We describe a multi-period optimization model, implemented in GAMS, to help the U.S. Air Force improve logistical efficiency. It determines the maximum on-time throughput of cargo and passengers that can be transported with a given aircraft fleet over a given network, subject to appropriate physical and policy constraints. The model can be used to help answer questions about selecting airlift assets and about investing or divesting in airfield infrastructure.

Topics: DTIC Archive, Morton, David P., NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OPERATIONS RESEARCH,...

We consider an integer stochastic knapsack problem (SKP) where the weight of each item is deterministic, but the vector of returns for the items is random with known distribution. The objective is to maximize the probability that a total return threshold is met or exceeded. We study several solution approaches. Exact procedures, based on dynamic programming (DP) and integer programming (IP), are developed for returns that are independent normal random variables with integral means and...

Topics: DTIC Archive, Morton, David P, TEXAS UNIV AT AUSTIN, *STOCHASTIC PROCESSES, *PROBLEM SOLVING,...

Decomposition and Monte Carlo sampling-based algorithms hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. In this paper, we develop a stopping rule theory for a class of algorithms that estimate bounds on the optimal objective function value by sampling. We provide rules for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence...

Topics: DTIC Archive, Morton, David P, NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OPERATIONS RESEARCH,...

Handling uncertainty in natural inflow is an important part of a hydroelectric scheduling model. In a stochastic programming formulation, natural inflow may be modeled as a random vector with known distribution, but the size of the resulting mathematical program can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We develop an enhanced Benders decomposition algorithm for solving multistage stochastic linear...

Topics: DTIC Archive, Morton, David P, NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OPERATIONS RESEARCH,...

This article considers the problem of bounding the expected value of a linear program (LP) containing random coefficients, 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 reformulation of the dual. These restricted-recourse bounds are more general and more easily computed than most other bounds...

Topics: DTIC Archive, Morton, David P, NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OPERATIONS RESEARCH,...