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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.

Math. Comput. Appl., Volume 16, Issue 2 (August 2011) – 23 articles , Pages 317-555

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Open AccessArticle
Effect of Abutment and Implant Shapes on Stresses in Dental Applications Using Fem
Math. Comput. Appl. 2011, 16(2), 546-555; https://doi.org/10.3390/mca16020546 - 01 Aug 2011
Cited by 6 | Viewed by 1041
Abstract
In this study, the effect of abutment and implant shapes on stresses in dental applications was investigated, numerically. During the numerical analysis, finite element method (FEM) was used due to a powerful stress analysis method. The three different abutment-implant systems based on producing [...] Read more.
In this study, the effect of abutment and implant shapes on stresses in dental applications was investigated, numerically. During the numerical analysis, finite element method (FEM) was used due to a powerful stress analysis method. The three different abutment-implant systems based on producing from different commercial firms were modeled. The Nextengine and Rhinoceros programs were used for three dimensional tooth scan and creation of the solid models. Additionally, Algor Fenpro analysis program was used for three dimensional stress analyses. According to obtained results, the Von Mises stress distributions on abutment, implant and cortical bone are affected from abutment and implant shapes, clearly. If it is possible, the using of any hole in the implant should not be used. Additionally, the bigger collars on the abutment provide to reduce of Von Mises stresses. Full article
Open AccessArticle
Simulation of Dilatometer Tests by Neural Networks
Math. Comput. Appl. 2011, 16(2), 535-545; https://doi.org/10.3390/mca16020535 - 01 Aug 2011
Cited by 1 | Viewed by 925
Abstract
Rock rigidity may be experienced in a wide range depending on several factors, and different methods can be used to consider their load-deformation behaviors. In this context, dilatometer tests (DTs) can be applied to obtain the modulus of elasticity of rock masses; therefore, [...] Read more.
Rock rigidity may be experienced in a wide range depending on several factors, and different methods can be used to consider their load-deformation behaviors. In this context, dilatometer tests (DTs) can be applied to obtain the modulus of elasticity of rock masses; therefore, it is possible to evaluate in-situ stress-strain behavior of rock masses realistically. Nevertheless, the application of this test is expensive as well as time-consuming, and necessitates mobilization of the equipment to construction site by trucks. The aim of this study is to simulate the load-deformation curve obtained of DT by neural networks (NNs). Therefore, the dilatometer test can be modeled as well as synthetic simulation of the test enables analyzers to characterize the material behavior. In order to investigate this, 50 different stress-deformation curves are obtained from DTs conducted on limestone formation underlying a dam (Dim dam) construction site in the Southern part of Turkey. The developed database by the curves was used for training and testing of the NN models. The results revealed that NN technique is quite successful for modeling the stress-deformation behavior of specific rocks based on DT results. It is therefore possible with the help of this alternative tool developed for the simulation of DT i) to model DT numerically, ii) to simulate the stress-strain behavior successfully, iii) to calculate the modulus of deformation efficiently, iv) to generate additional DT data synthetically, v) to develop material model alternatively, and vi) to make assumptions on the characterization of the rock mass behavior using previous information gathered by DTs. Full article
Open AccessArticle
Differential Quadrature Solution for One-Dimensional Aquifer Flow
Math. Comput. Appl. 2011, 16(2), 524-534; https://doi.org/10.3390/mca16020524 - 01 Aug 2011
Cited by 9 | Viewed by 802
Abstract
Differential Quadrature Method (DQM) has been applied to the solution of aquifer flow problems. Three examples from of each of the three one-dimensional aquifer flow equation problems, a confined aquifer flow with time dependent boundary conditions, a composite confined aquifer and an unconfined [...] Read more.
Differential Quadrature Method (DQM) has been applied to the solution of aquifer flow problems. Three examples from of each of the three one-dimensional aquifer flow equation problems, a confined aquifer flow with time dependent boundary conditions, a composite confined aquifer and an unconfined aquifer with seepage, were examined. The results of DQM solution were then compared with the results obtained from analytical solution, the Explicit Finite Differences Method and Implicit Finite Differences Method. Based on the comparison results, it was concluded that the DQM provides similar results but with relatively faster calculation speed, less nodes and memory usage. Full article
Open AccessArticle
An Integrated Neural Network Structure for Recognizing Autocorrelated and Trending Processes
Math. Comput. Appl. 2011, 16(2), 514-523; https://doi.org/10.3390/mca16020514 - 01 Aug 2011
Cited by 4 | Viewed by 708
Abstract
Data sets collected from industrial processes may have both a particular type of trend and correlation among adjacent observations (autocorrelation). In the present paper, an integrated neural network structure is used to recognize trend stationary first order autoregressive (trend AR(1)) process. The proposed [...] Read more.
