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PubMed1996

[Application of linear programming in optimizing nursing staff allocation in hospital].

After analysing the nurse work load of all departments in a certain hospital by comprehensive evaluation, the nursing staffs were allocated inappropriately was found. According to the work load of all departments, the optimal allocation of nursing staff was obtained with linear programming, so that the work load of all departments would be as identical as possible, and the disadvantages of differing in work load would be overcomed.

Humans↗
PubMed1994

Optimizing the herd calving pattern with linear programming and dynamic probabilistic simulation.

Until recently, little attention has been paid to the influence of seasonal variation in performance and prices on the optimal calving pattern of a herd. A method was developed to determine the herd calving pattern that is farm-specific and optimal with use of linear programming. The required technical and economic parameters are calculated with a dynamic probabilistic simulation model of the dairy herd. The approach was illustrated with a situation in which the objective was to maximize the gross margin of the herd and the annual milk production of the herd was restricted, resulting in an optimal calving pattern: all heifers calved during August. When, in addition, only home-reared replacement heifers were allowed to enter the herd, heifer calvings took place from July to October. The gross margin was reduced by only Dfl. .13/100 kg of milk ($1 US = 1.80 Dfl.) as a result of the additional constraint. The sensitivity of the optimal calving pattern of herd was determined for lower reproductive performance and when seasonal price variation was ignored. The method described herein is a flexible tool for determining the optimal calving pattern of herd, taking into account farm-specific inputs and constraints.

Animal Feed↗
PubMed2001

Linear programming optimization and a double statistical filter for protein threading protocols.

The design of scoring functions (or potentials) for threading, differentiating native-like from non-native structures with a limited computational cost, is an active field of research. We revisit two widely used families of threading potentials: the pairwise and profile models. To design optimal scoring functions we use linear programming (LP). The LP protocol makes it possible to measure the difficulty of a particular training set in conjunction with a specific form of the scoring function. Gapless threading demonstrates that pair potentials have larger prediction capacity compared with profile energies. However, alignments with gaps are easier to compute with profile potentials. We therefore search and propose a new profile model with comparable prediction capacity to contact potentials. A protocol to determine optimal energy parameters for gaps, using LP, is also presented. A statistical test, based on a combination of local and global Z-scores, is employed to filter out false-positives. Extensive tests of the new protocol are presented. The new model provides an efficient alternative for threading with pair energies, maintaining comparable accuracy. The code, databases, and a prediction server are available at http://www.tc.cornell.edu/CBIO/loopp.

Amino Acid Sequence↗
PubMed2004

Shim design using a linear programming algorithm.

The advent of open magnetic resonance imaging (MRI) scanners and dedicated MRI scanners tailored to specific body parts has led to an increasing number of noncylindrical MRI scanner geometries, for which noncylindrical gradients and shims are needed. These new scanner geometries are driving the need for fast, flexible shim design methods that can design shim coils for any geometry. A linear programming (LP) algorithm was developed to design minimum-power resistive shim coils on an arbitrary surface. These coils can be designed to produce any order shim field over an arbitrarily shaped target region, which can be placed anywhere within the coil. The resulting designs are relatively sparse and can be readily constructed. This algorithm was used to design and construct a seven-coil cylindrical shim set for a knee imaging magnet with a cylindrical homogeneous region. The algorithm was then used to design shim coils for a biradial head imager with an asymmetrically located spherical target region for brain imaging.

Algorithms↗
PubMed1992

Modifying diets to satisfy nutritional requirements using linear programming.

A computational method for constructing individually acceptable diets by modifying a chosen diet to meet nutritional requirements is described. The effects on food quantities of imposing different nutrient requirements on a sample diet are demonstrated and techniques which can ensure the acceptability to the individual of the modified diet are described. The starting point in the calculation is the person's current dietary intake. This is modified using linear programming methods which make the smallest changes to the food quantities to meet specific targets. Sequential modification can be used to identify changes that are acceptable to the individual. The computer program has been developed in collaboration with practising dietitians and is in use in some leading UK hospitals.

Dietetics↗
PubMed2005

Integer linear programming as a tool for constructing trees from quartet data.

The task of the quartet puzzling problem is to find a best-fitting binary X-tree for a finite n-set from confidence values for the 3n4 binary trees with exactly four leaves from X, its fitness being measured by the sum of the confidence values of all "induced" four-leaves subtrees. We describe a method for finding an exact solution of this problem by integer linear programming. Similar procedures can also be used for finding, e.g. best-fitting "circular" networks. A crucial problem in this context is, of course, how to obtain the input confidence values for the quartet trees. We propose to use inner products of rate-matrix diagonals calculated for pairs of taxa and present the trees resulting from applying our approach to two data sets of up to 36 mitochondrial sequences of mammals including an outgroup.

