Solver Function Research Articles

Development and testing of surface-based and water-based-diffusion kinetic models for studying hydrolysis and biogas production from cow manure

The hydrolytic step is usually considered the rate limiting step in the biological conversion of ligno-cellulose material into biofuels. Current optimization approach attempts to understand the mechanism of hydrolysis in order to boost production. In this study, the development and testing of a surface-based and a water-based-diffusion kinetic model for modeling biogas production from cow manure was conducted using total solid (TS) loading ranging from 8 to 10% (TS) in batch reactors. Parameter estimation using solver function of the Microsoft Excel Tool Pak revealed that, the second order water diffusion model was superior in predicting biogas production with correlation coefficients ranging from 0.9977 to 0.9995. In addition, the initial surface permeability flux of water (Kspf0) into the organic biomass and fragmentation of particles were observed to be independent events elicited by the action C1 and Cx factors respectively. The initial surface permeability flux of water was observed to increase as solids concentration increased from 8 to 9%TS while, fragmentation constants decreased. Maximum initial surface permeability flux of water (1.78E-05 m3/m2/day) was observed at 9% (TS) with a simultaneous minimization in the fragmentation rate (0.13/day). For optimal production of biofuels, appropriate quantity of C1-factor, the degree of crystallinity and particle size may be critical for efficient conversion.

A Methodology for Reducing Bench Strength in Information Technology Companies

One of the major risks in information technology (IT) project execution is the non-availability of resources with required skill sets to meet the project demands. To mitigate this risk, almost every IT organization maintains a portion of their resources on bench. The bench strength reduces the delay in starting the project due to the non- availability of skilled resources. But bench strength or buffer is cost to the company. A medium scale Indian IT company incurs around USD 142,347 monthly on maintaining the bench strength. Hence this study is undertaken to develop a methodology to reduce the bench strength in IT companies. The proposed methodology is to obtain an optimum mix of resources from bench and through recruitment to meet the demands at a minimum cost. This is done by formulating the problem as an integer programming problem. The problem aims to minimize the total cost of obtaining the skilled resources without violating the constraints on demand, bench strength availability and recruitment lead time. The problem can be solved using Microsoft excel solver function or any other optimization packages like CPLEX, Gurobi, etc. A case study on the application of proposed methodology is also discussed in the paper. The case study showed that the proposed methodology is superior to the existing practice of maintaining large bench strengths to meet the demands for resources with various skills.

Toward cost-effective staffing mixes for Veterans Affairs substance use disorder treatment programs.

BackgroundIn fiscal year (FY) 2008, 133,658 patients were provided services within substance use disorders treatment programs (SUDTPs) in the U.S. Department of Veterans Affairs (VA) health care system. To improve the effectiveness and cost-effectiveness of SUDTPs, we analyze the impacts of staffing mix on the benefits and costs of specialty SUD services. This study demonstrates how cost-effective staffing mixes for each type of VA SUDTPs can be defined empirically.MethodsWe used a stepwise method to derive prediction functions for benefits and costs based on patients’ treatment outcomes at VA SUDTPs nationally from 2001 to 2003, and used them to formulate optimization problems to determine recommended staffing mixes that maximize net benefits per patient for four types of SUDTPs by using the solver function with the Generalized Reduced Gradient algorithm in Microsoft Excel 2010 while conforming to limits of current practice. We conducted sensitivity analyses by varying the baseline severity of addiction problems between lower (2.5 %) and higher (97.5 %) values derived from bootstrapping.Results and conclusionsCompared to the actual staffing mixes in FY01-FY03, the recommended staffing mixes would lower treatment costs while improving patients’ outcomes, and improved net benefits are estimated from $1472 to $17,743 per patient.

OBJECT-ORIENTED PROGRAMMING IN MESHFREE ANALYSIS OF ELASTOSTATIC PROBLEMS

In this work, the main philosophy behind the object-oriented programming (OOP) of meshfree methods is discussed for solution of elastostatic problems. Objects and classes are constructed with respect to the structure of meshfree methods. Local radial point interpolation method (LRPIM) and meshless local Petrov-Galerkin (MLPG) method are used in local weak form in the program. Basic object oriented programming operators; encapsulation, inheritance and polymorphism are used for increasing modularity. Seven main classes and their subclasses are constructed for decreasing complexity. Additional storage modules and solver functions are implemented. As a result of this, new techniques on interpolations and integrations can be easily adapted to construction of shape functions in meshfree program structure. Objects are defined and implemented for solution of 2D elastostatic problems in MATLAB. Two elestostatic problems are solved in MATLAB OOP and their results are compared with results of a procedural program that is written in FORTRAN. Class designs and their hierarchy are discussed in details

