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PubMed1993

Diet planning for humans using mixed-integer linear programming.

Human diet planning is generally carried out by selecting the food items or groups of food items to be used in the diet and then calculating the composition. If nutrient quantities do not reach the desired nutritional requirements, foods are exchanged or quantities altered and the composition recalculated. Iterations are repeated until a suitable diet is obtained. This procedure is cumbersome and slow and often leads to compromises in composition of the final diets. A computerized model, planning diets for humans at minimum cost while supplying all nutritional requirements, maintaining nutrient relationships and preserving eating practices is presented. This is based on a mixed-integer linear-programming algorithm. Linear equations were prepared for each nutritional requirement. To produce linear equations for relationships between nutrients, linear transformations were performed. Logical definitions for interactions such as the frequency of use of foods, relationships between exchange groups and the energy content of different meals were defined, and linear equations for these associations were written. Food items generally eaten in whole units were defined as integers. The use of this program is demonstrated for planning diets using a large selection of basic foods and for clinical situations where nutritional intervention is desirable. The system presented begins from a definition of the nutritional requirements and then plans the foods accordingly, and at minimum cost. This provides an accurate, efficient and versatile method of diet formulation.

Algorithms↗

PubMed1985

Selecting mating pairs with linear programming techniques.

Mate selection can increase progency merit if overall merit is nonlinear for one or more component traits. An index of expected progeny merit could be calculated for all possible mating pairs, and the set of pairs with the highest progeny mean could be selected. There are serious computational problems for more than a few males and females. To select and mate f, females, and m, males, from n of each, with k0 females per male, would require (nf)(nm)f!/(k0!)m evaluations. Linear programming algorithms can determine the optimal strategy efficiently by considering only a subset of these possibilities. Let pi ij be the index of progency merit of the ith sire mated to the jth dam and Xij be the decision variable for that mating (restricted to 0 or 1). Then the problem of selecting mating pairs can be stated as: maximize sigma i sigma j pi ij Xij, subject to sigma i Xij less than or equal to 1, sigma j Xij less than or equal to k0, sigma i sigma j Xij = f, and Xij = 0 or 1. By including an artificial sire and an artificial dam and choosing appropriate merit values for the artificial matings, this problem can be solved by efficient "transportation" algorithms. These algorithms could be used to develop rational mating packages for dairy artificial insemination studs provided that an objective evaluation of progeny merit could be formulated, provided that merit is not simply additively inherited.

Animal Husbandry↗

PubMed2003

A linear programming approach to estimate the economic impact of bovine viral diarrhoea (BVD) at the whole-farm level in Scotland.

We combined epidemiological and economic concepts and modelling techniques, to integrate animal health into whole-farm business management. This allowed us to assess the relative contribution that disease prevention could make to whole-farm income and to the variability in farm income (risk). It also allowed us to assess disease losses in the context of a farm business rather than as a disease outbreak in isolation. A linear program ("MOTAD") establishes the combination of decision maker's activities that minimise risk for a given level of income within farm-business constraints. The MOTAD model was applied to farm-management decision making in Scottish cow-calf herds and was linked to an epidemiological model of bovine viral diarrhoea (BVD). When BVD was considered in isolation (i.e. without taking into account risk), the minimum expected total cost of BVD (sum of output losses plus expenditure on prevention) was similar whether the herd was susceptible to BVD or of unknown BVD-status at the outset. However, the expected total cost of BVD fell in response to increasing expenditure on prevention in 'susceptible' herds. This relationship was not apparent in herds of unknown BVD-status. As a consequence of this difference, 'susceptible' herds were better able to use investment in BVD biosecurity as a means to increase farm income at minimum risk than herds of unknown BVD-status. 'Susceptible' herds therefore were able to achieve high income targets with less-intensive production than herds of unknown BVD-status. This suggested that maintaining a cow-calf herd free of BVD contributes to farm income and risk management indirectly through its effect on the management of the whole farm. It follows that measurement of the economic impact of BVD requires a whole-farm perspective that includes a consideration of risk. Because farmers generally are considered to be risk adverse, this means that the least-cost disease-control option might not always be the preferred option.

