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A stochastic program SP with solution value z * can be approximately solved by sampling n realizations of the program's stochastic parameters, and by solving the resulting " approximating problem " for (x * n ; z * n). We show that, in expectation, z * n is a lower bound on z * and that this bound monotonically improves as n increases. The ÿrst result is… (More)

We study the problem of interdicting the arcs in a network in order to maximize the shortest s–t path length. " Interdiction " is an attack on an arc that destroys the arc or increases its effective length; there is a limited inter-diction budget. We formulate this bilevel, max–min problem as a mixed-integer program (MIP), which can be solved directly, but… (More)

The constrained shortest-path problem (CSPP) generalizes the standard shortest-path problem by adding one or more path-weight side constraints. We present a new algorithm for CSPP that Lagrangianizes those constraints, optimizes the resulting Lagrangian function , identifies a feasible solution, and then closes any optimality gap by enumerating… (More)

We apply new bilevel and trilevel optimization models to make critical infrastructure more resilient against terrorist attacks. Each model features an intelligent attacker (terrorists) and a defender (us), information transparency, and sequential actions by attacker and defender. We illustrate with examples of the US Strategic Petroleum Reserve, the US… (More)

Let G = (V,E) be an undirected graph whose edges may fail, and let G, denote G with a set K V specified. Edge failures are assumed to be statistically independent and to have known probabilities. The K-terminal reliability of G,, denoted R(G,), is the probability that all vertices in K are connected by working edges. Computing K-terminal reliability is an… (More)

We describe JOINT DEFENDER, a new two-sided optimization model for planning the pre-positioning of defensive missile interceptors to counter an attack threat. In our basic model, a defender prepositions ballistic missile defense platforms to minimize the worst-case damage an attacker can achieve; we assume that the attacker will be aware of defensive… (More)

A " proliferator " seeks to complete a first small batch of fission weapons as quickly as possible, whereas an " interdictor " wishes to delay that completion for as long as possible. We develop and solve a max-min model that identifies resource-limited interdiction actions that maximally delay completion time of the proliferator's weapons project, given… (More)

W e describe a new algorithm for computing the efficient frontier of the " bi-objective maximum-flow network-interdiction problem. " In this problem, an " interdictor " seeks to interdict (destroy) a set of arcs in a capacitated network that are Pareto-optimal with respect to two objectives, minimizing total interdiction cost and minimizing maximum flow.… (More)

We consider the problem of bounding the expected value of a linear program (LP) containing random coeecients, with applications to solving two-stage stochastic programs. An upper bound for minimizations is derived from a restriction of an equivalent, penalty-based formulation of the primal stochastic LP, and a lower bound is obtained from a restriction of a… (More)

We develop a factoring (partitioning) algorithm for enumerating near-minimum-weight s-t cuts in directed and undirected graphs, with application to network interdiction. " Near-minimum " means within a factor of 1+6 of the minimum for some 6 ≥ 0. The algorithm requires only polynomial work per cut enumerated provided that 6 is sufficiently (not trivially)… (More)