bv_cvxbook_extra_exercises

Assuming the cost is mostly fuel cost convexity of i

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Unformatted text preview: ability that the smuggler makes it to the destination node undetected is j ∈P pj , where P ⊂ {1, . . . , m} is (the set of edges on) the smuggler’s path. We assume that the smuggler knows the detection failure probabilities and will take a path that maximizes the probability of making it to the destination node undetected. We let P max denote this maximum probability (over paths). (Note that this is a function of the edge detection failure probabilities.) The edge detection failure probability on an edge depends on how much interdiction resources are allocated to the edge. Here we will use a very simple model, with xj ∈ R+ denoting the effort (say, yearly budget) allocated to edge j , with associated detection failure probability pj = e−aj xj , where aj ∈ R++ are given. The constraints on x are a maximum for each edge, x xmax , and a total T x ≤ B. budget constraint, 1 (a) Explain how to solve the problem of choosing the interdiction effort vector x ∈ Rm , subject to the constraints, so as to minimize P max . Partial credit wi...
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