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- Warren B Powell
- 2009

The first step in solving a stochastic optimization problem is providing a mathematical model. How the problem is modeled can impact the solution strategy. In this chapter, we provide a flexible modeling framework that uses a classic control-theoretic framework, avoiding devices such as one-step transition matrices. We describe the five fundamental elements… (More)

In a sequential Bayesian ranking and selection problem with independent normal populations and common known variance, we study a previously introduced measurement policy which we refer to as the knowledge-gradient policy. This policy myopically maximizes the expected increment in the value of information in each time period, where the value is measured… (More)

We consider a Bayesian ranking and selection problem with independent normal rewards and a correlated multivariate normal belief on the mean values of these rewards. Because this formulation of the ranking and selection problem models dependence between alternatives' mean values, algorithms may utilize this dependence to perform efficiently even when the… (More)

We consider a class of problems of scheduling n jobs on m identical, uniform, or unrelated parallel machines with an objective of minimizing an additive criterion. We propose a decomposition approach for solving these problems exactly. The decomposition approach rst formulates these problems as an integer program, and then reformulates the integer program,… (More)

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new class of methods for nonparametric regression. Given a data set of input-response pairs, the DP-GLM produces a global model of the joint distribution through a mixture of local generalized linear models. DP-GLMs allow both continuous and categorical inputs, and can model the… (More)

I n a companion paper (Godfrey and Powell 2002) we introduced an adaptive dynamic programming algorithm for stochastic dynamic resource allocation problems, which arise in the context of logistics and distribution, fleet management, and other allocation problems. The method depends on estimating separable nonlinear approximations of value functions, using a… (More)

- Warren B Powell
- 2002

We address the problem of modeling long-term energy policy and investment decisions while retaining the important ability to capture fine-grained variations in intermittent energy and demand, as well as storage. In addition, we wish to capture sources of uncertainty such as future energy policies, climate, and technological advances, in addition to the… (More)

I n this paper, we consider a stochastic and time-dependent version of the min-cost integer multicommodity-flow problem that arises in the dynamic resource allocation context. In this problem class, tasks arriving over time have to be covered by a set of indivisible and reusable resources of different types. The assignment of a resource to a task removes… (More)