Continuous trees: A quadrature technique for modeling sequential decision problems with dependent, continuous variables

A quadrature technique to evaluate models for sequential decision problems with continuous random variables and probabilistic dependence is presented. This technique, called the "Continuous Tree" algorithm, models a large decision problem as a combination of several small problems by taking advantage of the probabilistic independence that exists in the original problem. Because the algorithm is able to exploit computational efficiencies resulting from probabilistic independence, the required solution time often only grows polynomially with the number of variables in the model. This growth is in contrast to the traditional "rollback" solution method where the solution time grows exponentially with the number of variables. Hence, it is possible to analyze much larger models with the "Continuous Tree" algorithm than is practical with the rollback method.; This algorithm models uncertainties with mixtures of 4-parameter probability distributions. This algorithm uses quadrature to estimate distributions for functions of random variables. Probabilistic dependence is modeled with curve-fit tables.; An operations management application of the "Continuous Tree" algorithm, a dual source selection problem under scheduling uncertainty, is presented. The time complexity, the accuracy, and methods to verify accuracy of this algorithm are presented. A closed form solution for a 3-point discrete approximation that matches the first four central moments of a probability distribution is derived. The accuracy of this 4-moment matching approximation is compared to traditional discrete approximation techniques.