Applying VNPSO Algorithm to Solve the Many-to-Many Hub Location-Routing Problem in a Large scale

One way to increase the companies’ performance and reducing their costs is to concern the transportation industry. Many-to-many hub location-routing problem (MMHLRP) is one of the problems that can affect the process of transportation costs. The problem of MMHLRP is one of the NP-HARD problems. Hence, solving it by exact methods is not affordable; however it was first solved by Benders decomposition algorithm. Modeling and the solving algorithm is able to solve the problem with 100 nodes. In this study, using VNPSO (a combination of the two methods VNS and PSO) was suggested to solve MMHLRP in large-scale. Given high similarity of the results obtained in small scale, using a random sample confirmed that the proposed method was able to solve problem MMHLRP with 300 nodes and acceptable accuracy and speed

A new formulation and branch-and-cut method for single-allocation hub location problems

A new compact formulation for uncapacitated single-allocation hub location problems with fewer variables than the previous Integer Linear Programming formulations in the literature is introduced. Our formulation works even with costs not based on distances and not satisfying triangle inequality. Moreover, costs can be given in aggregated or disaggregated way. Different families of valid inequalities that strengthen the formulation are developed and a branch-and-cut algorithm based on a relaxed version of the formulation is designed, whose restrictions are inserted in a cut generation procedure together with two sets of valid inequalities. The performance of the proposed methodology is tested on well-known hub location data sets and compared to the most recent and efficient exact algorithms for single-allocation hub location problems. Extensive computational results prove the efficiency of our methodology, that solves large-scale instances in very competitive times

Hub Location Problems with Profit Considerations

This thesis studies profit maximizing hub location problems. These problems seek to find the optimal number and locations of hubs, allocations of demand nodes to these hubs, and routes of flows through the network to serve a given set of demands between origin-destination pairs while maximizing total profit. Taking revenue into consideration, it is assumed that a portion of the demand can remain unserved when it is not profitable to be served. Potential applications of these problems arise in the design of airline passenger and freight transportation networks, truckload and less-than-truckload transportation, and express shipment and postal delivery. Firstly, mathematical formulations for different versions of profit maximizing hub location problems are developed. Alternative allocation strategies are modeled including multiple allocation, single allocation, and $r$-allocation, as well as allowing for the possibility of direct connections between non-hub nodes. Extensive computational analyses are performed to compare the resulting hub networks under different models, and also to evaluate the solution potential of the proposed models on commercial solvers with emphasis on the effect of the choice of parameters. Secondly, revenue management decisions are incorporated into the profit maximizing hub location problems by considering capacities of hubs. In this setting, the demand of commodities are segmented into different classes and there is available capacity at hubs which is to be allocated to these different demand segments. The decision maker needs to determine the proportion of each class of demand to serve between origin-destination pairs based on the profit to be obtained from satisfying this demand. A strong mixed-integer programming formulation of the problem is presented and Benders-based algorithms are proposed to optimally solve large-scale instances of the problem. A new methodology is developed to strengthen the Benders optimality cuts by decomposing the subproblem in a two-phase fashion. The algorithms are enhanced by the integration of improved variable fixing techniques. Computational results show that large-scale instances with up to 500 nodes and 750,000 commodities of different demand segments can be solved to optimality, and that the proposed algorithms generate cuts that provide significant speedups compared to using Pareto-optimal cuts. As precise information on demand may not be known in advance, demand uncertainty is then incorporated into the profit maximizing hub location problems with capacity allocation, and a two-stage stochastic program is developed. The first stage decision is the locations of hubs, while the assignment of demand nodes to hubs, optimal routes of flows, and capacity allocation decisions are made in the second stage. A Monte-Carlo simulation-based algorithm is developed that integrates a sample average approximation scheme with the proposed Benders decomposition algorithm. Novel acceleration techniques are presented to improve the convergence of the algorithm. The efficiency and robustness of the algorithm are evaluated through extensive computational experiments. Instances with up to 75 nodes and 16,875 commodities are optimally solved, which is the largest set of instances that have been solved exactly to date for any type of stochastic hub location problems. Lastly, robust-stochastic models are developed in which two different types of uncertainty including stochastic demand and uncertain revenue are simultaneously incorporated into the capacitated problem. To embed uncertain revenues into the problem, robust optimization techniques are employed and two particular cases are investigated: interval uncertainty with a max-min criterion and discrete scenarios with a min-max regret objective. Mixed integer programming formulations for each of these cases are presented and Benders-based algorithms coupled with sample average approximation scheme are developed. Inspired by the repetitive nature of sample average approximation scheme, general techniques for accelerating the algorithms are proposed and instances involving up to 75 nodes and 16,875 commodities are solved to optimality. The effects of uncertainty on optimal hub network designs are investigated and the quality of the solutions obtained from different modeling approaches are compared under various parameter settings. Computational results justify the need for embedding both sources of uncertainty in decision making to provide robust solutions

Robust intermodal hub location under polyhedral demand uncertainty

In this study, we consider the robust uncapacitated multiple allocation p-hub median problem under polyhedral demand uncertainty. We model the demand uncertainty in two different ways. The hose model assumes that the only available information is the upper limit on the total flow adjacent at each node, while the hybrid model additionally imposes lower and upper bounds on each pairwise demand. We propose linear mixed integer programming formulations using a minmax criteria and devise two Benders decomposition based exact solution algorithms in order to solve large-scale problems. We report the results of our computational experiments on the effect of incorporating uncertainty and on the performance of our exact approaches. © 2016 Elsevier Ltd

Multiple Allocation Hub Interdiction and Protection Problems: Model Formulations and Solution Approaches

In this paper, we present computationally efficient formulations for the multiple allocation hub interdiction and hub protection problems, which are bilevel and trilevel mixed integer linear programs, respectively. In the hub interdiction problem, the aim is to identify a subset of r critical hubs from an existing set of p hubs that when interdicted results in the maximum post-interdiction cost of routing flows. We present two alternate ways of reducing the bilevel hub interdiction model to a single level optimization problem. The first approach uses the dual formulation of the lower level problem. The second approach exploits the structure of the lower level problem to replace it by a set of closest assignment constraints (CACs). We present alternate sets of CACs, study their dominance relationships, and report their computational performances. Further, we propose refinements to CACs that offer computational advantages of an order-of-magnitude compared to the one existing in the literature. Further, our proposed modifications offer structural advantages for Benders decomposition, which lead to substantial computational savings, particularly for large problem instances. Finally, we study and solve large scale instances of the trilevel hub protection problem exactly by utilizing the ideas developed for the hub interdiction problem