Agriculture↗

PubMed2006

Optimization of HDR brachytherapy dose distributions using linear programming with penalty costs.

Prostate cancer is increasingly treated with high-dose-rate (HDR) brachytherapy, a type of radiotherapy in which a radioactive source is guided through catheters temporarily implanted in the prostate. Clinicians must set dwell times for the source inside the catheters so the resulting dose distribution minimizes deviation from dose prescriptions that conform to patient-specific anatomy. The primary contribution of this paper is to take the well-established dwell times optimization problem defined by Inverse Planning by Simulated Annealing (IPSA) developed at UCSF and exactly formulate it as a linear programming (LP) problem. Because LP problems can be solved exactly and deterministically, this formulation provides strong performance guarantees: one can rapidly find the dwell times solution that globally minimizes IPSA's objective function for any patient case and clinical criteria parameters. For a sample of 20 prostates with volume ranging from 23 to 103 cc, the new LP method optimized dwell times in less than 15 s per case on a standard PC. The dwell times solutions currently being obtained clinically using simulated annealing (SA), a probabilistic method, were quantitatively compared to the mathematically optimal solutions obtained using the LP method. The LP method resulted in significantly improved objective function values compared to SA (P = 1.54 x 10(-7)), but none of the dosimetric indices indicated a statistically significant difference (P < 0.01). The results indicate that solutions generated by the current version of IPSA are clinically equivalent to the mathematically optimal solutions.

Algorithms↗

PubMed2004

Classification of HIV-1-mediated neuronal dendritic and synaptic damage using multiple criteria linear programming.

The ability to identify neuronal damage in the dendritic arbor during HIV-1-associated dementia (HAD) is crucial for designing specific therapies for the treatment of HAD. To study this process, we utilized a computer-based image analysis method to quantitatively assess HIV-1 viral protein gp120 and glutamate-mediated individual neuronal damage in cultured cortical neurons. Changes in the number of neurites, arbors, branch nodes, cell body area, and average arbor lengths were determined and a database was formed (http://dm.ist.unomaha. edu/database.htm). We further proposed a two-class model of multiple criteria linear programming (MCLP) to classify such HIV-1-mediated neuronal dendritic and synaptic damages. Given certain classes, including treatments with brain-derived neurotrophic factor (BDNF), glutamate, gp120 or non-treatment controls from our in vitro experimental systems, we used the two-class MCLP model to determine the data patterns between classes in order to gain insight about neuronal dendritic damages. This knowledge can be applied in principle to the design and study of specific therapies for the prevention or reversal of neuronal damage associated with HAD. Finally, the MCLP method was compared with a well-known artificial neural network algorithm to test for the relative potential of different data mining applications in HAD research.

Animals↗

PubMed2003

Inferring strengths of protein-protein interactions from experimental data using linear programming.

MOTIVATION: Several computational methods have been proposed for inference of protein-protein interactions. Most of the existing methods assume that protein-protein interaction data are given as binary data (i.e. whether or not each protein pair interacts). However, multiple biological experiments are performed for the same protein pairs and thus the ratio (strength) of the number of observed interactions to the number of experiments is available for each protein pair. RESULTS: We propose a new method for inference of protein-protein interactions from such experimental data. This method tries to minimize the errors between the ratios of observed interactions and the predicted probabilities in training data, where this problem is formalized as a linear program based on a probabilistic model. We compared the proposed method with the association method, the EM method and the SVM-based method using real interaction data. It is shown that a variant of the method is comparable to existing methods for binary data. It is also shown that the method outperforms existing methods for numerical data. AVAILABILITY: Programs transforming input data into LP format files are available upon request.

Algorithms↗

PubMed2002

Use of linear programming to estimate impact of changes in a hospital's operating room time allocation on perioperative variable costs.