Data sets collected from industrial processes may have both a particular type of trend and correlation among adjacent observations (autocorrelation). In the present paper, an integrated neural network structure is used to recognize trend stationary first order autoregressive (trend AR(1)) process. The proposed integrated structure operates as follows. (i) First a combined neural network structure (CNN), that is composed of appropriate number of linear vector quantization (LVQ) and multi layer perceptron (MLP) neural networks, is used to recognize the trended data, (ii) then, the Elman’s recurrent neural network (ENN) is used to diagnose the autocorrelation through the data. Correct classification rate is used as performance criteria. Results indicate that proposed structure is effective and competitive with other combined neural network structures. Full article
Open AccessArticle
The Differential Transformation Method and Pade Approximant for a Form of Blasius Equation
Math. Comput. Appl. 2011, 16(2), 507-513; https://doi.org/10.3390/mca16020507 - 01 Aug 2011
Cited by 12 | Viewed by 968
Abstract
Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. The aim of this study is to overcome this difficulty by using Padé approximation with the differential transform method (DTM) on a [...] Read more.
Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. The aim of this study is to overcome this difficulty by using Padé approximation with the differential transform method (DTM) on a form of classical Blasius equation. The obtained results are compared with, for the first time, the ones obtained by using a modified form of Adomian decomposition method (ADM). Furthermore, in order to see the consistency of solutions, they are also compared with the ones obtained by using variational iteration method (VIM). Full article
Open AccessArticle
Hermite Series Solutions of Linear Fredholm Integral Equations
Math. Comput. Appl. 2011, 16(2), 497-506; https://doi.org/10.3390/mca16020497 - 01 Aug 2011
Cited by 3 | Viewed by 659
Abstract
A matrix method for approximately solving linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Hermite series approximation. The method is based on first taking the truncated Hermite series expansions of the functions in equation and then [...] Read more.
A matrix method for approximately solving linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Hermite series approximation. The method is based on first taking the truncated Hermite series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear system of algebraic equations with unknown Hermite coefficients. In addition, some equations considered by other authors are solved in terms of Hermite polynomials and the results are compared. Full article
Open AccessArticle
An Integrated Intuitionistic Fuzzy Multi Criteria Decision Making Method for Facility Location Selection
Math. Comput. Appl. 2011, 16(2), 487-496; https://doi.org/10.3390/mca16020487 - 01 Aug 2011
Cited by 42 | Viewed by 1468
Abstract
The facility location selection, which is one of the important activities in strategic planning for a wide range of private and public companies, is a multi-criteria decision making problem including both quantitative and qualitative criteria. Traditional methods for facility location selection can not [...] Read more.
The facility location selection, which is one of the important activities in strategic planning for a wide range of private and public companies, is a multi-criteria decision making problem including both quantitative and qualitative criteria. Traditional methods for facility location selection can not be effectively handled because information can not be represented by precise information under many conditions. This paper proposes the integration of intuitionistic fuzzy preference relation aiming to obtain weights of criteria and intuitionistic fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method aiming to rank alternatives for dealing with imprecise information on selecting the most desirable facility location. To illustrate the application of the proposed method, a practical application is given. Full article
Open AccessArticle
Differential Quadrature Solutions of the Generalized Burgers–Fisher Equation with a Strong Stability Preserving High-Order Time Integration
Math. Comput. Appl. 2011, 16(2), 477-486; https://doi.org/10.3390/mca16020477 - 01 Aug 2011
Cited by 4 | Viewed by 699
Abstract
Numerical solutions of the generalized Burgers-Fisher equation are presented based on a polynomial-based differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a third-order strong stability preserving Runge-Kutta scheme in time [...] Read more.
Numerical solutions of the generalized Burgers-Fisher equation are presented based on a polynomial-based differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a third-order strong stability preserving Runge-Kutta scheme in time have been used. The proposed technique successfully worked to give reliable results in the form of numerical approximation converging very rapidly. The computed results have been compared with the exact solution to show the required accuracy of the method. The approximate solutions to the nonlinear equations were obtained. The approach is seen to be a very reliable alternative to the rival techniques for realistic problems. Full article
Open AccessArticle
Search on Results of Ibm for Region between 120 ≤ A ≤ 150: 120-128Te and 122-134 Xe Nuclei
Math. Comput. Appl. 2011, 16(2), 467-476; https://doi.org/10.3390/mca16020467 - 01 Aug 2011
Cited by 6 | Viewed by 688
Abstract
In this work, the energy levels and transition probabilities B(E2) of some even-even Te (Z=52, N=68-80 and N=84) and even-even Xe nuclei (Z=54, N=68-80 and N=84-88) have been investigated by using the interacting boson model [...] Read more.
