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NURSE SCHEDULING USING MATHEMATICAL-PROGRAMMING

OPERATIONS RESEARCH 1976年第5期24卷 857-870页

作者： MILLER, HE PIERSKALLA, WP RATH, GJ RENSSELAER POLYTECH INST TROYNY 12181 NORTHWESTERN UNIV EVANSTONIL 60201

This paper formulates the nurse-scheduling problem as one of selecting a configuration of nurse schedules that minimize an objective function that balances the trade-off between staffing coverage and schedule preferences of individual nurses, subject to certain feasibility constraints on the nurse schedules. The problem is solved by a cyclic coordinate descent algorithm. We present results pertaining to a six-month application to a particular hospital unit and draw comparisons between the algorithm and hospital-generated schedules.

关键词： Nurses Staffing Algorithms Scheduling Cost functions Minimization of cost Mathematical models Rotation objective functions

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Frameworks for latent variable multivariate regression

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JOURNAL OF CHEMOMETRICS 1996年第1期10卷 31-45页

作者： Burnham, AJ Viveros, R MacGregor, JF MCMASTER UNIV DEPT CHEM ENGNHAMILTONON L8S 4K1CANADA

A set of frameworks for latent variable multivariate regression method is developed. The first two of these frameworks describe the objective functions satisfied by the latent variables chosen in canonical coordinates regression (CCR), reduced rank regression (RRR) and SIMPLS. These frameworks show the methods as a natural progression from CCR (maximizing correlation) to SIMPLS (maximizing covariance) via RRR (which is an intermediate method). These frameworks are unique in that they look at these methods in terms of latent variables in both the X- and Y-spaces. This adds insight to the nature of the latent variables being chosen. These frameworks are then extended to include PLS for latent variables beyond the first component. This new framework provides a detailed description of the objective function satisfied by PLS latent variables for the multivariate case. It also includes CCR, RRR and SIMPLS, allowing comparisons between the methods. A further framework suggests a new method, undeflated PLS (UDPLS), which adds insight to the effect of the deflation process on PLS. The impact of the objective functions on each of the methods is illustrated on real data from a mineral sorting plant.

关键词： latent variables multivariate regression PLS SIMPLS reduced rank regression canonical co-ordinate regression PCR objective functions

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Operations-Focused Optimized Theater Weather Sensing Strategies

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MILITARY OPERATIONS RESEARCH 2016年第3期21卷 51-71页

作者： Geyer, Andrew J. Hall, Shane N. Moore, James T. Air Force Inst Technol Wright Patterson AFB OH 45433 USA

This article describes a method that optimally deploys weather sensors of all types in a battlefield environment. Gridded climatology models are used to determine an estimate for the weighted frequency of occurrence of operationally significant inclement weather events. That data is used to formulate a series of preemptive binary integer linear programs (BILPs) that maximize detection of expected operationally significant inclement weather occurrences within the constraints of feasibility of sensor deployment, sensor operational lifespan and the sensor's ability to detect the operationally significant inclement weather elements. The preemptive BILPs are combined into a single objective function that maintains the preemptive nature of the original objective functions. The BILP solutions are described as a meteorology and oceanographic collection plan supporting a particular military campaign. A method for sensitivity analysis of differing BILP optimal solutions is provided. Various randomly generated instances of the problem are solved to optimality and analyzed to demonstrate that the problem formulation accurately captures all aspects of the operational environment. This quantitative analysis of alternative battlefield weather sensing strategies was not possible before the development of this methodology.