BACKGROUND: Administrators at hospitals with a fixed annual budget may want to focus surgical services on priority areas to ensure its community receives the best health services possible. However, many hospitals lack the detailed managerial accounting data needed to ensure that such a change does not increase operating costs. The authors used a detailed hospital cost database to investigate by how much a change in allocations of operating room (OR) time among surgeons can increase perioperative variable costs. METHODS: The authors obtained financial data for all patients who underwent outpatient or same-day admit surgery during a year. Linear programming was used to determine by how much changing the mix of surgeons can increase total variable costs while maintaining the same total hours of OR time for elective cases. RESULTS: Changing OR allocations among surgeons without changing total OR hours allocated will likely increase perioperative variable costs by less than 34%. If, in addition, intensive care unit hours for elective surgical cases are not increased, hospital ward occupancy is capped, and implant use is tracked and capped, perioperative costs will likely increase by less than 10%. These four variables predict 97% of the variance in total variable costs. CONCLUSIONS: The authors showed that changing OR allocations among surgeons without changing total OR hours allocated can increase hospital perioperative variable costs by up to approximately one third. Thus, at hospitals with fixed or nearly fixed annual budgets, allocating OR time based on an OR-based statistic such as utilization can adversely affect the hospital financially. The OR manager can reduce the potential increase in costs by considering not just OR time, but also the resulting use of hospital beds and implants.

Accounting↗

PubMed1999

Patient flows and optimal health-care resource allocation at the macro-level: a dynamic linear programming approach.

In this paper we present a deterministic allocation model in which a patient's health-state changes due to health-care interventions. This change in a patient's health-state has a direct effect on the patient's expected future need for health-care. Hence, current allocation decisions determine to some extent the set of possible allocation decisions in the future. In order to take this into account we have formulated a dynamic linear programming version of a patient-flow system. This enables us to describe the effects of using different objective functions on the optimum level and composition of the provision of health services within given resource constraints. The linear programming approach enables the quantification of the health effects and therefore the desirability of the (re-)allocation of health-care resources. We provide some simulation results in order to illustrate the working of the model.

Health Care Rationing↗

PubMed2000

Whole-herd optimization with the Cornell Net Carbohydrate and Protein System. I. Predicting feed biological values for diet optimization with linear programming.

We developed a diet optimizer for least-cost diet formulation with the Cornell Net Carbohydrate and Protein System (CNCPS) using linear programming. The CNCPS model is intrinsically nonlinear, and feed biological values vary with animal and feed characteristics. To allow linear diet optimization, we first used the CNCPS model to generate biological values to characterize the energy and protein content of each feed for the specific group for which the diet was being formulated. The biological values used were metabolizable energy (Mcal/kg), metabolizable protein [(% dry matter (DM)], passage rate (%/h), bacteria yield efficiencies (g/g), and degradation rate of the carbohydrate B2 fraction (%/h). In addition, the ruminal balances for nitrogen and peptides were included in the optimizer to optimize ruminal degradation of fiber. The objective function was to minimize diet cost subject to animal requirement and feed availability constraints. The animal constraints were set by requirements for DM intake (kg/d), metabolizable energy (Mcal/kg), metabolizable protein (%DM), and effective neutral detergent fiber (%DM) for a given level of production. Data from a dairy farm were used to evaluate this linear diet optimizer. Across all classes of dairy cattle, the CNCPS 4.0 model typically obtained a solution in less than six iterations that met the requirements with nearly 100% accuracy. We conclude this linear optimizer can be used to accurately formulate least-cost diets with the CNCPS model.

Animals↗

PubMed2005

A linear programming approach for identifying a consensus sequence on DNA sequences.

