Traffic management during an evacuation and the decision of where to locate the shelters are of critical importance to the performance of an evacuation plan. From the evacuation management authority's point of view, the desirable goal is to minimize the total evacuation time by computing a system optimum (SO). However, evacuees may not be willing to take long routes enforced on them by a SO solution; but they may consent to taking routes with lengths not longer than the shortest path to the nearest shelter site by more than a tolerable factor. We develop a model that optimally locates shelters and assigns evacuees to the nearest shelter sites by assigning them to shortest paths, shortest and nearest with a given degree of tolerance, so that the total evacuation time is minimized. As the travel time on a road segment is often modeled as a nonlinear function of the flow on the segment, the resulting model is a nonlinear mixed integer programming model. We develop a solution method that can handle practical size problems using second order cone programming techniques. Using our model, we investigate the importance of the number and locations of shelter sites and the trade-off between efficiency and fairness. © 2014 Elsevier Ltd

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We study the computational aspects of the single-assignment p-hub center problem on the basis of a basic model and a new model. The new model's performance is substantially better in CPU time than dierent linearizations of the basic model. We also prove the NP-Hardness of the problem. Ó 2000 Elsevier Science B.V. All rights reserved.Keywords: Hub location; Modeling; Complexity Hub location problems arise when it is desirable to consolidate and disseminate¯ows at certain centralized locations called hubs. Typical applications arise in airline passenger travel (Toh and Higgins, 1985), cargo delivery (Kuby and Gray, 1993), and message delivery in computer communication networks (Klincewicz, 1998).The existing studies in the literature on hub location have almost exclusively focused on the p-hub median problem which involves the minimization of the total cost. The case with p 1Y 2 is posed by O'Kelly (1986) and the case for general p is formulated as a quadratic binary program by O'Kelly (1987). Dierent linearizations of the basic model of O'Kelly (1987) are investigated by Aykin (1995), Campbell (1994), Campbell (1996, Krishnamoorthy (1996, 1998), Skorin-Kapov et al. (1996).Our focus in this paper is on the minimax criterion which is essentially unstudied in the literature. The minimax criterion is traditionally used in location applications to minimize the adverse effects of worst case scenarios in providing emergency service. In hub location, even though emergency service protection does not seem to be an issue, the minimax criterion is still important from the viewpoint of minimizing the maximum dissatisfaction of passengers in air travel and minimizing the worst case delivery time in cargo delivery systems. The latter case is particularly important for delivery of perishable or time sensitive items.The literature on hub location under the minimax criterion is restricted to two papers. The

In this paper, we concentrate on the service structure of ground-transportation based cargo delivery companies. The transient times that arise from nonsimultaneous arrivals at hubs (typically spent for unloading, loading, and sorting operations) can constitute a significant portion of the total delivery time for cargo delivery systems. The latest arrival hub location problem is a new minimax model that focuses on the minimization of the arrival time of the last item to arrive, taking into account journey times as well as the transient times at hubs. We first focus on a typical cargo delivery firm operating in Turkey and observe that stopovers are essential components of a ground-based cargo delivery system. The existing formulations of the hub location problem in the literature do not allow stopovers since they assume direct connections between demand centers and hubs. In this paper, we propose a generic mathematical model, which allows stopovers for the latest arrival hub location problem. We improve the model using valid inequalities and lifting. We present computational results using data from the US and Turkey.

The traditionally studied hub location problems in the literature pay attention to flight times but not to transient times spent at hubs for unloading, loading, and sorting operations. The transient times may constitute a significant portion of the total delivery time for cargo delivery systems. We focus on the minimization of the arrival time of the last arrived item in cargo delivery systems and develop a model that correctly computes the arrival times by taking into account both the flight times and the transient times. Nonlinear and linear integer formulations are given and computational results are provided. The effects of delays on the system performance are analyzed.Hub Location, Minimax, Latest Arrival