关键词： Sensors Military operations objective functions Weather conditions Military campaigns Operations research Meteorological radar Optimal solutions

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Sensitivity and Interaction Analysis Based on Sobol' Method and Its Application in a Distributed Flood Forecasting Model

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WATER 2015年第6期7卷 2924-2951页

作者： Wan, Hui Xia, Jun Zhang, Liping She, Dunxian Xiao, Yang Zou, Lei Wuhan Univ State Key Lab Water Resources & Hydropower Engn S Wuhan 430072 Peoples R China Wuhan Univ Hubei Collaborat Innovat Ctr Water Resources Secu Wuhan 430072 Peoples R China

Sensitivity analysis is a fundamental approach to identify the most significant and sensitive parameters, helping us to understand complex hydrological models, particularly for time-consuming distributed flood forecasting models based on complicated theory with numerous parameters. Based on Sobol' method, this study compared the sensitivity and interactions of distributed flood forecasting model parameters with and without accounting for correlation. Four objective functions: (1) Nash-Sutcliffe efficiency (E-NS);(2) water balance coefficient (WB);(3) peak discharge efficiency (E-P);and (4) time to peak efficiency (E-TP) were implemented to the Liuxihe model with hourly rainfall-runoff data collected in the Nanhua Creek catchment, Pearl River, China. Contrastive results for the sensitivity and interaction analysis were also illustrated among small, medium, and large flood magnitudes. Results demonstrated that the choice of objective functions had no effect on the sensitivity classification, while it had great influence on the sensitivity ranking for both uncorrelated and correlated cases. The Liuxihe model behaved and responded uniquely to various flood conditions. The results also indicated that the pairwise parameters interactions revealed a non-ignorable contribution to the model output variance. Parameters with high first or total order sensitivity indices presented a corresponding high second order sensitivity indices and correlation coefficients with other parameters. Without considering parameter correlations, the variance contributions of highly sensitive parameters might be underestimated and those of normally sensitive parameters might be overestimated. This research laid a basic foundation to improve the understanding of complex model behavior.

关键词： sensitivity analysis interaction analysis correlated parameters objective functions flood magnitudes Sobol’ method

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Importance sampling and Mean-Square error in neural detector training

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NEURAL PROCESSING LETTERS 2002年第3期16卷 259-276页

作者： Sanz-González, JL Andina, D Seijas, J Univ Politecn Madrid ETSI Telecomun Dept SSR E-28040 Madrid Spain

This letter deals with the use of Importance Sampling (IS) techniques and the Mean-Square (MS) error in neural network training, for applications to detection in communication systems. Topics such as modifications of the MS objective function, optimal and suboptimal IS probability density functions, and adaptive importance sampling are presented. A genetic algorithm was used for the neural network training, having considered adaptive IS techniques for improving MS error estimations in each iteration of the training. Also, some experimental results of the training process are shown in this letter. Finally, we point out that the mean-square error (estimated by importance sampling) attains quasi-optimum training in the sense of minimum error probability (or minimum misclassification error).

关键词： adaptive importance sampling detectors error probability genetic algorithms importance sampling techniques Mean-Square error Monte Carlo simulations neural network training objective functions

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STATIONARY POLICIES IN DYNAMIC-PROGRAMMING MODELS UNDER COMPACTNESS ASSUMPTIONS

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MATHEMATICS OF OPERATIONS RESEARCH 1983年第3期8卷 366-372页

作者： SCHAL, M Universitä Bonn

The present work deals with the usual stationary decision model of dynamic programming. The imposed convergence condition on the expected total rewards is so general that both the negative (unbounded) case and the positive (unbounded) case are included. However, the gambling model studied by Dubins and Savage is not covered by the present model. In addition to the convergence condition, a continuity and compactness condition is imposed. The main result states that the supremum of the expected total rewards under all stationary policies is equal to the supremum under all (possibly randomized and non-Markovian) policies.

关键词： Dynamic programming Topological compactness objective functions Decision making models Dynamic modeling Programming models Mathematical functions Bells Optimal policy

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APPROXIMATIONS AND SENSITIVITY IN MULTIobjective RESOURCE-ALLOCATION

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OPERATIONS RESEARCH 1980年第1期28卷 114-128页

作者： KEEFER, DL POLLOCK, SM UNIV MICHIGAN ANN ARBOR MI 48109 USA

This paper addresses the modeling of resource allocation planning problems having uncertainties, multiple competing objectives, organizational constraints, and continuous decision variables. The application of multiobjective decision analysis leads to a nonlinear programming formulation in which the objective function is the expectation of a multiattribute utility function. If a set of independence conditions holds, this function can be decomposed into appropriately scaled sums and products of one-dimensional expected utility functions. Approximations that greatly simplify the data acquisition for, and the construction of, the one-dimensional expected utility functions are discussed. Sensitivity analyses indicate that optimal solutions to such models are robust with respect to changes in the required data, but may be seriously in error if certain popular, but overly simplified, forms for the objective function are assumed.

