HUB LOCATION-ROUTING problem is a practical subject in the last decades. This study considers a many-to-many HUB LOCATION-ROUTING problem where the best locations of HUBs and tours for each HUB are determined with simultaneous pickup and delivery. First, an optimization model is proposed to minimize the total sum of fixed costs of locating HUBs, the costs of handling, traveling, assigning, and transportation costs. To find practical solutions, the HUBs have constrained capacity, in which single allocations can service every node to the HUBs. What is more, the balancing requisites are imposed on the network by allocating the appropriate number of demand nodes to the HUBs. Then the problem is solved using GAMS software for small-size instances of the problem. Due to the NP-hard nature of the problem, the proposed optimization model is solved by the Genetic Algorithm (GA) and Imperialist Competitive Algorithm (ICA). For the problem instances, the comparative results indicate that GA has a better performance compared to ICA, and incorporating capacity and balancing considerations can influence the reduction of costs of the investigated network.

In a HUB location problem network, the flow originated from an origin and shipped to a destination via some selected intermediate nodes called HUB nodes since using a discount factor of HUBs. The HUB nodes are fully interconnected in the traditional HUB location problem. In any origin-destination path there exists at least one HUB element. Rather than directly connecting any pair of locations, all the paths are handled by the HUB node. In this paper, a general configuration of HUB location problems is considered. The model is presented for HUB LOCATION-ROUTING problem which any network topology can be structured. This model application is in the public transportation, telecommunication systems and financial networks. Incomplete HUB network is designed in the model. Furthermore, location and routing decisions are considered simultaneously in the model besides multiple allocation strategy. Moreover, non-HUB nodes can be connected directly. Objective function of this model minimizes transshipment cost of flows and cost of constructing the network. Family of valid inequalities and some preprocessing are proposed to strengthening the model linear relaxation lower bound and improving solution time. Computational results over test problems driven from the literature show that using all valid inequalities and preprocessing perform better than using each of them separately and solve the model in a reasonable solution time.

Efficient flow management is critical in transportation and logistics, with HUB networks playing a key role in optimizing these processes. The HUB arc location problem has recently emerged as a new framework that emphasizes HUB arcs while allowing for isolated HUBs. This paper extends the HUB arc location problem by incorporating set-up costs into the optimization model. A heuristic algorithm is developed to enhance HUB network design, considering both the flow of goods and the associated HUB set-up costs. Additionally, a detailed sensitivity analysis is conducted to assess the impact of strategic adjustments on optimization outcomes. By reducing the discount factor for inter-HUB flows and increasing the number of exogenous HUB arcs, significant improvements in route optimization and cost reduction are achieved. This research challenges traditional approaches to HUB network design and opens the door for further exploration of the dynamics within HUB networks. A deeper understanding of these networks can lead to more efficient and resource-optimized transportation systems, potentially transforming flow management into a more cost-effective and sustainable process.

The HUB location problem (HLP) is one of the most important and widely used issues in telecommunication and transportation (freight and passenger) network design. HUB location problem deals with locating the HUB facilities in the network and determine the pattern based on the non-HUB nodes assignment to each HUB so that a specific objective function is optimized. HUBs are intermediate facilities that perform a set of tasks such as consolidation, break-bulk, sorting, etc. In other words, the traffic flows (cargo, passengers, or data) in the network rather than being sent directly from their origins to their destinations, are routed via these intermediate facilities. Established HUBs in these networks can be disrupted because of events and natural disasters or deliberate disturbances during their use and in such a case an enormous cost is imposed on the operating companies. Therefore, it is crucial to have a suitable plan for reducing destructive effects of disrupted HUBs in the network. In this study, an uncapacitated single allocation HUB location problem under HUB disruption is considered. It is assumed that every open HUB in the network can fail and become unavailable after installation, in which case, the customers originally assigned to that HUB, are either reassigned to other operational HUBs or they do not receive service for which a penalty must be paid. The problem has been modeled as a two-stage stochastic program in which the decisions on HUB locations are made in the first phase. In second phase when disruption scenario has occurred, the allocation of non-HUB nodes to HUBs takes place in second phase with regard to the operational HUBs. A hybrid metaheuristic algorithm based on the adaptive large neighborhood search (ALNS) and simulated annealing (SA) is proposed for solving it. Extensive computational experiments based on the CAB and TR data sets are conducted. Results show the high efficiency of the proposed solution method.

European Corn Borer Ostrinia nubilalis HUB. Sub sp. Persica (Lep.: Pyralidae) is known as a polyphagous insect, cause injury to corn, cotton, rice, poplar nursery and etc. Products of Bacillus thuringiensis, strains Kurstaki and Thuringiensis were evaluated on the host larval instars using spores and crystals. Bioassay was carried out the first larval star of the pest reared on different concentrations of strains added to the artificial diet. Seventy two hours after rearing, dead larvae were counted and lethal concentration to get 50 percent mortality in population (Lc50) was determined and compared with commercial product, Dipd. Results indicated that B. thuringiensis var. Kurstaki (Lc50= 420.2 ppm) like Dipe (Lc50= 414.2 ppm) were more effective than B. thuringiensis var. Thuringiensis (Lc50 = 3892.72 ppm). The second bioassay was done to determine the effective time to get lethal dose of B. thuringiensis by second larval instar of the host which reared on artificial diet, containing 2000 ppm of spores and crystals of Kurstaki strain. The mortality rate was estimated 17.2%, 50% and 82% after 2, 10.8 and 72 hours, respectively. The third bioassay was carried out to verify susceptibility of larval stages when they reared on 500 ppm of B. thuringiensis var. Kurstaki. Results indicated that the first larval instar was significantly more susceptible than third instar. The fifth instar was less susceptible compare to other instars at (a=5%).

This paper presents the hierarchical cycle HUB location problem. This new problem is an extension of the cycle HUB location problem (CHLP). It is a three-layered HUB network problem where the top level consists of a cycle network connecting the so-called central HUBs and the second and third level are unions of star networks connecting the intermediate HUBs to central HUBs and the demand centers to intermediate and central HUBs, respectively. The problem is to decide on the locations of a predetermined number of intermediate and central HUBs and the connections in order to minimize the total routing cost in the resulting network. We also propose two mixed integer linear programming formulations for the problem. The behavior of the proposed models, in terms of solution time, is evaluated on the basis of an extensive computational study on Turkish pastal network dataset. The results achieved by CPLEX and Xpress solvers, based on the proposed MILP formulation, are compared to each other. We have also reduced the time to solve the problem by changing the parameters of the solver.

The optimal locating of facilities has large effects on economic benefits, providing satisfactory service and levels of customer satisfaction. The decision of facilities location mostly is a long-term and strategic decision of the large private and public companies and reliability is important to make this strategic decision so that the system continues to operate with the least damage in case of stop working or failure of one of the components. This paper at the first time 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, while there is the possibility of direct connection between non-HUB nodes. Due to the NP hard nature of the model, genetic algorithm is use in order to solve the defined problem and the numerical results illustrate the genetic algorithm has better performance than the GAMS in terms of speed, it also shows great quality answers. The results of the sensitivity analysis show that considering the protection approach has reduced the total cost.