In this work, the energy levels and transition probabilities B(E2) of some even-even Te (Z=52, N=68-80 and N=84) and even-even Xe nuclei (Z=54, N=68-80 and N=84-88) have been investigated by using the interacting boson model (IBM-1 and IBM-2). The results were compared with some previous experimental and theoretical values. It was seen that an acceptable degree of agreement between the predictions of the model (IBM-1 and IBM-2) and the experiment is achieved. Full article
Open AccessArticle
Evaluation of Optimal Sensor Placement Techniques for Parameter Identification in Buildings
Math. Comput. Appl. 2011, 16(2), 456-466; https://doi.org/10.3390/mca16020456 - 01 Aug 2011
Cited by 3 | Viewed by 682
Abstract
This paper addresses the application of six different optimal sensor placement (OSP) techniques in buildings. These techniques are the EFfective Independence (EFI), Optimal Driving Point (ODP), Non-Optimal Driving Point (NODP), Effective Independence Driving Point Residue (EFI-DPR), Singular Value Decomposition (SVD) and the Sensor [...] Read more.
This paper addresses the application of six different optimal sensor placement (OSP) techniques in buildings. These techniques are the EFfective Independence (EFI), Optimal Driving Point (ODP), Non-Optimal Driving Point (NODP), Effective Independence Driving Point Residue (EFI-DPR), Singular Value Decomposition (SVD) and the Sensor Set Expansion (SSE) methods. A toolbox OPTISEP is developed by the author for this purpose within the context of this paper. The techniques are compared among themselves by using various criteria. The overall results show that the SSE Technique is the best. First, the technique results in a dramatic reduction in the computational effort. Second, it allows a civil engineer to specify a set of locations that they absolutely want to keep in the final sensor configuration. Mozst importantly, while the sensor distribution estimated by other techniques is mainly concentrated in a certain storey of the building, SSE gives a homogeneous sensor distribution throughout the building. Finally, it is shown that the technique i s also robust against noise in the measurements. Full article
Open AccessArticle
Numerical Solution for Solving Burger's-Fisher Eguation by Using Iterative Methods
Math. Comput. Appl. 2011, 16(2), 443-455; https://doi.org/10.3390/mca16020443 - 01 Aug 2011
Cited by 5 | Viewed by 1009
Abstract
In this paper, a Burger’s-Fisher equation is solved by using the Adomian’s decomposition method (ADM) , modified Adomian’s decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution [...] Read more.
In this paper, a Burger’s-Fisher equation is solved by using the Adomian’s decomposition method (ADM) , modified Adomian’s decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods. Full article
Open AccessArticle
Continuous Dependence for the Damped Nonlinear Hyperbolic Equation
Math. Comput. Appl. 2011, 16(2), 437-442; https://doi.org/10.3390/mca16020437 - 01 Aug 2011
Cited by 3 | Viewed by 622
Abstract
This paper gives the continuous dependence of solutions for the damped nonlinear hyperbolic equation. Full article
Open AccessArticle
The Prediction of Swell Percent and Swell Pressure by Using Neural Networks
Math. Comput. Appl. 2011, 16(2), 425-436; https://doi.org/10.3390/mca16020425 - 01 Aug 2011
Cited by 25 | Viewed by 791
Abstract
Expansive soils exhibit significantly high volumetric deformations and so pose a serious threat to stability of the structures and foundations. Thus, determination of their swelling properties (i.e. swelling potential and swell pressure) becomes essential. However, measurement of the swelling properties is time-consuming and [...] Read more.