Journal Article↗
PubMed1989

Linear programming models for cost reimbursement.

Tamura, Lauer, and Sanborn (1985) reported a multiple regression approach to the problem of determining a cost reimbursement (rate-setting) formula for facilities providing long-term care (nursing homes). In this article we propose an alternative approach to this problem, using an absolute-error criterion instead of the least-squares criterion used in regression, with a variety of side constraints incorporated in the derivation of the formula. The mathematical tool for implementation of this approach is linear programming (LP). The article begins with a discussion of the desirable characteristics of a rate-setting formula. The development of a formula with these properties can be easily achieved, in terms of modeling as well as computation, using LP. Specifically, LP provides an efficient computational algorithm to minimize absolute error deviation, thus protecting rates from the effects of unusual observations in the data base. LP also offers modeling flexibility to impose a variety of policy controls. These features are not readily available if a least-squares criterion is used. Examples based on actual data are used to illustrate alternative LP models for rate setting.

Computer Simulation↗
PubMed1987

Linear programming analysis of VA/Q distributions: average distribution.

The defining equations of the multiple inert gas elimination technique are underdetermined, and an infinite number of VA/Q ratio distributions exists that fit the same inert gas data. Conventional least-squares analysis with enforced smoothing chooses a single member of this infinite family whose features are assumed to be representative of the family as a whole. To test this assumption, the average of all ventilation-perfusion ratio (VA/Q) distributions that are compatible with given data was calculated using a linear program. The average distribution so obtained was then compared with that recovered using enforced smoothing. Six typical sets of inert gas data were studied. In all sets but one, the distribution recovered with conventional enforced smoothing closely matched the structure of the average distribution. The single exception was associated with the broad log-normal VA/Q distribution, which is rarely observed using the technique. We conclude that the VA/Q distribution conventionally recovered approximates a simple average of all compatible distributions. It therefore displays average features and only that degree of fine structural detail that is typical of the family as a whole.

Aging↗
PubMed1985

Solution of the multiple dosing problem using linear programming.

A system theoretical approach to drug concentration-time data analysis is introduced after the discussion of some relevant concepts as they are used in system theory. The merits of this approach are demonstrated in multiple dosing problem. It is shown that dosage minimization without stringent constraints does not result in the desired therapeutic effect. In a different optimization the discrepancy between the actual and the desired time-histories of the relevant substance's plasma concentration is minimized. It is shown that both of these optimizations can be reduced to linear programming problems which are easily solvable with today's computers. These methods are demonstrated in a case study of dopaminergic substitution in Parkinson's disease where computer simulations show them to yield excellent results. Finally, the limits of this approach are also discussed.

Biometry↗
PubMed1986

A diagnostic method that uses causal knowledge and linear programming in the application of Bayes' formula.

Bayes' formula has been applied extensively in computer-based medical diagnostic systems. One assumption that is often made in the application of the formula is that the findings in a case are conditionally independent. This assumption is often invalid and leads to inaccurate posterior probability assignments to the diagnostic hypotheses. This paper discusses a method for using causal knowledge to structure findings according to their probabilistic dependencies. An inference procedure is discussed which propagates probabilities within a network of causally related findings in order to calculate posterior probabilities of diagnostic hypotheses. A linear programming technique is described that bounds the values of the propagated probabilities subject to known probabilistic constraints.

Bayes Theorem↗
PubMed1998

Linear programming based approach to the derivation of a contact potential for protein threading.

This paper proposes a novel method of deriving a contact potential (a pair score function) for protein threading. In this method, the constraint that the score of the native threading is minimum over all possible threadings is expressed in a form of linear inequalities, and then parameters defining the contact potential are determined by applying a program package of linear programming. The most important advantage of this method over the previous methods is that this method can learn a score function from a small number of training data. The proposed method was evaluated using Lathrop and Smith's algorithm for finding optimal threadings and was shown to be effective for computing nearly correct threadings.

Amino Acid Sequence↗
PubMed2004

A mixed integer linear programming (MILP) framework for inferring time delay in gene regulatory networks.