Optimum Blending Requirements for EVA Modified Binder

Increase in traffic, new axle configurations and high temperature demands the use of modified binders for resisting the stresses induced in pavement. Ethylene Vinyl Acetate (EVA) is a plastomer, which is a copolymer obtained by copolymerization of ethylene and vinyl acetate. Though a potential modifier, problems of phase separation have been encountered attributable to the presence two separate phases of bitumen and polymer which are incompatible with each other. This paper focuses on obtaining the optimum blending requirement for EVA copolymer. A VG 10 binder was modified at varying percentages of EVA from 1 to 7%. Modification was carried out at different combination of mixing temperature, blending time and shear rate and a total of 80 combinations were obtained. Statistical package for social sciences (SPSS) and SOLVER function was used to assess the optimum blending requirement. Further the paper evaluated the optimum modifier content for obtaining a homogenous blend which could be stable at high temperature. Physical and rheological properties of the modified binder was also evaluated and compared with the base binder. It was found that temperature is the most critical parameter for EVA modification. Shear rate had the minimum influence over obtaining a storage stable blend. Fluorescence microscopy showed change in morphology as the modifier content increased, which could be used to assess the optimum modifier content for modification. Rheological response of the modified binder significantly improved. EVA modification was found to be best suited at high temperatures and could be very effective to resist rutting of mixtures.

Compute Critical and Normal Depths of Arch and Elliptical Pipes

AbstractArch and elliptical pipes are commonly used as roadway culverts. The pipe section is composed of three radii, which result in complex equations to compute cross-sectional geometry and hydraulic parameters, such as normal and critical depths. Basic sizing charts do not allow direct calculation of hydraulic properties of these pipe sections. Therefore, general formulas were developed to compute hydraulic properties for any given arch pipe cross section. An Excel workbook capable of calculating normal and critical depths for given flow rates was created using the developed formulas and the solver function. Worksheets to compute geometric properties and water surface profiles using the direct-step method were also developed. These user-friendly worksheets are useful for hydraulic design and analysis of arch and elliptical culverts. A case study was conducted on several standard pipe geometries to demonstrate the comparative results from the developed workbook and existing sizing charts.

Behavior of the Lubricating Film between Sinusoidal Roughened Surfaces

A theoretical model of roughened sliding surfaces with a sinusoidal profile is applied in the context of determining the pressure distribution, positive load support, and maximal hydrodynamic pressure in the lubricating film. Considered are surfaces with identical asperity heights and wave number characteristics. The obtained relations are verified numerically with the aid of the bvp4c solver and other functions for numeric calculations of the MATLAB® program. The influence of the wave number and asperity heights on the load support and maximal positive pressure is investigated parametrically over the wide range of gap-to-asperity-height ratios and wave number roughness characteristics. In addition, the cavitation and maximal pressures are compared. Specially developed MATLAB® programs permit to calculate pressure distribution, positive load support, and maximal hydrodynamic pressure in the lubricating film by the derived expressions.

Estimation of Parameters related to SFTSV (Severe Febrile Thrombocytopenia Syndrome Virus) Transmission of Sheep in Shandong, China

In this study, it has been carried out that estimation of mathematical models of SFTSV (severe febrile thrombocytopenia syndrome virus) transmission between sheep in Shandong, China. Data used in the system identification is obtained by observing the cohort group of sheep in Shandong Province, China by Chinese scientists. Observation of the cohort was carried out approximately every week, and it was measured that the number of SFTSV antibody positive animals. As a mathematical model, endemic SIR model was selected. System identification is performed using the solver function of the spreadsheet. The software and solver were Microsoft Excel2010 and GRG (Generalized Reduced Gradient) nonlinear method. After complemented of observed values with polynomial curve, logistic curve and the Gompertz curves, the system identification was conducted and initial values of parameters and initial value of variable were estimated. As the result of system identification, the value of basic reproduction indicating virus transmission was estimated as the value of 34-45. This system identification is included many estimation. However the result suggested that this disease has strong infectious force.

Using Excel's Solver Function To Facilitate Reciprocal Service Department Cost Allocations

The reciprocal method of service department cost allocation requires linear equations to be solved simultaneously. These computations are often so complex as to cause the abandonment of the reciprocal method in favor of the less sophisticated and theoretically incorrect direct or step-down methods. This article illustrates how Excel's Solver Function can be used to greatly simplify the reciprocal cost allocation method. Solver Function users will be pleased to see how easy it is to let Excel do the mathematics once the linear equations are formulated.

