Oleg A. Prokopyev We introduce a generalized value function of a mixed-integer program, which is simultaneously parameterized by its objective and right-hand side. We describe its fundamental properties, which we exploit through three algorithms to calculate it. We then show how this generalized value function can be used to reformulate two classes of mixed-integer optimization problems: two-stage stochastic … Read more
Multistage stochastic mixed-integer programming is a powerful modeling paradigm appropriate for many problems involving a sequence of discrete decisions under uncertainty; however, they are difficult to solve without exploiting special structures. We present scenario-tree decomposition to establish bounds for unstructured multistage stochastic mixed-integer programs. Our method decomposes the scenario tree into a number of smaller … Read more
We consider two-stage quadratic integer programs with stochastic right-hand sides, and present an equivalent reformulation using value functions. We fi rst derive some basic properties of value functions of quadratic integer programs. We then propose a two-phase solution approach. The first phase constructs the value functions of quadratic integer programs in both stages. The second phase … Read more
Virtual private networks (VPN) are often used to distribute live content, such as video or audio streams, from a single source to a large number of destinations. Streaming caches or splitters are deployed in these multicast networks to allow content distribution without overloading the network. In this paper, we consider two combinatorial optimization problems that … Read more