Multiple Allocation Hub Location Problem Research Articles

Reliable multiple allocation hub location problem under disruptions

Reliable multiple allocation hub location problem under disruptions

Capacitated multiple allocation hub location problems under the risk of interdiction: model formulations and solution approaches

Capacitated multiple allocation hub location problems under the risk of interdiction: model formulations and solution approaches

Capacitated Air/Rail Hub Location Problem With Uncertainty: A Model, Efficient Solution Algorithm, and Case Study

Well-designed multi-modal transportation networks are crucial for our connected world. For instance, the excessive construction of railway tracks in China, at speeds up to 350 km/h, makes it necessary to consider the interaction of rail with air transportation for network design. In this study, we propose a model for an air/rail multi-modal, multiple allocation hub location problem with uncertainty on travel demands. Our model is unique in that it integrates features from the existing literature on multi-modal hub location problem (including hub-level capacities, link capacities, direct links, travel cost and time, transit costs and uncertainty), which have not been considered simultaneously, given its high computational complexity. We formulate this model with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n^{4})$ </tex-math></inline-formula> variables and show that the implementation of a Benders decomposition algorithm is inherently hard, because of the cubic number of variables in the master problem. Furthermore, we derive an iterative network design algorithm and additional improvement strategies: MMHUBBI which resolves a restricted problem by the solver CPLEX and MMHUBBI-DIRECT which re-designs the transportation network by a heuristic. Our evaluation on real-world dataset for Chinese domestic transportation shows that MMHUBBI provides a significant speed-up on all instances, compared to using CPLEX, while obtaining near-optimal solutions. MMHUBBI-DIRECT further reduces the runtime/memory usage but provides solutions with worse quality. We believe that our study contributes towards the design of more realistic multi-modal hub location problems.

Competitive multiple allocation hub location problem considering primary and backup routes

Competitive multiple allocation hub location problem considering primary and backup routes

A conditional [formula omitted]-mean approach to risk-averse stochastic multiple allocation hub location problems

This paper addresses risk-averse stochastic hub location problems where the risk is measured using the conditional β-mean criterion. Three variants of the classical multiple allocation hub location problem, namely the p-hub median, the p-hub maximal covering, and the weighted p-hub center problems are studied under demand data uncertainty represented by a finite set of scenarios. Novel mixed-integer linear programming formulations are proposed for the problems and exact algorithms based on Benders decomposition are developed for solving large instances of the problems. A large set of computational tests are conducted so that the efficiency of the proposed algorithms is proved and the effect of various input parameters on the optimal solutions is analyzed.

The Capacitated Multiple Allocation Hub Location Problem under Demand Uncertainty and Excess Capacity with Possibilistic Programing Approach

Facility location is a factor of competitiveness and demand satisfaction. Using a hub on the network can facilitate communication across the network and reduce costs. In the current study, with regards to demand uncertainty, operational costs of the hub, and building extra capacity in the hub it has been aimed to develop a mathematical programing model for the middle hub location problem with a certain capacity,. Due to the presence of the uncertainty in the problem’s parameters, the possibilistic programing approach which is a subset of fuzzy programing has been used. The proposed model has been investigated via GAMS software and the CPLX solver. Finally, the proposed model has been validated by the dataset obtained from Iran Aviation Dataset (IAD) for a round-trip, and the proper locations for facilities in each level and allocation of the customers to the facilities, were determined by the obtained Pareto analysis answer.

Experimental evaluation of meta-heuristics for multi-objective capacitated multiple allocation hub location problem

Multi-objective capacitated multiple allocation hub location problem (MOCMAHLP) is a variation of classic hub location problem, which deals with network design, considering both the number and the location of the hubs and the connections between hubs and spokes, as well as routing of flow on the network. In this study, we offer two meta-heuristic approaches based on the non-dominated sorting genetic algorithm (NSGA-II) and archived multi-objective simulated annealing method (AMOSA) to solve MOCMAHLP. We attuned AMOSA based approach to obtain feasible solutions for the problem and developed five different neighborhood operators in this approach. Moreover, for NSGA-II based approach, we developed two novel problem-specific mutation operators. To statistically analyze the behavior of both algorithms, we conducted experiments on two well-known data sets, namely Turkish and Australian Post (AP). Hypervolume indicator is used as the performance metric to measure the effectiveness of both approaches on the given data sets. In the experimental study, thorough tests are conducted to fine-tune the proposed mutation types for NSGA-II and proposed neighborhood operators for AMOSA. Fine-tuning tests reveal that for NSGA-II, mutation probability does not have a real effect on Turkish data set, whereas lower mutation probabilities are slightly better for AP data set. Moreover, among the AMOSA based neighborhood operators, the one which adds/removes a specific number of links according to temperature (NS-5) performs better than the others for both data sets. After analyzing different operators for both algorithms, a comparison between our NSGA-II based and AMOSA based approaches is performed with the best settings. As a result, we conclude that both of our algorithms are able to find feasible solutions of the problem. Moreover, NSGA-II performs better for larger, whereas AMOSA performs better for smaller size networks.

