We present a column-generation model and branch-and-price-and-cut algorithm for origin-destination integer multicommodity flow problems. The origin-destination integer multicommodity flow problem is a constrained version of the linear multicommodity flow problem in which flow of a commodity (defined in this case by an origin-destination pair) may use only one path from origin to destination. Branch-and-price-and-cut is a variant of branch-and-bound, with bounds provided by solving linear programs using column-and-cut generation at nodes of the branch-and-bound tree. Because our model contains one variable for each origindestination path, for every commodity, the linear programming relaxations at nodes of the branch-and-bound tree are solved using column generation, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality. We devise a new branching rule that allows columns to be generated efficiently at each node of the branch-and-bound tree. Then, we describe cuts (cover inequalities) that can be generated at each node of the branch-and-bound tree. These cuts help to strengthen the linear programming relaxation and to mitigate the effects of problem symmetry. We detail the implementation of our combined columnand-cut generation method and present computational results for a set of test problems arising from telecommunications applications. We illustrate the value of our branching rule when used to find a heuristic solution and compare branch-and-price and branch-and-price-and-cut methods to find optimal solutions for highly capacitated problems.

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• Annual total direct and indirect costs related to infections with the hepatitis C virus (HCV) in the United States were estimated at $5.46 billion in 1997. Davis et al. (2011) estimated that all-cause health care costs for managed care organization (MCO) enrollees with HCV were $20,961 per patient per year (PPPY), of which $6,864 PPPY was HCV-related, from 2002 through 2006.• The burden of illness for HCV is predicted to grow over the next 2 decades, partly due to increased prevalence of advanced liver disease (AdvLD) in the current HCV population. What is already known about this subjectAll-Cause and METHODS: This retrospective, matched cohort study included patients aged at least 18 years and with at least 6 months of continuous enrollment in a large managed care organization (MCO) claims database from July 1, 2001, through March 31, 2010. Patients with a diagnosis of HCV (ICD-9-CM codes 070.54, 070.70) were identified and stratified into those with and without AdvLD, defined as decompensated cirrhosis (ICD-9-CM codes 070. 44, 070.71, 348.3x, 456.0, 456.1, 456.2x, 572.2, 572.3, 572.4, 782.4, 789.59); hepatocellular carcinoma (HCC, ICD-9-CM code 155); or liver transplant (ICD-9-CM codes V42.7, 50.5 or CPT codes 47135, 47136). For patients without AdvLD, the index date was the first HCV diagnosis date observed at least 6 months after the first enrollment date, and at least 6 months of continuous enrollment after the index date were required. HCV patients without AdvLD were stratified into those with and without compensated cirrhosis (ICD-9-CM codes 571.2, 571.5, 571.6). For patients with AdvLD, the index date was the date of the first AdvLD diagnosis observed at least 6 months after the first enrollment date, and at least 1 day of enrollment after the index date was required. Cases were matched in an approximate 1:10 ratio to comparison patients without an HCV diagnosis or AdvLD diagnosis who met all other inclusion criteria based on gender, age, hospital referral region state, pre-index health care costs, alcoholism, human immunodeficiency virus/acquired immune deficiency syndrome (HIV/AIDS), and a modified Charlson Comorbidity Index. For the HCV and comparison patient cohorts, PPPY all-cause costs to the payer were calculated as total allowed charges summed across all patients divided by total patient-days of follow-up for the cohort, multiplied by 365, inflation-normalized to 2009 dollars. Because the calculation of PPPY cost generated a single value for each cohort, bootstrapping was used to generate descriptive statistics. Incremental PPPY costs for HCV patients relative to non-HCV patients were calculated as between-group differences in PPPY costs. T-tests for independent samples were used to compare costs between case and comparison cohorts.RESULTS: A total of 34,597 patients diagnosed with HCV, 78.0% with HCV without AdvLD, 4.4% with compensated cirrhosis, 12.3% with decompensated cirrhosis, 2.8% with HCC, and 2.6% with liver transplant, were matched to 330,435 comparison patients. Mean (SD) age of al...

Introduction The study objective was to build a machine learning model to predict incident mild cognitive impairment, Alzheimer's Disease, and related dementias from structured data using administrative and electronic health record sources. Methods A cohort of patients (n = 121,907) and controls (n = 5,307,045) was created for modeling using data within 2 years of patient's incident diagnosis date. Additional cohorts 3–8 years removed from index data are used for prediction. Training cohorts were matched on age, gender, index year, and utilization, and fit with a gradient boosting machine, lightGBM. Results Incident 2‐year model quality on a held‐out test set had a sensitivity of 47% and area‐under‐the‐curve of 87%. In the 3‐year model, the learned labels achieved 24% (71%), which dropped to 15% (72%) in year 8. Discussion The ability of the model to discriminate incident cases of dementia implies that it can be a worthwhile tool to screen patients for trial recruitment and patient management.

Given a flight schedule, which is a set of flight segments with specified departure and arrival times, and a set of aircraft, the fleet assignment problem is to determine which aircraft type should fly each flight segment. The objective is to maximize revenue minus operating costs. In the basic fleet assignment problem considered by Hane et al. (Hane, C. A., C. Barnhart, E. L. Johnson, R. E. Marsten, G. L. Nemhauser, G. Sigismondi. 1995. The fleet assignment problem: Solving a large-scale integer program. Math. Programming 70 211–232.) a daily, domestic fleet assignment problem is modeled and solved with up to eleven fleets and 2,500 flight legs. This paper provides modeling devices for including maintenance and crew considerations into the basic model while retaining its solvability.