MOTIVATION: Maximum-likelihood methods for solving the consensus sequence identification (CSI) problem on DNA sequences may only find a local optimum rather than the global optimum. Additionally, such methods do not allow logical constraints to be imposed on their models. This study develops a linear programming technique to solve CSI problems by finding an optimum consensus sequence. This method is computationally more efficient and is guaranteed to reach the global optimum. The developed method can also be extended to treat more complicated CSI problems with ambiguous conserved patterns. RESULTS: A CSI problem is first formulated as a non-linear mixed 0-1 optimization program, which is then converted into a linear mixed 0-1 program. The proposed method provides the following advantages over maximum-likelihood methods: (1) It is guaranteed to find the global optimum. (2) It can embed various logical constraints into the corresponding model. (3) It is applicable to problems with many long sequences. (4) It can find the second and the third best solutions. An extension of the proposed linear mixed 0-1 program is also designed to solve CSI problems with an unknown spacer length between conserved regions. Two examples of searching for CRP-binding sites and for FNR-binding sites in the Escherichia coli genome are used to illustrate and test the proposed method. AVAILABILITY: A software package, Global Site Seer for the Microsoft Windows operating system is available by http://www.iim.nctu.edu.tw/~cjfu/gss.htm

Algorithms↗

PubMed1985

An integer linear programming model of staff retention and termination based on multiattribute utility theory.

An integer linear programming formulation was used to model several staffing alternatives available to the director of a recreation therapy department. The utility function of the decision maker was assessed using two attributes of effectiveness: performance and experience. Two utility approximations were obtained for each staff member based upon the average performance rating and number of years of experience both as a recreation therapist and at the facility. The utility obtained was viewed as a proxy for, and a comparative measure of, effectiveness, which considers the criteria of training and experience. The individuals who comprise the most effective combination of therapists, given staff reductions, were obtained by maximizing the sum of staff values. The first constraint set involved a budgetary constraint, coverage constraints, and an EEOC policy restriction. The coverage restriction and the budget were varied to reflect changes in the department resources. The model was validated with the department supervisor for the case of a one-position, 10% budget decrease.

Employment↗

PubMed1981

A linear programming model for determining efficient combinations of 8-, 10-, and 12-hour shifts.

I have formulated a linear programming model to determine changes in efficiency and productivity that would result from scheduling personnel to work combinations of 8-, 10-, and 12-hour shifts in a section of our pulmonary medicine department. My objective was to minimize the number of staff hours worked each day, subject to the constraints imposed by the levels of staffing required during each hour of the day. I found that a combination of 8-, 10- and 12-hour shifts could increase productivity 8.1% and reduce personnel requirements by one full-time equivalent. Salary expenses would decrease 7.5% if overtime were not paid for the extended hours of the 10- and 12-hour shifts. Two considerations in implementing the proposed schedule are the willingness of staff to work extended hours and the necessity of developing a format for communication between therapists who work discontinuous shifts.

Hospital Bed Capacity, 100 to 299↗

PubMed1998

A linear programming assessment of the profit from strategies to reduce the prevalence of Staphylococcus aureus mastitis.

We used a linear programming model to estimate the financial returns to a Staphylococcus aureus testing and control program over a 1-year period for a 100-cow herd, with a 8636-kg rolling-herd average. Six tests, which vary in sensitivity from 0.80 to 0.98 and specificity of 0.99, were examined in simulated herds with 10, 20 and 30% prevalence of S. aureus infection. Sensitivity of these results to a range of assumptions regarding rolling-herd average, milk price, somatic cell-count premium, and cost and cure rate of dry treatment were examined to determine the profits from the program. The profits of a control program are most dependent upon prevalence, cell-count premium, and cost of dry treatment. In our simulation for a 100-cow herd, a testing and control program appears to cost less than US$10 per cow per year, and pays for itself within 1 yr, except under the lowest prevalence and most-adverse conditions (low yield, high cost of dry treatment, or low SCC premium.

Animals↗

PubMed2000

Corrigendum to "A linear programming assessment of the profit from strategies to reduce the prevalence of Staphylococcus aureus mastitis" [Prev. Vet. Med. 33 (1998) 183-193].

