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The authors developed a model that incorporates two mathematical innovations for designing a personalized treatment plan tailored specifically to a diabetes patient's unique dose-effect characteristics. Diabetes affects 422 million people globally, costing over $825 billion per year. In the United States, about 30.3 million live with the illness. Current diabetes management focuses on close monitoring of a patient's blood glucose level, while the clinician experiments with dosing strategy based on clinical guidelines and his or her own experience. In this work, we propose a model for designing a personalized treatment plan tailored specifically to the patient's unique dose-effect characteristics. Such a plan is more effective and efficient—for both treatment outcome and treatment cost—than current trial-and-error approaches. Our approach incorporates two key mathematical innovations. First, we develop a predictive dose-effect model that uses fluid dynamics, a compartmental model of partial differential equations, constrained least-square optimization, and statistical smoothing. The model leverages a patient's routine self-monitoring of blood glucose and prescribed medication to establish a direct relationship between drug dosage and drug effect. This answers a fundamental century-long puzzle on how to predict dose effect without using invasive procedures to measure drug concentration in the body. Second, a multiobjective mixed-integer programming model incorporates this personalized dose-effect knowledge along with clinical constraints and produces optimized plans that provide better glycemic control while using less drug. This is an added benefit because diabetes is costly to treat as it progresses and requires continuous intervention. Implemented at Grady Memorial Hospital, our system reduces the hospital cost by $39,500 per patient for pregnancy cases where a mother suffers from gestational diabetes. This is a decrease of more than fourfold in the overall hospital costs for such cases. For type 2 diabetes, which accounts for about 90%–95% of all diagnosed cases of diabetes in adults, our approach leads to improved blood glucose control using less medication, resulting in about 39% savings ($40,880 per patient) in medical costs for these patients. Our mathematical model is the first that (1) characterizes personalized dose response for oral antidiabetic drugs; and (2) optimizes outcome and dosing strategy through mathematical programming. [ABSTRACT FROM AUTHOR]

A parallel implementation of a disjunctive cutting-plane algorithm in a distributed memory environment is described. Guided by a selection of difficult instances from MIPLIB and real instances obtained from brain-tumor research, various strategies of cut synchronization are considered, and their influence on speedup, communication overhead, load balance, and effectiveness in closing the integrality gap are studied. The parallel cutting-plane algorithm is coupled with an LP-based heuristic to assist in returning a good quality integer feasible solution upon termination of the parallel process. The parallel implementation is sufficiently coarse grained to yield an average of less than 6% of the total time performing tasks associated with communication overhead, and it provides reasonable speedup when executing in parallel. Noticeable differences in load-balance scores are observed, depending on the number of processors used, the synchronization scheme used, and the structure of the MIP problem instance. Nevertheless, the synergism of the combined collection of cuts generated locally on each processor is effective in closing the integrality gap in all cases, and there is minimal variability in the amount of the gap closed as the number of processors varies. In particular, the degree of decentralization, as governed by the synchronization schemes, has little effect on the overall quality of the cuts generated. [ABSTRACT FROM AUTHOR]

Presents theoretical results that pertain to the independent set polytope. Construction of the conflict hypergraph from an independence system; Information on the hypercliques in the knapsack polytope; Notion of lifting in a conlifct hyperg raph setting.

Numerical experiments for a parallel implementation of a branch-and-bound mixed 0/1 integer programming code are presented. Among its features, the code includes cutting- plane generation at the root node, and employs a new branching-variable selection rule within the search tree. The code runs on a loosely-coupled cluster of workstations using TreadMarks as the parallel software platform. Numerical tests were performed on all mixed 0/1 MIPLIB instances as well as two previously unsolved MIP instances, one arising from telecommunication networks and the other a multicommodity flow problem. [ABSTRACT FROM AUTHOR]

A nonlinear 0/1 mixed integer programming model is presented for a constrained discriminant analysis problem. The model places restrictions on the numbers of misclassifications allowed among the training entities, and incorporates a ‘reserved judgment’ region to which entities whose classifications are difficult to determine may be allocated. Two linearizations of the model are given — one heuristic and one exact. Numerical results from real-world machine-learning datasets are presented. [ABSTRACT FROM AUTHOR]

A branch-and-cut IP solver is developed for a class of structured 0/1 integer programs arising from a truck dispatching scheduling problem. This problem involves a special class of knapsack equality constraints. Families of facets for the polytopes associated with individual knapsack constraints are identified. In addition, a notion of "conflict graph" is utilized to obtain an approximating node-packing polytope for the convex hull of all 0/1 solutions. The branch-and-cut solver generates cuts based on both the knapsack equality constraints and the approximating node-packing polytope, and incorporates these cuts into a tree-search algorithm that uses problem reformulation and linear programming-based heuristics at each node in the search tree to assist in the solution process. Numerical experiments are performed on large-scale real instances supplied by Texaco Trading & Transportation, Inc. The optimal schedules correspond to cost savings for the company and greater job satisfaction for drivers due to more balanced work schedules and income distribution. [ABSTRACT FROM AUTHOR]