A Relax-and-Decomposition Algorithm for a p-Robust Hub Location Problem (original) (raw)
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The single allocation hub location problem: a robust optimisation approach
European J. of Industrial Engineering, 2015
Design of hub-and-spoke networks or the hub location problem is one of the most important problems in operational research and has many applications in different areas of transportation, logistics, and telecommunications. In this paper, a relatively new version of the single allocation hub location problem is addressed, in which quantity of the commodity flows between pairs of customer nodes are of stochastic nature. The objective here is to determine the number, location, and capacity of the hubs and also to allocate the customers to these hubs in such a way that transferring all the commodities in the network is ensured with a very high probability (capacity constraints associated with the hubs are not violated). At the same time, total expected system-wide costs will be minimised. A robust optimisation approach is employed to model the problem with a standard optimisation package being used to solve it. Results obtained via numerical experiments show the capability of the presented robust model to immunise the system against violation of capacity constraints with a relatively small cost increase, known as the robustness cost. [
Novel Reliable Uncapacitated P-Hub Location Problems Under Uncertainty
International Journal of Fuzzy System Applications, 2018
Hubs are facilities to collect, arrange and distribute commodities in telecommunication networks, cargo delivery systems, etc. In this article, it will study two popular hub location problems (p-hub center and p-hub maximal covering problems) under uncertainty. First, novel reliable uncapacitated p-hub location problems are introduced based on considering the failure probability of hubs, in which the parameters are random fuzzy variables, but the decision variables are real variables. Then, the proposed hub location problems under uncertainty are solved by new methods using random fuzzy chance-constrained programming based on the idea of possibility theory. These methods can satisfy optimistic and pessimistic decision makers under uncertain framework. Finally, some benchmark problems are solved as numerical examples to clarify the described methods and show their efficiency.
Benders decomposition for the uncapacitated multiple allocation hub location problem
Computers & Operations Research, 2008
In telecommunication and transportation systems, the uncapacitated multiple allocation hub location problem (UMAHLP) arises when we must flow commodities or information between several origin–destination pairs. Instead of establishing a direct node to node connection from an origin to its destination, the flows are concentrated with others at facilities called hubs. These flows are transported on links established between hubs, being then splitted and delivered to its final destination. Systems with this sort of topology are named hub-and-spoke (HS) systems or hub-and-spoke networks. They are designed to exploit the scale economies attainable through the shared use of high capacity links between hubs. Therefore, the problem is to find the least expensive HS network, selecting hubs and assigning traffic to them, given the demands between each origin–destination pair and the respective transportation costs. In the present paper, we present efficient Benders decomposition algorithms based on a well known formulation to tackle the UMAHLP. We have been able to solve some large instances, considered ‘out of reach’ of other exact methods in reasonable time.
Mathematical model for P-hub location problem under simultaneous disruption
Journal of Industrial and Systems Engineering, 2018
The optimal locating of facilities has large effects on economic benefits, providing satisfactory service and levels of customer satisfaction. One of the new topics discussed in location problems is hub location and hub facilities are subject to unpredictable disruptions. This paper proposes a nonlinear integer model for reliable single allocation hub location problem that considers backup hub, alternative routes, and also uses fortification approach to improve the network reliability. Due to the NP hard nature of the model, we use genetic algorithm in order to solve the defined problem and the numerical results illustrate the applicability of the proposed model as well as the efficiency of solution procedure.
Scientia Iranica
The critical and undeniable role of hubs in telecommunication and networking brings about some precautions to be taken to protect networks against any disruption. In this paper, a multi-objective model in a group of hub location problems, referred to as protection models for survivable network design, is developed. In fact, this model is a hub location problem that aims to maximize the potential ow between the origin and destination node pairs in the network, which has the minimum potential ow among all O-D pairs, including multiple assignment and backup routes. In addition, it concerns the xed cost of installation of the hub facilities. A fuzzy goal programming method is applied to solve the model. Di erent scenarios are implemented using Turkish data set and also numerical experiments are presented to illustrate the advantages of the proposed model in some aspects, compared to previous models. The results can give useful insights into telecommunication network design.
Exact decomposition algorithms for nonlinear location and hub location problems
Middle East Technical University, 2018
, 172 pages Developing exact solution algorithms to solve difficult optimization problems is one of the most important subjects in the operations research literature. In this dissertation, we develop Benders decomposition based exact solution algorithms (BDTAs) for handling nonlinearity in three selected nonlinear integer location/hub location problems. The first and second problem include nonlinear capacity constraints, while in the last problem, both objective function and the capacity constraints are nonlinear. In our decomposition algorithms, we used problem specific, logic based feasibility and optimality cuts. In addition to BDTAs, we propose a MISOCP reformulation for solving the nonlinear integer model, which arises in wireless local area networks, to optimality by using commercial solvers. Our computational study demonstrates that the performance of MISOCP is better than that of Benders decomposition based algorithms. This reformulation is general for any convex objective function as long as the constraints have the same structure as those in the first problem that we studied in this dissertation. The second problem includes nonlinear constraints in which product of binary variables exist and we develop a branch-and-check algorithm with several enhancement steps. In the last problem, nonlinear terms in the objective function and constraints are handled in Benders decomposition scheme. Our computational study demonstrates that the performance of Benders decomposition type algorithm is better than that of commercial solvers for especially difficult instances.
University of Kashan, 2024
The Hub Location Problem (HLP) is a significant problem in combinatorial optimization consisting of two main components: location and network design. The HLP aims to develop an optimal strategy for various applications, such as product distribution, urban management, sensor network design, computer network, and communication network design. Additionally, the upgrading location problem arises when modifying specific components at a cost is possible. This paper focuses on upgrading the uncapacitated multiple allocation p-hub median problem (u-UMApHMP), where a predetermined budget and bound of changes are given. The aim is to modify certain network parameters to identify the p-hub median that improves the objective function value concerning the modified parameters. We propose a non-linear mathematical formulation for u-UMApHMP to achieve this goal. Then, we employ the McCormick technique to linearize the model. Subsequently, we solve the linearized model using the CPLEX solver and the Benders decomposition method. Finally, we present experimental results to demonstrate the effectiveness of the proposed approach.
Bi-objective p-hub Location Problems by Fatih Bilen
2017
In this thesis, we introduce, model, and solve bi-objective hub location problems. The two well-known hub location problems from the literature, the p-hub median and p-hub center problems, are unified under a bi-objective setting considering the single, multiple, and r-allocation strategies. We developed a 3-index and a 4-index mixed-integer programming formulation for each of the allocation strategies. All the formulations are tested on the CAB dataset from the literature using a commercial optimization software. We observe the effect of different priorities given to the objectives on the locations of hub nodes, allocations, and the CPU time requirements with different allocation strategies under different values of problem parameters.