We used a linear programming model to estimate the financial returns to a Staphylococcus aureus testing and control program over a 1-year period for a 100-cow herd, with a 8636kg rolling-herd average. Six tests, which vary in sensitivity from 0.80 to 0.98 and specificity of 0.99, were examined in simulated herds with 10, 20, and 30% prevalence of S. aureus infection. Sensitivity of these results to a range of assumptions regarding rolling-herd average, milk price, somatic cell-count premium, and cost and cure rate of dry treatment were examined to determine the profits from the program. The profits of a control program are most dependent upon prevalence and cell-count premium. In our simulation for a 100-cow herd, a testing and control program results in a profit ranging from US$1.50 to US$20 per cow per year, except under the lowest prevalence and most-adverse conditions (low yield or low SCC premium).

Agriculture↗

PubMed2006

Identification of nutritionally adequate mixtures of vegetable oils by linear programming.

OBJECTIVE: To determine the types and proportions of vegetable oils to recommend for a healthy diet. METHODS: Optimal vegetable oil combinations were designed, using linear programming and, as decision variables, nine single oils and 29 basic food items. 'Oil models' were run to determine whether reasonable amounts of individuals oils or oil mixtures satisfied a set of constraints on essential fatty acids and vitamin E. 'Meal models' were run to test whether selected mixtures could be used as the sole source of added fat in a meal that met micronutrient and macronutrient recommendations. RESULTS: The cheapest mixture (0.97 euro L(-1)) that solved the oil models contained 81% rapeseed and 19% sunflower oils. About 10-15 g of this mixture, alone or with olive, soya bean, wheat germ or walnut oils, also solved the meal models. Mixtures that contained a high proportion (>or=50%) of the tasty olive and walnut oils also solved the models but were more expensive (4.9 euro L(-1) and 8.5 euro L(-1), respectively). CONCLUSIONS: The consumption of a mixture composed of rapeseed and sunflower oils in a 4 : 1 proportion is an inexpensive and simple way to meet current dietary recommendations for essential fatty acids and vitamin E, favouring overall dietary nutrient adequacy.

Cost-Benefit Analysis↗

PubMed1982

Reversed-phase high-performance liquid chromatographic separation of saccharin, caffeine and benzoic acid using non-linear programming.

A method is described which allows a chromatographic assay to be optimized with respect to the time needed to complete an analysis, while maintaining good resolution. The method introduces an operational research technique called linear programming. It was used to optimize the eluent composition for the assay of saccharin, caffeine and benzoic acid and resulted in a significant reduction in the analysis time.

Benzoates↗

PubMedDate not supplied

The use of efficiency linear programs for sensitivity analysis in medical decision making.

Sensitivity analysis in most medical problems is a complex process involving repeated calculations that can be computationally cumbersome, and its results are only approximate. The authors present a linear program-based approach that reveals the optimum strategies in a decision problem when event probabilities are not known exactly but their value ranges are available. Its application in a clinical decision-making situation is demonstrated. The approach promises to provide a flexible, precise, and computationally efficient technique for sensitivity analysis in medical decision making.

Aged↗

PubMedDate not supplied

Impact of a cost constraint on nutritionally adequate food choices for French women: an analysis by linear programming.

OBJECTIVE: To predict, for French women, the impact of a cost constraint on the food choices required to provide a nutritionally adequate diet. DESIGN: Isocaloric daily diets fulfilling both palatability and nutritional constraints were modeled in linear programming, using different cost constraint levels. For each modeled diet, total departure from an observed French population's average food group pattern ("mean observed diet") was minimized. RESULTS: To achieve the nutritional recommendations without a cost constraint, the modeled diet provided more energy from fish, fresh fruits and green vegetables and less energy from animal fats and cheese than the "mean observed diet." Introducing and strengthening a cost constraint decreased the energy provided by meat, fresh vegetables, fresh fruits, vegetable fat, and yogurts and increased the energy from processed meat, eggs, offal, and milk. For the lowest cost diet (ie, 3.18 euros/d), marked changes from the "mean observed diet" were required, including a marked reduction in the amount of energy from fresh fruits (-85%) and green vegetables (-70%), and an increase in the amount of energy from nuts, dried fruits, roots, legumes, and fruit juices. IMPLICATIONS: Nutrition education for low-income French women must emphasize these affordable food choices.

Adolescent↗