A comparative study of the influence of shift factor equations on master curve construction

This paper evaluates the applicability of different shifting techniques for constructing complex modulus master curves using the time-temperature superposition principle (TTSP). A database of complex modulus results of unmodified bitumens, polymer modified bitumens (PMBs), bitumen-filler mastics, unaged and aged bitumens was used together with a Generalized Logistic Sigmoidal Model to assess the validity of seven different shifting approaches. Except for the Laboratoire Central des Ponts et Chaussees (LCPC) method, the construction of master curves was done using the Generalised Logistic Sigmoidal Model and non-linear least squares regression optimization with the aid of the Microsoft Excel Spreadsheet Solver function. The goodness-of-fit for the various shifting techniques and functions was assessed through graphical and statistical methods. From the study, it was found that a numerical shift approach using non-linear least squares produced the best fit between experimental and predicted data in terms of both graphical and goodness-of-fit statistics. The ranking of the other shifting techniques consisted of the LCPC approach, followed by the William, Landel and Ferry (WLF), Modified Kaelble, Viscosity Temperature Susceptibility (VTS), Arrhenius and Log-Linear methods. However, most of the equations are basically empirical and they are not expected to be strictly obeyed by any materials. Discrepancies were still evident, even for the better functions, for those materials that demonstrated a deviation from the thermorheological simplicity of the rheological behaviour as found for highly structured bitumens following high degrees of polymer modification and/or oxidative ageing.

Erratum to: Fitting net photosynthetic light-response curves with Microsoft Excel - a critical look at the models

In this study, we presented the most commonly employed net photosynthetic light-response curves (PN/I curves) fitted by the Solver function of Microsoft Excel. Excel is attractive not only due to its wide availability as a part of the Microsoft Office suite but also due to the increased level of familiarity of undergraduate students with this tool as opposed to other statistical packages. In this study, we explored the use of Excel as a didactic tool which was built upon a previously published paper presenting an Excel Solver tool for calculation of a net photosynthetic/chloroplastic CO2-response curve. Using the Excel spreadsheets accompanying this paper, researchers and students can quickly and easily choose the best fitted PN/I curve, selecting it by the minimal value of the sum of the squares of the errors. We also criticized the misuse of the asymptotic estimate of the maximum gross photosynthetic rate, the light saturation point estimated at a specific percentile of maximum net photosynthetic rate, and the quantum yield at zero photosynthetic photon flux density and we proposed the replacement of these variables by others more directly linked to plant ecophysiology.

A spreadsheet for calculation of ingredients for standardization of requeijão cremoso

The standardization of requeijão cheese quality characteristics is a processing stage which is directly influenced by the chemical composition of the raw material. Fat and water concentrations are the main factors that cause variation in quality properties of the requeijão and, when not thoroughly controlled, may cause a lack in standardization of the food. Calculations of ingredients for effective standardization must be made in relation to the final product through of iterative calculations, which makes the manual process unfeasible. Thus, the objective of the present study was to develop a spreadsheet for ingredient calculation, with restrictions being the different concentrations of fat and water in order to standardize the final products. The spreadsheet was developed using the Excel 2007® Solver function, with just four input data: quantity of mass, water and fat content of the mass and fat content of the cream. The optimal solution was that which maximizes the amount of final product while meeting the stipulated constraints of fat and water. Results obtained with the spreadsheet were validated by processing the requeijão cheeses and comparison of the theoretical and practical parameters using the t-test. There was no significant difference between fat and water contents (p>0.10) estimated and verified in practice. Therefore, the use of the spreadsheet proved to be efficient for standardization of requeijão formulations.

Discussion of “Parameter Estimation of the Nonlinear Muskingum Model Using Parameter-Setting-Free Harmony Search” by Zong Woo Geem