关键词： Approximation Utility functions Expected utility Decision analysis objective functions Error rates Budget allocation Interpolation Sensitivity analysis

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CAPACITY EXPANSION IN CONVEX COST NETWORKS WITH UNCERTAIN DEMAND

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OPERATIONS RESEARCH 1975年第6期23卷 1172-1178页

作者： LEONDES, CT NANDI, RK UNIV CALIF LOS ANGELESCA 90024

The purpose of this investigation is to suggest a simple algorithm for solving capacity expansion problems in networks with uncertain demand. We assume that the cost of expanding the capacity of each arc is a convex function and that there is a concave salvage value each arc is a convex function and that there is a concave salvage value associated with excess capacity. We adopt the two-stage programming approach but with the essential difference that our independent variable is an assumed first-stage demand. We show that the objective function of the equivalent convex program is a convex function of the assumed first-stage demand and use this fact to propose an algorithm. [ABSTRACT FROM AUTHOR]

关键词： Algorithms Capacity costs Cost functions objective functions Optimal solutions

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OPTIMIZING SINGLE VEHICLE MANY-TO-MANY OPERATIONS WITH DESIRED DELIVERY TIMES .1. SCHEDULING

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TRANSPORTATION SCIENCE 1985年第4期19卷 378-410页

作者： SEXTON, TR BODIN, LD SUNY STONY BROOK STONY BROOK NY 11794 USA UNIV MARYLAND COLLEGE PK MD 20742 USA

A set of n customers is given. Each customer has a desired point of pickup, a desired point of delivery and a desired time of delivery. The problem is to determine the order of pickup and delivery and the times of pickup and delivery of these n customers by a single vehicle in order to minimize total customer inconvenience. Here, a mathematical programming formulating of this problem is subjected to Benders' decomposition procedure. The result is a heuristic routing and scheduling algorithm which is shown to produce high quality solutions in reasonable computation time by testing on moderately sized real data bases from both Gaithers-burg, Maryland, and Baltimore, Maryland. This study is divided into two parts, the first detailing the scheduling analysis and the second focusing on the routing component.

关键词： Scheduling Vehicles Algorithms Vehicle operation Unit costs Travel time Supply Heuristics objective functions

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Low probability high consequence considerations in routing hazardous material shipments

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TRANSPORTATION SCIENCE 1997年第3期31卷 237-251页

作者： Sherali, HD Brizendine, LD Glickman, TS Subramanian, S KPMG PEAT MARWICK WASHINGTONDC 20036

This paper is concerned with the development and analysis of a mathematical model for determining a route that attempts to reduce the risk of low probability-high consequence accidents related with the transportation. of hazardous materials. The approach adopted considers trade-offs between the conditional expectation of a catastrophic outcome given that an accident has occurred, and more traditional measures of risk dealing with the expected value of the consequence and the accident probability on a selected path. More specifically, the problem we address involves finding a path that minimizes the conditional expectation objective value, subject to the expected value of the consequence being lesser than or equal to a specified value nu, and the probability of an accident on the path being also constrained to be no more than some value eta. The values nu and eta are user-prescribed and could be prompted by the solution to the shortest path problems that minimize the respective corresponding linear risk functions. The proposed model is a discrete, fractional programming problem that is solved using a specialized branch-and-bound approach. A numerical example is provided for the sake of illustration, and some computational experience on randomly generated test cases is provided to study the effort required to solve this problem in different instances. The model is also tested using realistic data associated with a case concerned with routing hazardous materials through the roadways of Bethlehem, Pennsylvania. Data acquisition as well as algorithmic computational issues are discussed.

关键词： Hazardous waste Automobile accidents objective functions Algorithms Hazardous substances Death Conditional probabilities Shipments Preprocessing

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