Expansive soils exhibit significantly high volumetric deformations and so pose a serious threat to stability of the structures and foundations. Thus, determination of their swelling properties (i.e. swelling potential and swell pressure) becomes essential. However, measurement of the swelling properties is time-consuming and requires special and expensive equipment. With this in view, efforts were made to develop artificial neural network (ANN) and multiple regression analysis (MRA) models that can be employed for estimating swell percent and swell pressure. To achieve this, the results of free swell tests performed on statically compacted specimens of Kaolinite-Bentonite clay mixtures with varying soil properties were used. Two different ANN (ANN-1 and ANN-2) and MRA (MRA-1 and MRA-2) models have been developed: ANN-1 and MRA-1 models for predicting swell percent and ANN-2 and MRA-2 models for predicting swell pressure. The results obtained from ANN and MRA models were compared vis-à-vis those obtained from the experiments. The values predicted from the ANN models match the experimental values much better than those obtained from MRA models. Moreover, several performance indices such as determination coefficient (R2), variance account for (VAF), mean absolute error (MAE), and root mean square error (RMSE) were calculated to check the prediction capacity of the ANN and MRA models developed. The obtained indices make it clear that the constructed ANN models have shown higher prediction performance than MRA models. It has been demonstrated that the ANN models can be used satisfactorily to predict swell percent and swell pressure as a rapid inexpensive substitute for laboratory techniques. Full article
Open AccessArticle
A New Expression for Radial Distribution Function of Nuclear Matter
Math. Comput. Appl. 2011, 16(2), 414-424; https://doi.org/10.3390/mca16020414 - 01 Aug 2011
Cited by 3 | Viewed by 645
Abstract
A Variational Monte Carlo Method (VMC) is used for the calculations of radial distribution function of nuclear matter. Urbana 14 v potential is used for the nucleon-nucleon interactions in the calculations. The new expression for radial distribution function of nuclear matter is obtained [...] Read more.
A Variational Monte Carlo Method (VMC) is used for the calculations of radial distribution function of nuclear matter. Urbana 14 v potential is used for the nucleon-nucleon interactions in the calculations. The new expression for radial distribution function of nuclear matter is obtained by fitting of Monte Carlo simulations results to a function. Full article
Open AccessArticle
Experimental and Comparative Study of Different Fibers on the Strength and Failure of Quasi-Isotropic Plastic Composite with a Hole
Math. Comput. Appl. 2011, 16(2), 404-413; https://doi.org/10.3390/mca16020404 - 01 Aug 2011
Viewed by 600
Abstract
In the present study, the effects of different types of fibers on the strength and failure Mechanism of quasi-isotropic silicon carbide/epoxy composite laminate with reinforced hole has been carried out experimentally. The composite panels under compression loadings have been investigated In order to [...] Read more.
In the present study, the effects of different types of fibers on the strength and failure Mechanism of quasi-isotropic silicon carbide/epoxy composite laminate with reinforced hole has been carried out experimentally. The composite panels under compression loadings have been investigated In order to verify the experimental results were compared with the finite element method. A rectangular element with nine nodes has been chosen. Composite plate is meshed into 64 elements and 288 nodes with simply supported and in-plane loading conditions. Two types of reinforcement boundary conditions were investigated; adhesive bonded and snug-fit unbounded plug. For each case, five different sizes of hole diameter were used. And also three different types of reinforcing material (steel, aluminum and Eglass) were employed. Full article
Open AccessArticle
The Effects of Temperature and Thermal Stresses on Impact Damage in Laminated Composites
Math. Comput. Appl. 2011, 16(2), 392-403; https://doi.org/10.3390/mca16020392 - 01 Aug 2011
Cited by 10 | Viewed by 642
Abstract
The aim of this study is to investigate the effects of temperature and thermal residual stresses on the impact behavior and damage of unidirectional glass/epoxy laminated composites. To this end, thermal stress analyses of the laminates with lay-ups [90/0/0/90]s, [90/0/45/45]s, [0/90/45/-45]s were carried [...] Read more.
The aim of this study is to investigate the effects of temperature and thermal residual stresses on the impact behavior and damage of unidirectional glass/epoxy laminated composites. To this end, thermal stress analyses of the laminates with lay-ups [90/0/0/90]s, [90/0/45/45]s, [0/90/45/-45]s were carried out under temperatures of 20, 90 and -50 °C by using ANSYS software. Damage parameters proposed by Hou et al. [13] were used for failure analyses. Also, the impact tests on the laminated composites were performed at the impact energies ranging from 5 J to 55 J under the mentioned temperatures. The specific energy values and impact parameters were obtained and compared for each type of specimens and temperatures. The results obtained from both thermal stress analyses and impact tests indicated that the contribution of thermal stresses to impact damage increases with decreasing temperature and therefore, the stresses at low temperatures have a significant effect on the impact damage and parameters of unidirectional laminated composites. Full article
Open AccessArticle
Recovering Sinusoids from Noisy Data Using Bayesian Inference with Simulated Annealing
Math. Comput. Appl. 2011, 16(2), 382-391; https://doi.org/10.3390/mca16020382 - 01 Aug 2011
Viewed by 665
Abstract
In this paper, we studied Bayesian analysis proposed by Bretthorst[6] for a general signal model equation and combined it with a simulated annealing (SA) algorithm to obtain a global maximum of a posterior probability density function (PDF) for frequencies. Thus, this analysis offers [...] Read more.
