a b s t r a c tDetermining the locations of facilities for prepositioning supplies to be used during a disaster is a strategic decision that directly affects the success of disaster response operations. Locating such facilities close to the disaster-prone areas is of utmost importance to minimize response time. However, this is also risky because the facility may be disrupted and hence may not support the demand point(s). In this study, we develop an optimization model that minimizes the risk that a demand point may be exposed to because it is not supported by the located facilities. The purpose is to choose the locations such that a reliable facility network to support the demand points is constructed. The risk for a demand point is calculated as the multiplication of the (probability of the) threat (e.g., earthquake), the vulnerability of the demand point (the probability that it is not supported by the facilities), and consequence (value or possible loss at the demand point due to threat). The vulnerability of a demand point is computed by using fault tree analysis and incorporated into the optimization model innovatively. To our knowledge, this paper is the first to use such an approach. The resulting non-linear integer program is linearized and solved as a linear integer program. The locations produced by the proposed model are compared to those produced by the p-center model with respect to risk value, coverage distance, and covered population by using several test problems. The model is also applied in a real problem. The results indicate that taking the risk into account explicitly may create significant differences in the risk levels.

a b s t r a c tThis paper defines and studies the multi-terminal maximum-flow network-interdiction problem (MTNIP) in which a network user attempts to maximize flow in a network among K P 3 pre-specified node groups while an interdictor uses limited resources to interdict network arcs to minimize this maximum flow. The paper proposes an exact (MTNIP-E) and an approximating model (MPNIM) to solve this NP-hard problem and presents computational results to compare the models. MTNIP-E is obtained by first formulating MTNIP as bi-level min-max program and then converting it into a mixed integer program where the flow is explicitly minimized. MPNIM is binary-integer program that does not minimize the flow directly. It partitions the node set into disjoint subsets such that each node group is in a different subset and minimizes the sum of the arc capacities crossing between different subsets. Computational results show that MPNIM can solve all instances in a few seconds while MTNIP-E cannot solve about one third of the problems in 24 hour. The optimal objective function values of both models are equal to each other for some problems while they differ from each other as much as 46.2% in the worst case. However, when the postinterdiction flow capacity incurred by the solution of MPNIM is computed and compared to the objective value of MTNIP-E, the largest difference is only 7.90% implying that MPNIM may be a very good approximation to MTNIP-E.

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We study the deployment planning problem (DPP) that may roughly be defined as the problem of the planning of the physical movement of military units, stationed at geographically dispersed locations, from their home bases to their designated destinations while obeying constraints on scheduling and routing issues as well as on the availability and use of various types of transportation assets that operate on a multimodal transportation network. The DPP is a large-scale real-world problem for which analytical models do not exist. We propose a model for solving the problem and develop a solution methodology which involves an effective use of relaxation and restriction that significantly speeds up a CPLEX-based branch-and-bound. The solution times for intermediate-sized problems are around 1 h at maximum, whereas it takes about a week in the Turkish Armed Forces to produce a suboptimal feasible solution based on trial-and-error methods. The proposed model can be used to evaluate and assess investment decisions in transportation infrastructure and transportation assets as well as to plan and execute cost-effective deployment operations at different levels of planning.

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