Hub location problem with balanced round-trip flows on hub links

This paper addresses the classical single and multiple allocation hub location problems with fully interconnected hubs, in which the balanced round-trip flows on hub links are considered in the strategic decision making process. The use of balanced round-trip flows on hub links is motivated by the need to decrease the empty-trip rate of vehicles and increase the full-load rate of vehicles. Mixed-integer programming models are presented for single and multiple allocation versions of the problems. Numerical experiments with the CAB and AP datasets are performed to analyse the impacts of balanced flows on the network configurations and the utilisation of service resources. Experimental results show that the number of located hubs tends to decrease with a decrease in the allowable unbalanced round-trip degree of the hub link flows. The utilisation rate of transportation resources can be significantly improved with a small increase in the traditional operating cost. Moreover, a better modelling of economies of scale can be achieved when considering balanced flows. [Received: 22 September 2019; Accepted: 15 March 2020]

Hub location problem with balanced round-trip flows on hub links

This paper addresses the classical single and multiple allocation hub location problems with fully interconnected hubs, in which the balanced round-trip flows on hub links are considered in the strategic decision making process. The use of balanced round-trip flows on hub links is motivated by the need to decrease the empty-trip rate of vehicles and increase the full-load rate of vehicles. Mixed-integer programming models are presented for single and multiple allocation versions of the problems. Numerical experiments with the CAB and AP datasets are performed to analyse the impacts of balanced flows on the network configurations and the utilisation of service resources. Experimental results show that the number of located hubs tends to decrease with a decrease in the allowable unbalanced round-trip degree of the hub link flows. The utilisation rate of transportation resources can be significantly improved with a small increase in the traditional operating cost. Moreover, a better modelling of economies of scale can be achieved when considering balanced flows. [Received: 22 September 2019; Accepted: 15 March 2020]

Bi-objective load balancing multiple allocation hub location: a compromise programming approach

In this paper we address unbalanced spatial distribution of hub-level flows in an optimal hub-and-spoke network structure of median-type models. Our study is based on a rather general variant of the multiple allocation hub location problems with fixed setup costs for hub nodes and hub edges in both capacitated and uncapacitated variants wherein the number of hub nodes traversed along origin-destination pairs is not constrained to one or two as in the classical models.. From the perspective of an infrastructure owner, we want to make sure that there exists a choice of design for the hub-level sub-network (hubs and hub edges) that considers both objectives of minimizing cost of transportation and balancing spatial distribution of flow across the hub-level network. We propose a bi-objective (transportation cost and hub-level flow variance) mixed integer non-linear programming formulation and handle the bi-objective model via a compromise programming framework. We exploit the structure of the problem and propose a second-order conic reformulation of the model along with a very efficient matheuristics algorithm for larger size instances.

Robust uncapacitated multiple allocation hub location problem under demand uncertainty: minimization of cost deviations

The hub location–allocation problem under uncertainty is a real-world task arising in the areas such as public and freight transportation and telecommunication systems. In many applications, the demand is considered as inexact because of the forecasting inaccuracies or human’s unpredictability. This study addresses the robust uncapacitated multiple allocation hub location problem with a set of demand scenarios. The problem is formulated as a nonlinear stochastic optimization problem to minimize the hub installation costs, expected transportation costs and expected absolute deviation of transportation costs. To eliminate the nonlinearity, the equivalent linear problem is introduced. The expected absolute deviation is the robustness measure to derive the solution close to each scenario. The robust hub location is assumed to deliver the least costs difference across the scenarios. The number of scenarios increases size and complexity of the task. Therefore, the classical and improved Benders decomposition algorithms are applied to achieve the best computational performance. The numerical experiment on CAB and AP dataset presents the difference of resulting hub networks in stochastic and robust formulations. Furthermore, performance of two Benders decomposition strategies in comparison with Gurobi solver is assessed and discussed.

Particle swarm optimization for uncapacitated multiple allocation hub location problem under congestion

In this paper we address the hub location problem in which capacity restrictions are introduced into the objective function as a penalty cost to represent their congestion effects on respective hubs. The goal of hub location problems is to locate an optimal set of hubs while minimizing sum of the transportation and opening costs under various constraints such as number of hubs, delay time and capacities of hubs. Moreover, we propose a more realistic variant of the problem where the capacities of hubs are not only a limitation in selecting the hubs. In practice, capacities of hubs are predicted by a strategic plan, but these predictions generally fail to meet the expectations due to changes in the flow in future and competitive nature of air transportation. A particle swarm optimization (PSO) is proposed to handle the complex nature of this problem and shorten the computing times. The performance of the proposed PSO is analyzed comparatively on the Australia Post (AP) data sets. The numerical results show that the proposed method can find the optimal solutions in less computation time in comparison with the earlier multiple allocation hub location models.