First of all, the discusser would like to thank the author for using parameter-setting-free harmony search (PSF-HS) to estimate the parameters of the nonlinear Muskingum model and would like to draw attention to some points and suggest a practical way for parameter estimation of the nonlinear Muskingum model. In the original paper, the available methods for the parameter estimation of the nonlinear Muskingum model are impliedly classified as two groups. This division consists of (1) mathematical techniques, and (2) phenomenon-mimicking algorithms. However, it is notable that the procedures such as the neuro-fuzzy approach (Chu 2009) that cannot be classified in these two groups can be utilized for the purpose of estimating the parameters of the nonlinear Muskingum model. The discusser is unanimous with the author that the methods of the former group have weaknesses of the complex derivative requirement and/or initial vector assumption of design parameters, and the trouble of the methods of the latter group is that these methods need the determination of the algorithm parameters. However, it is notable that the latter group is randomly searched for the optimal solution, and some uncertainties that may cause different solutions on different runs existed when using the phenomenon-mimicking algorithms to estimate the parameters of the nonlinear Muskingum model. In this discussion, an alternative way was proposed for the parameter estimation to avoid the sensitivity analyses of either algorithm parameters or initial values assumption of the hydrologic parameters. In this procedure during two stages the methods of the mathematical techniques and phenomenon-mimicking algorithms are used. In this way, at first stage the phenomenonmimicking algorithm is run, and after a few seconds in the middle of the operation, the model can be stopped. In the second stage, the values obtained for the hydrologic parameters from the phenomenon-mimicking algorithm are considered as the initial guess of the hydrologic parameters for the mathematical technique. In this condition, the sensitivity analyses of either algorithm parameters or initial values assumption are not necessary. Therefore, finding the optimal solution can be done in the shortest operating time. If the near-optimal result is achieved in the first run of the mathematical technique, it is possible that the optimal result is reached with one extra run of the mathematical technique at the second stage. If infeasible, divergent, or faraway-optimal results are achieved, the procedure must be repeated from the first stage, but these results do not happen with a high probability. For this procedure, two combinations of methods are offered. These combinations consist of (1) genetic algorithm (GA; Mohan 1997) and Nelder-Mead simplex algorithm (NMS; Barati 2011) as GANMS, and (2) evolutionary (EV; Premium Solver Platform 2010) and Broyden–Fletcher–Goldfarb–Shanno technique (BFGS; Geem 2006; Premium Solver Platform 2010) as EV-BFGS. The GA-NMS and EV-BFGS procedures can be modeled by the Optimization Tool add-in of MATLAB software (Yang et al. 2005) and by the Excel Solver function add-in of Microsoft Excel software (Premium Solver Platform 2010), respectively. Therefore, these two procedures are widely available for engineers, and hydrologists

Determination of protein concentration for protein–protein conjugates using ultraviolet absorption

The present study reports a method to determine the total protein concentration or concentration of a protein of interest in a protein–protein conjugate using ultraviolet absorption, after determining the molar ratio of proteins in the conjugates, from which an extinction coefficient can be calculated. A Microsoft Excel solver-based template using amino acid analysis data was developed for determining the molar ratio. The percent mass of each protein in the conjugate is calculated from the amino acid composition data using the least squares method in the Microsoft Excel solver function, and the percent mass is converted to molar portion of each protein using corresponding molecular weight. A molar ratio is obtained by dividing the molar portion of protein 1 by the molar portion of protein 2. A weighted extinction coefficient is calculated using the molar ratio, and the total protein concentration is determined using ultraviolet absorption at 280nm. The accuracy of the method was verified using mixtures of known proteins. The present study provides a rapid, simple and accurate method for determining protein concentration in protein–protein conjugates.

Synthesis of palm oil-based trimethylolpropane ester as potential biolubricant: Chemical kinetics modeling

The environmental impact of large amounts of lubricants from mineral oils has become an increasingly important issue. The use of rapidly biodegradable lubricants, vegetable products as well as modified vegetable oil esters, could significantly reduce the environmental pollution compared to mineral oils. A kinetic/mathematical model describing chemical transesterification of palm oil-based methyl esters (POMEs) with trimethylolpropane (TMP) to polyol esters has been developed. The kinetics of the transesterification reaction was modeled as three distinct elementary reversible series–parallel reaction mechanisms. The model considers the transesterification reaction to take place in both forward and reverse directions. The resulting kinetics equations were solved using ode45 solver function in MATLAB, where the rate constants of the proposed kinetic model were determined by minimization of errors based on the optimum criteria of statistical analysis and by comparing the component concentrations at maximum and at equilibrium. The forward and reverse rate constants of all three steps involved in the transesterification reaction were reported. The validity of the model was tested by comparing the observed experimental values with the theoretical calculated data. A good correlation between simulated results and experimental data was observed, confirming that the model was able to predict the rate constants with plausible accuracy. The new proposed kinetic model would facilitate the design of a pilot-scale chemical reactor for the transesterification of POME with TMP to obtain palm oil-based polyol esters as a potential biolubricant.

