Dynamic planning under uncertainty for theater airlift operations

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007.Includes bibliographical references (p. 92-93).In this thesis, we analyze intratheater airlift operations, and propose methods to improve the planning process. The United States Air Mobility Command is responsible for the air component of the world wide U.S. military logistics network. Due to the current conflict in Iraq, a small cell within Air Mobility Command, known as Theater Direct Delivery, is responsible for supporting ongoing operations by assisting with intratheater airlift. We develop a mathematical programming approach to schedule airlift missions that pick up and deliver prioritized cargo within time windows. In our approach, we employ composite variables to represent entire missions and associated decisions, with each decision variable including information pertaining to the mission routing and scheduling, and assigned aircraft and cargo. We compare our optimization-based approach to one using a greedy heuristic that is representative of the current planning process. Using measures of efficiency and effectiveness, we evaluate and compare the performance of these different approaches. Finally, we adjust selected parameters of our model and measure the resulting changes in operating performance of our solutions, and the required computational effort to generate the solutions.by Kiel M. Martin.S.M

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Fuel Efficiency Assessment with DEA

In this study, Data Envelopment Analysis (DEA) is used to calculate Air Mobility Command (AMC) airlift fuel efficiency for C-17 aircraft. Fuel is a strategic asset for the United States Air Force and suitable alternatives are not yet feasible or available in the quantity required. The Air Force is pursuing several initiatives to conserve energy and operate more efficiently while sustaining the same level of effectiveness and safety. In order to manage these initiatives, it must measure how well it is doing. To measure airlift efficiency, the AMC Fuel Efficiency Office established a 7 factor weighted Fuel Efficiency Index (FEI). To produce a monthly score, AMC assigned weights for each factor. DEA does not require such a priori assumptions and finds the best set of weights that will help each mission to represent itself in the best manner. The results showed that DEA and FEI agree in trends but a DEA Slack-Based Measure better differentiates inefficiencies than other methods used in the study. Also, the results showed that for current Air Mobility flights, at least 10% input excess or output shortfall occurs each month

Parallel algorithms for two-stage stochastic optimization

We develop scalable algorithms for two-stage stochastic program optimizations. We propose performance optimizations such as cut-window mechanism in Stage 1 and scenario clustering in Stage 2 of benders method for solving two-stage stochastic programs. A naive implementation of benders method has slow convergence rate and does not scale well to large number of processors especially when the problem size is large and/or there are integer variables in Stage 1. Parallelization of stochastic integer programs pose very unique characteristics that make them very challenging to parallelize. We develop a Parallel Stochastic Integer Program Solver (PSIPS) that exploits nested parallelism by exploring the branch-and-bound tree vertices in parallel along with scenario parallelization. PSIPS has been shown to have high parallel efficiency of greater than 40% at 120 cores which is significantly greater than the parallel efficiency of state-of-the-art mixed-integer program solvers. A significant portion of the time in this branch-and-bound solver is spent in optimizing the stochastic linear program at the root vertex. Stochastic linear programs at other vertices of the branch-and-bound tree take very less iterations to converge because they can inherit benders cut from their parent vertices and/or the root. Therefore, it is important to reduce the optimization time of the stochastic linear program at the root vertex. We propose two decomposition schemes namely the Split-and-Merge (SAM) method and the Lagrangian Decomposition and Merge (LDAM) method that significantly increase the convergence rate of benders decomposition. SAM method gives up to 64% reduction in solution time while also giving significantly higher parallel speedups as compared to the naive benders method. LDAM method, on the other hand, has made it possible to solve otherwise intractable stochastic programs. We further provide a computational engine for many real-time and dynamic problems faced by US Air Mobility Command. We first propose a stochastic programming solution to the military aircraft allocation problem with consideration for disaster management. Then, we study US AMC's dynamic mission re-planning problem and propose a mathematical formulation that is computationally feasible and leads to significant savings in cost as compared to myopic and deterministic optimization. It is expected that this work will provide the springboard for more robust problem solving with HPC in many logistics and planning problems