In this paper, an optimization based modeling and solution framework for inferring gene regulatory networks while accounting for time delay is described. The proposed framework uses the basic linear model of gene regulation. Boolean variables are used to capture the existence of discrete time delays between the various regulatory relationships. Subsequently, the time delay that best fits the expression profiles is inferred by minimizing the error between the predicted and experimental expression values. Computational experiments are conducted for both in numero and real expression data sets. The former reveal that if time delay is neglected in a system a priori known to be characterized with time delay then a significantly larger number of parameters are needed to describe the system dynamics. The real microarray data example reveals a considerable number of time delayed interactions suggesting that time delay is ubiquitous in gene regulation. Incorporation of time delay leads to inferred networks that are sparser. Analysis of the amount of variance in the data explained by the model and comparison with randomized data reveals that accounting for time delay explains more variance in real rather than randomized data.

Computational Biology↗
PubMed2003

Multicriteria optimization of biochemical systems by linear programming: application to production of ethanol by Saccharomyces cerevisiae.

In this study we present a method for simultaneous optimization of several metabolic responses of biochemical pathways. The method, based on the use of the power law formalism to obtain a linear system in logarithmic coordinates, is applied to ethanol production by Saccharomyces cerevisiae. Starting from an experimentally based kinetic model, we translated it to its power law equivalent. With this new model representation, we then applied the multiobjective optimization method. Our intent was to maximize ethanol production and minimize each of the internal metabolite concentrations. To ensure cell viability, all optimizations were carried out under imposed constraints. The different solutions obtained, which correspond to alternative patterns of enzyme overexpression, were implemented in the original model. We discovered few discrepancies between the S-system-optimized steady state and the corresponding optimized state in the original kinetic model, thus demonstrating the suitability of the S-system representation as the basis for the optimization procedure. In all optimized solutions, the ATP level reached its maximum and any increase in its activity positively affected the optimization process. This work illustrates that in any optimization study no single criteria is of general application being the multiobjective and constrained task the proper way to address it. It is concluded that the proposed multiobjective method can serve to carry out, in a single study, the general pattern of behavior of a given metabolic system with regard to its control and optimization.

Algorithms↗
PubMed1995

Application of linear programming in bull selection for a dairy herd.

Approximately 70% of dairy cows are inseminated with semen from bulls provided by commercial artificial insemination centers. To help producers in the selection process, artificial insemination centers publish information regarding production and type traits associated with each bull. Producers must decide from these lists which bulls to use, how often they are to be used, and to which cows they should be allocated. The bulls selected have a direct effect on cost of semen for the herd and genetic improvement in production of future generations. In general, producers' goals are to replace poor genes through strategic culling (not breeding certain cows) with better genes through semen purchases in an economically efficient manner. The cost of semen, however, is realized immediately, whereas economic returns from the traits selected are dependent on the realization of future cash flows. Higher production returns are needed to justify using more expensive bulls. The purposes of the study reported here were to examine the bull selection portfolio of a 450-cow commercial dairy herd in southeastern Pennsylvania and to use linear optimizing programming to select a genetically similar group of bulls at a much lower cost than that the producer had been using. This approach of dominant decision-making can be generalized and implemented for various dairy from conditions.

Animals↗
PubMed1978

Monitoring normal and malignant human white blood cells by the use of linear programmed thermal degradation mass spectrometry.

A new methodology has been applied to the analysis of human white blood cells obtained both from donors with normal white cells and from donors having one of several cytologically identified leukemias. The analytical process makes use of evolution patterns of molecular fragments generated during the well controlled degradation of the cells. The process has been shown to be effective both in grouping together malignant cells that originate from the same diseases and in distinguishing between malignant cells originating from different diseases. The reproducibility of the method has been demonstrated.

Computers↗
PubMed2001

Linear programming of inlet pressure or flow-rate in isothermal gas chromatography with near-vacuum outlet pressure.

The equation of motion for a peak in a gas chromatography experiment is shown to be exact whenever the column outlet pressure is approximately zero. Based on steady-state assumptions, this equation is solved for an isothermal analysis with a single-ramp inlet-pressure or flow-rate program. Theoretical calculations of retention times are confirmed experimentally for two n-alkanes using a capillary column connected to a mass-selective detector. A slight but consistent discrepancy between theoretical and measured results is interpreted as a failure of the steady-state assumption when the magnitude of the rate of change of inlet pressure is large.

Chromatography, Gas↗
PubMed1987

Emergence temperature indices and relative retention times of pesticides and industrial chemicals determined by linear programmed temperature gas chromatography.

Emergence temperature indices and relative retention times of nearly 600 pesticides and industrial chemicals are sequentially tabulated to provide a basis for the identification of unknowns detected on methyl silicone columns when programmed temperature gas chromatography is used. A technique of normalizing column parameters is described to enable duplication of the tabulated data on columns which have different dimensions, amount of stationary phase, and/or other operating parameters. Suggestions for enhancing the precision with which these data can be reproduced on other equipment are presented.

Chromatography, Gas↗