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We develop a sequential sampling procedure for a class of stochastic programs. We assume that a sequence of feasible solutions with an optimal limit point is given as input to our procedure. Such a sequence can be generated by solving a series of sampling problems with increasing sample size, or it can be found by any other viable method. Our procedure… (More)

Determining whether a solution is of high quality (optimal or near optimal) is fundamental in optimization theory and algorithms. In this paper, we develop Monte Carlo sampling-based procedures for assessing solution quality in stochastic programs. Quality is defined via the optimality gap and our procedures' output is a confidence interval on this gap. We… (More)

Given the natural variability and uncertainties in long-term predictions, reliability is a critical design factor for water supply systems. However, the large scale of the problem and the correlated nature of the involved uncertainties result in models that are often intractable. In this paper, we consider a municipal water supply system over a 15-year… (More)

The goal of this panel was to discuss the state of the art in simulation optimization research and practice. The participants included representation from both academia and industry, where the latter was represented by participation from a leading software provider of optimization tools for simulation. This paper begins with a short introduction to… (More)

T he disjunctive decomposition (D 2) algorithm has emerged as a powerful tool to solve stochastic integer programs. In this paper, we consider two-stage stochastic integer programs with binary first-stage and mixed-binary second-stage decisions and present several computational enhancements to D 2. First, we explore the use of a cut generation problem… (More)

We develop an algorithm for two-stage stochastic programming with a convex second stage program and with uncertainty in the right-hand side. The algorithm draws on techniques from bounding and approximation methods as well as sampling-based approaches. In particular, we sequentially refine a partition of the support of the random vector and, through… (More)

Keywords: Reclaimed water distribution system Stochastic optimization Demand and network growth uncertainty Water resources management a b s t r a c t A significantdbut underutilizeddwater resource is reclaimed water, i.e., treated wastewater that is reintroduced for various purposes. Especially in water scarce regions, reclaimed water is often the only… (More)

We develop a sequential sampling procedure for solving a class of stochastic programs. A sequence of feasible solutions, with at least one optimal limit point, is given as input to our procedure. Our procedure estimates the optimality gap of a candidate solution from this sequence, and if that point estimate is sufficiently small then we stop. Otherwise, we… (More)

Monte Carlo sampling-based methods are frequently used in stochastic programming when exact solution is not possible. A critical component of Monte Carlo sampling-based methods is determining when to stop sampling to ensure the desired quality of the solutions. In this paper, we develop stopping rules for sequential sampling procedures that depend on the… (More)

Monte Carlo sampling-based estimators of optimality gaps for stochastic programs are known to be biased. When bias is a prominent factor, estimates of optimality gaps tend to be large on average even for high-quality solutions. This diminishes our ability to recognize high-quality solutions. In this paper, we present a method for reducing the bias of the… (More)