exactly one hub, and both hub capacity and vehicle capacity are considered. A new mixed-integer programming formulation for the problem is provided, and a solution algorithm is developed on the basis of the column generation scheme to exactly solve the problem for the first time. The pricing subproblem is solved by a bidirectional labelling algorithm, and the master problem is strengthened by valid inequalities. Numerical experiments are conducted on the instances generated from the Australian Post dataset to test the performance of the model and the developed algorithm. Computational results prove that the algorithm outperforms the CPLEX and is able to provide optimal solutions for instances with up to 35 non-hub nodes and high-quality solutions for instances with 40 non-hub nodes within reasonable computational time, which indicates the feasibility and efficiency of the model and algorithm proposed.

Stochastic single allocation hub location problems with balanced utilization of hub capacities

This paper presents a stochastic formulation for capacitated single allocation hub location problems with uncertain demands, in which the balanced utilization of hub capacities is considered in the strategic decision making process. The demands are assumed to be independent random variables with known normal probability distributions. A stochastic programming model with joint chance constraints is established and then transformed into a second-order mixed-integer cone programming model. Furthermore, the proposed model is approximated by using piecewise tangent approximation and piecewise linear approximation techniques. For the approximated models, alternative reformulations are developed, and valid inequalities are employed to add to alternative reformulations. Extensive numerical experiments with CAB and AP data sets are conducted to evaluate the performance of the proposed methods, and analyze the configuration of hub-and-spoke networks and the utilization of hub capacities. Experimental results show that the optimal solution of proposed models can be obtained by using the two approximation techniques with a small number of tangent and linear segments. The developed alternative reformulations and valid inequalities can significantly improve computational efficiency. The entire unbalanced utilization degree of hub capacities can be greatly reduced with a small rise in the traditional operating cost.

A hybridization of an evolutionary algorithm and a parallel branch and bound for solving the capacitated single allocation hub location problem

In this study, we propose a hybrid optimization method, consisting of an evolutionary algorithm (EA) and a branch-and-bound method (BnB) for solving the capacitated single allocation hub location problem (CSAHLP). The EA is designed to explore the solution space and to select promising configurations of hubs (the location part of the problem). Hub configurations produced by the EA are further passed to the BnB search, which works with fixed hubs and allocates the non-hub nodes to located hubs (the allocation part of the problem). The BnB method is implemented using parallelization techniques, which results in short running times. The proposed hybrid algorithm, named EA-BnB, has been tested on the standard Australia Post (AP) hub data sets with up to 300 nodes. The results demonstrate the superiority of our hybrid approach over existing heuristic approaches from the existing literature. The EA-BnB method has reached all the known optimal solutions for AP hub data set and found new, significantly better, solutions on three AP instances with 100 and 200 nodes. Furthermore, the extreme efficiency of the implementation of this hybrid algorithm resulted in short running times, even for the largest AP test instances.

A Multi-objective Imperialist Competitive Algorithm for a Capacitated Single-allocation Hub Location Problem

In this paper, we present a novel multi-objective mathematical model for capacitated single allocation hub location problem. There are the vehicle capacity constraint and capacity restrictions amount of the incoming flow to the hub while the balancing requirements of incoming quantities of flow to the each hub is considered. Moreover, there is a set of available capacities for each potential hub, among which one can be chosen. The multiple objectives are to minimize total cost of the networks regarding minimizing maximum travel time between nodes. Due to NP-Hard property of our problem, this model is solved by a multi-objective imperialist competitive algorithm (MOICA) and finally, to prove its efficiency, the related results are compared with the results obtained by the well-known multi-objective evolutionary algorithm, called NSGA-II. The associated results confirm the efficiency and the effectiveness of our proposed MOICA to provide good solutions, especially for medium and large-sized problems.

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.

Solution approaches for the capacitated single allocation hub location problem using ant colony optimisation

Hub and spoke type networks are often designed to solve problems that require the transfer of large quantities of commodities. This can be an extremely difficult problem to solve for constructive approaches such as ant colony optimisation due to the multiple optimisation components and the fact that the quadratic nature of the objective function makes it difficult to determine the effect of adding a particular solution component. Additionally, the amount of traffic that can be routed through each hub is constrained and the number of hubs is not known a-priori. Four variations of the ant colony optimisation meta-heuristic that explore different construction modelling choices are developed. The effects of solution component assignment order and the form of local search heuristics are also investigated. The results reveal that each of the approaches can return optimal solution costs in a reasonable amount of computational time. This may be largely attributed to the combination of integer linear preprocessing, powerful multiple neighbourhood local search heuristic and the good starting solutions provided by the ant colonies.

Capacitated single allocation hub location problem—A bi-criteria approach

A different approach to the capacitated single allocation hub location problem is presented. Instead of using capacity constraints to limit the amount of flow that can be received by the hubs, we introduce a second objective function to the model (besides the traditional cost minimizing function), that tries to minimize the time to process the flow entering the hubs. Two bi-criteria single allocation hub location problems are presented: in a first model, total time is considered as the second criteria and, in a second model, the maximum service time for the hubs is minimized. To generate non-dominated solutions an interactive decision-aid approach developed for bi-criteria integer linear programming problems is used. Both bi-criteria models are tested on a set of instances, analyzing the corresponding non-dominated solutions set and studying the reasonableness of the hubs flow charge for these non-dominated solutions. The increased information provided by the non-dominated solutions of the bi-criteria model when compared to the unique solution given by the capacitated hub location model is highlighted.

Solution algorithms for the capacitated single allocation hub location problem

In this paper, we present an efficient approach for solving capacitated single allocationhub location problems. We use a modified version of a previous mixed integer linearprogramming formulation developed by us for p‐hub median problems. This formulationrequires fewer variables and constraints than those traditionally used in the literature. Wedevelop good heuristic algorithms for its solution based on simulated annealing (SA) andrandom descent (RDH). We use the upper bound to develop an LP‐based branch and boundsolution method. The problem, as we define it, finds applications in the design of postaldelivery networks, particularly in the location of capacitated mail sorting and distributioncentres. We test our algorithms on data obtained from this application. To the best of ourknowledge, this problem has not been solved in the literature. Computational results arepresented indicating the usefulness of our approach.

Location of Urban Logistic Terminals as Hub Location Problem

In this paper the problems of locating urban logistic terminals are studied as hub location problems that due to a large number of potential nodes in big cities belong to hard non-polynomial problems, the so-called NP-problems. The hub location problems have found wide application in physical planning of transport and telecommunication systems, especially systems of fast delivery, networks of logistic and distribution centres and cargo traffic terminals of the big cities, etc. The paper defines single and multiple allocations and studies the numerical examples. The capacitated single allocation hub location problems have been studied, with the provision of a mathematical model of selecting the location for the hubs on the network. The paper also presents the differences in the possibilities of implementing the exact and heuristic methods to solve the actual location problems of big dimensions i.e. hub problems of the big cities.