Summary. We introduce a general formulation for dimension reduction and coefficient estimation in the multivariate linear model. We argue that many of the existing methods that are commonly used in practice can be formulated in this framework and have various restrictions. We continue to propose a new method that is more flexible and more generally applicable. The method proposed can be formulated as a novel penalized least squares estimate. The penalty that we employ is the coefficient matrix's Ky Fan norm. Such a penalty encourages the sparsity among singular values and at the same time gives shrinkage coefficient estimates and thus conducts dimension reduction and coefficient estimation simultaneously in the multivariate linear model. We also propose a generalized cross-validation type of criterion for the selection of the tuning parameter in the penalized least squares. Simulations and an application in financial econometrics demonstrate competitive performance of the new method. An extension to the non-parametric factor model is also discussed.

B ased on the recent incidents of H5N1, H1N1, and influenza pandemics in history (1918, 1957, and 1968) experts believe that a future influenza pandemic is inevitable and likely imminent. Although the severity of influenza pandemics vary, evidence suggests that an efficient and rapid response is crucial for mitigating morbidity, mortality, and costs to society. Hence, preparing for a potential influenza pandemic is a high priority of governments at all levels (local, state, federal), nongovernmental organizations (NGOs), and companies. In a severe pandemic, when a large number of people are ill, infected persons and their families may have difficulty purchasing and preparing meals. Various government agencies and NGOs plan to provide meals to these households. In this paper, in collaboration with the American Red Cross, we study food distribution planning during an influenza pandemic. We develop a disease spread model to estimate the spread pattern of the disease geographically and over time, combine it with a facility location and resource allocation network model for food distribution, and develop heuristics to find near-optimal solutions for large instances. We run our combined disease spread and facility location model for the state of Georgia and present the estimated number of infections and the number of meals needed in each census tract for a one-year period along with a design of the supply chain network. Moreover, we investigate the impact of voluntary quarantine on the food demand and the food distribution network and show that its effects on food distribution can be significant. Our results could help decision makers prepare for a pandemic, including how to allocate limited resources and respond dynamically.

Abstract:In this article, we define a scheduling/packing problem called the Job Splitting Problem, motivated by the practices in the printing industry. There are n types of items to be produced on an m-slot machine. A particular assignment of the types to the slots is called a "run" configuration and requires a setup cost. Once a run begins, the production continues according to that configuration and the "length" of the run represents the quantity produced in each slot during that run. For each unit of production in excess of demand, there is a waste cost. Our goal is to construct a production plan, i.e., a set of runs, such that the total setup and waste cost is minimized. We show that the problem is strongly NP-hard and propose two integer programming formulations, several preprocessing steps, and two heuristics. We also provide a worst-case bound for one of the heuristics. Extensive tests on real-world and randomly generated instances show that the heuristics are both fast and effective, finding near-optimal solutions.

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Recent incidents of avian flu (H5N1) in Asia and the pandemic influenza cases in history (1918, 1957 and 1968) suggest that a future pandemic influenza is inevitable and likely imminent. Governments and non-governmental organizations prepare response plans on how to react to a pandemic influenza. In this paper, we study the logistics side of the problem, specifically, food distribution logistics during the pandemic influenza. For this purpose, we develop a disease spread model that assists in estimating the food need geographically at a given time. Then, we develop an integrated solution approach called the Dynamic Update Approach to build the food distribution network. We run our integrated disease spread and facility location model for the state of Georgia and present the estimated number of infections and meals needed in each census tract for a one year period.