An improved method of fitting experimental data to the Hoek–Brown failure criterion

In this study, a special fitting technique is proposed to apply the Hoek–Brown failure criterion to available laboratory strength data collected on samples of Ankara andesites. The original method of fitting the Hoek–Brown failure criterion using the spreadsheet and the fitting method utilized in the RocLab software are statistically compared with this new modified nonlinear fitting technique. The Hoek–Brown failure parameters obtained by a simple multiple regression technique, utilizing the solver function within an Excel spreadsheet and the revised least squares procedure significantly improved the fitness of the Hoek–Brown envelope especially within the tensile and high confining stresses. The Brazilian tensile strength is found to be a useful parameter to fix a rock failure criterion at low confining stresses, particularly, in the tensile region. If tensile, uniaxial and triaxial test results are available, when compared to two existing fitting methods the modified multiple regression method is found to predict more precise tensile and compressive strengths, and material constant mi for the Hoek–Brown failure criterion.

Optimization Problem of Excel Programming Calculation for Mayonnaise Prescription

The method combining linear programming theory and computer technology, affords the possibility for the Optimization problem of food prescription in engineering design. Excel's Solver function may be used to solve problems with up to 200 decision variables, enough to calculate the most problems about food prescription. Combined design requirement of mayonnaise prescription, the decision variables, constraint condition and mathematics model of cost are established. The optimization prescription of minimum cost is gotten through the function of Excel programming calculation. It may provide valuable reference for the application of computer in prescription design.

Simulasi Perdagangan Kontrak Berjangka CPO pada Bursa Malaysia dengan Cyclic Forecasting Periode Januari-Desember 2009

Crude palm oil (CPO) is one commodity that could be consumed and also as one alternative of non- fossil fuel: biodiesel. Since 2006, CPO commodity trade has its significant raise, followed by forward contract trade. The increasing of CPO price in 2006 is the lowest in historic analysis data period 2007-2008. Cyclic forecasting model is used following cycle pattern of twice-a-year, with a combination of Solver function in Ms. Excel that could minimize MSE as 161,02, Beta 0,0688 and intercept in -11,0396. Cyclic forecasting period is supposed to be used along with technical analysis, using stop loss to reduce risk. It needs additional research to adjust confidence level so VaR value is not too high that could fix trading strategy along this research.

Calibration of the Mechanistic–Empirical Pavement Design Guidefor Flexible Pavement Design in Arkansas

Because of potential differences between national and local conditions, the Mechanistic–Empirical Pavement Design Guide (MEPDG) should be calibrated to a local level. Arkansas has invested heavily in efforts to implement the MEPDG. This paper summarizes the initial local calibration of flexible pavement models in the MEPDG for Arkansas. Data from the Long-Term Pavement Performance (LTPP) database and local pavement management system (PMS) were used. The solver function in Microsoft Excel was used to optimize the coefficients for alligator cracking. Iterative runs of the MEPDG by means of discrete calibration coefficients were conducted to optimize rutting models. In general, the alligator cracking and rutting models are improved by calibration. However, a question remains about the suitability of the calibrated models for routine design. Many default values were used in the MEPDG because of a lack of data. It is recommended that additional sites be established and a more robust data collection procedure be implemented for future calibration efforts. The difference in the definitions of transverse cracking between the MEPDG and the LTPP may be critical to data collection and identification. Thermal cracking should be specifically identified in a transverse cracking survey to calibrate the transverse cracking model in MEPDG. The procedure using LTPP and PMS data for local calibration of the MEPDG in Arkansas is established. Additional development of database software for data manipulation, preprocessing, and quality control—under way in Arkansas—will significantly streamline the calibration process.

A comparison of some numerical methods in solving 1-D steady-state advection dispersion reaction equation

This article is devoted to giving comprehensive description about some numerical schemes in solving 1-D transport and reaction differential equation under steady-state condition. The schemes used include the finite difference method, the shooting method, and the collocation method. Besides those schemes, this article also provides brief review of the continually stirred tank reactors (CSTRs) approach compared with the partial differential equations (PDEs) model that makes use of pdepe solver function of MATLAB. Based on the results obtained, it is shown that the finite difference method is less accurate compared with other methods, especially when the Dirichlet condition is applied. When Neumann condition is used, however, all schemes show almost similar accuracy for small step sizes. Although the CSTRs system generally results in error three to four times greater than PDEs model for the same grid spacing, its inaccuracy can be lowered by increasing the number of cells. Moreover, a simple application in developing dissolved oxygen sag curve for nontidal large river or estuary has strongly offered another possibility of pdepe solver to be used in either teaching-learning processes or even further applications in water quality modelling.