Output analysis for approximated stochastic programs

Because of incomplete information and also for the sake of numerical tractability one mostly solves an approximated stochastic program instead of the underlying ''true'' decision problem. However, without an additional analysis, the obtained output (the optimal value and optimal solutions of the approximated stochastic program) should not be used to replace the sought solution of the ''true'' problem. Methods of output analysis have to be tailored to the structure of the problem and they should also reflect the source, character and precision of the input data. The scope of various approaches based on results of asymptotic and robust statistics, of the moment problem and on general results of parametric programming will be discussed from the point of view of their applicability and possible extensions

Improved stochastic optimization of railway timetables

We present a general model to find the best allocation of a limited amount of supplements (extra minutes added to a timetable in order to reduce delays) on a set of interfering railway lines. By the best allocation, we mean the solution under which the weighted sum of expected delays is minimal. Our aim is to finely adjust an already existing and well-functioning timetable. We model this inherently stochastic optimization problem by using two-stage recourse models from stochastic programming, building upon earlier research from the literature. We present an improved formulation, allowing for an efficient solution using a standard algorithm for recourse models. We show that our model may be solved using any of the following theoretical frameworks: linear programming, stochastic programming and convex non-linear programming, and present a comparison of these approaches based on a real-life case study. Finally, we introduce stochastic dependency into the model, and present a statistical technique to estimate the model parameters from empirical data

Optimization models for resource allocation under perturbation.

Optimization Models for Resource allocation are investing in how to make the best use of available but limited resources in order to achieve the best results. In strategic planning, resource allocation is a plan for using available resources, especially in the near future, to achieve the goals of the future. It is a process of allocating resources during the entire planning horizon and among the various units. Resource allocation plans can be decided by using mathematical programming. In this dissertation, the research has been focused on how to allocate resources in the uncertain environment. The mathematical programming formulations for the resource allocation model under severe uncertainty will be studied. In particular, we will focus on solving the stability issues of the traditional probabilistic model. We propose an approach consisting of solving a sequence of convex robust optimization models with unknown-but-bounded random variables along with the stochastic programming to pursue the allocation performance for the expected overall objective value. Our theoretical results show that the proposed approach can always obtain an equivalent or a better expected revenue with the corresponding allocation, while significantly reducing the risk under perturbations. Although this method requires solving two convex mathematical programming models, both models are solved within a timely manner thanks to their convex model instances and with effective, and less, computationally demanding algorithms. With the increasing threats from public health emergencies, such as earthquakes, tornados, pandemic flus, or terrorist attacks, high attention has been paid to the public health response to a pandemic from federal to national level, together with local health departments, and the health-care community. Various organizations cooperate with each other to strengthen the preparedness for the pandemic and disastrous emergencies, thus to improve the public health. The Strategic National Stockpile (SNS) is maintained by the Centers for Disease Control and Prevention (CDC) and the U.S. Department of Health and Human Services (DHHS) for the United States in the event of a shortage of local medical resources or other unanticipated supply problems. The SNS is the United States’ national repository of antibiotics, vaccines, chemical antidotes, antitoxins, and other critical medical equipment and supplies. It has the capability to supplement or re-supply local health authorities with necessary materials for relief action within the response time in as little as 12 hours. The pilot study is done with the support of Kentucky SNS to determine the capacity allocation plan for each county in order to maximize the health benefit under various uncertainties, which can never be accurately estimated. We thereby employ a heuristic method named “resource reservation” to suggest the resource allocation plan for Kentucky SNS