Efficient simulated annealing based solution approaches to the competitive single and multiple allocation hub location problems

Hub location problems (HLPs) constitute an important class of problems in logistics with numerous applications in passenger/cargo transportation, postal services, telecommunications, etc. This paper addresses the competitive single and multiple allocation HLPs where the market is assumed to be a duopoly. Two firms (decision makers) sequentially decide on the configuration of their hub networks trying to maximize their own market shares. The customers choose one firm based on the cost of service provided by these firms. Mathematical formulations are presented for the problems of the first and second firms (the leader and the follower, respectively) and Simulated Annealing (SA) based solution algorithms are proposed for solving these problems both in single and multiple allocation settings. Extensive computational experiments show the capability of the proposed solution algorithms to obtain the optimal solutions in short computational times. Some managerial insights are also derived based on the obtained results.

A capacitated hub location problem under hose demand uncertainty

In this study, we consider a capacitated multiple allocation hub location problem with hose demand uncertainty. Since the routing cost is a function of demand and capacity constraints are imposed on hubs, demand uncertainty has an impact on both the total cost and the feasibility of the solutions. We present a mathematical formulation of the problem and devise two different Benders decomposition algorithms. We develop an algorithm to solve the dual subproblem using complementary slackness. In our computational experiments, we test the efficiency of our approaches and we analyze the effects of uncertainty. The results show that we obtain robust solutions with significant cost savings by incorporating uncertainty into our problem.

A Tabu Search Based Solution Approach to the Competitive Multiple Allocation Hub Location Problem

A Tabu Search Based Solution Approach to the Competitive Multiple Allocation Hub Location Problem

Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach

The hub location problem arises in a variety of domains such as transportation and telecommunication systems. In many real-world situations, hub facilities are subject to disruption. This paper deals with the multiple allocation hub location problem in the presence of facilities failure. To model the problem, a two-stage stochastic formulation is developed. In the proposed model, the number of scenarios grows exponentially with the number of facilities. To alleviate this issue, two approaches are applied simultaneously. The first approach is to apply sample average approximation to approximate the two stochastic problem via sampling. Then, by applying the multiple cuts Benders decomposition approach, computational performance is enhanced. Numerical studies show the effective performance of the SAA in terms of optimality gap for small problem instances with numerous scenarios. Moreover, performance of multi-cut Benders decomposition is assessed through comparison with the classic version and the computational results reveal the superiority of the multi-cut approach regarding the computational time and number of iterations.

A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities

This study focuses on the development of a modeling framework for multi-period stochastic capacitated multiple allocation hub location problems. We consider a planning horizon divided into several time periods. Uncertainty is assumed for the demands. The decisions to make concern the location of the hubs, their initial capacity, the capacity expansion of existing hubs and the transportation between origin–destination pairs. The goal is to minimize the total expected cost. For the situation in which uncertainty can be captured by a finite set of scenarios each occurring with some estimated probability we derive the extensive form of the deterministic equivalent. The resulting model is compact. However, it includes a set of binary variables that becomes too large for medium and large instances of the problem and thus hardly can it be tackled by a general optimization solver. For this reason, enhancements are proposed to the model making it possible to solve optimally instances that could not be solved using the initial model. This is confirmed by the computational tests performed using the well-known CAB data.

An adaptive large neighborhood search heuristic for solving the reliable multiple allocation hub location problem under hub disruptions

An adaptive large neighborhood search heuristic for solving the reliable multiple allocation hub location problem under hub disruptions

Matheuristics for optimizing the network in German wagonload traffic

In this paper, we consider a capacitated multiple allocation hub location problem derived from a practical application in network design of German wagonload traffic. Due to the difficulty to solve even small data sets to optimality, we present two matheuristics: a local search matheuristic and an extension of an evolutionary algorithm matheuristic. Computational results are presented to demonstrate and compare the efficiency of both approaches for real-sized instances.

2-Stage stochastic programming approach for hub location problem under uncertainty: A case study of air network of Iran

In this paper 2-stage stochastic programming has been developed for formulating stochastic uncapacitated multiple allocation hub location problem. This problem is studied under three cases. The first, stochastic demand, the second, stochastic transportation cost and the third, integrated stochastic, which is compounded of first and second cases. A case of air network in Iran is used to evaluate proposed formulations and computational results obtained by GAMS are presented. The results show that considering uncertainty into formulation could cause in different solutions.