In this paper, we studied Bayesian analysis proposed by Bretthorst[6] for a general signal model equation and combined it with a simulated annealing (SA) algorithm to obtain a global maximum of a posterior probability density function (PDF) for frequencies. Thus, this analysis offers different approach to finding parameter values through a directed, but random, search of the parameter space. For this purpose, we developed a Mathematica code of this Bayesian approach together with SA and used it for recovering sinusoids from noisy data. Simulations results support its effectiveness. Full article
Open AccessArticle
An Improved Vogel's Approximation Method for the Transportation Problem
Math. Comput. Appl. 2011, 16(2), 370-381; https://doi.org/10.3390/mca16020370 - 01 Aug 2011
Cited by 12 | Viewed by 2061
Abstract
Determining efficient solutions for large scale transportation problems is an important task in operations research. In this study, Vogel’s Approximation Method (VAM) which is one of well-known transportation methods in the literature was investigated to obtain more efficient initial solutions. A variant of [...] Read more.
Determining efficient solutions for large scale transportation problems is an important task in operations research. In this study, Vogel’s Approximation Method (VAM) which is one of well-known transportation methods in the literature was investigated to obtain more efficient initial solutions. A variant of VAM was proposed by using total opportunity cost and regarding alternative allocation costs. Computational experiments were carried out to evaluate VAM and improved version of VAM (IVAM). It was seen that IVAM conspicuously obtains more efficient initial solutions for large scale transportation problems. Performance of IVAM over VAM was discussed in terms of iteration numbers and CPU times required to reach the optimal solutions. Full article
Open AccessArticle
A Method for Ranking of Fuzzy Numbers Using New Weighted Distance
Math. Comput. Appl. 2011, 16(2), 359-369; https://doi.org/10.3390/mca16020359 - 01 Aug 2011
Cited by 20 | Viewed by 744
Abstract
In this paper, the researchers proposed a modified new weighted distance method to rank fuzzy numbers. The modified method can effectively rank various fuzzy numbers, their images and overcome the shortcomings of the previous techniques. The proposed model is studied for a broad [...] Read more.
In this paper, the researchers proposed a modified new weighted distance method to rank fuzzy numbers. The modified method can effectively rank various fuzzy numbers, their images and overcome the shortcomings of the previous techniques. The proposed model is studied for a broad class for fuzzy numbers and class of functions the membership of which is formed on the basis of the template ( ) max (0.1 ) s  x   x . This article also used some comparative examples to illustrate the advantage of the proposed method. Full article
Open AccessArticle
The Curvature of a Bézier Control Polyline
Math. Comput. Appl. 2011, 16(2), 350-358; https://doi.org/10.3390/mca16020350 - 01 Aug 2011
Viewed by 752
Abstract
The role of differential geometry in describing a curve can not be denied. The differential forms defined for Bézier curves which are widely used in computer aided geometric design, plays a significant role in classification and image processing of curves. For this reason, [...] Read more.
The role of differential geometry in describing a curve can not be denied. The differential forms defined for Bézier curves which are widely used in computer aided geometric design, plays a significant role in classification and image processing of curves. For this reason, the definitions such as Serret-Frenet frame, curvature and torsion which are described for Bézier curves are very important in computer aided geometric design. In this paper, in addition to these definitions we have also defined a new classification by applying angular curvature used for planar curves in computational geometry to Bézier control polygon. Full article
Open AccessArticle
A Novel Method for Multiple Attribute Decision-Making of Continuous Random Variable under Risk with Attribute Weight Unknown
Math. Comput. Appl. 2011, 16(2), 340-349; https://doi.org/10.3390/mca16020340 - 01 Aug 2011
Cited by 3 | Viewed by 604
Abstract
The extension of the fuzzy TOPSIS method based on the combination weight is presented to deal with multiple attribute decision-making problems under risk where the attribute value takes the form of the continuous random variable on the bounded intervals. First, the risk decision [...] Read more.
The extension of the fuzzy TOPSIS method based on the combination weight is presented to deal with multiple attribute decision-making problems under risk where the attribute value takes the form of the continuous random variable on the bounded intervals. First, the risk decision matrix is normalized by the transformation of the density function, and the variation coefficient method is used to determine the objective weights based on the expectations of the random variables. Subsequently, according to the maximizing rule of the weighted synthetic value of alternatives, the synthetic weight model is established. Then, the ideal solution and negative ideal solution is defined, the distances between the alternatives and the ideal/negative ideal solutions, and the relative closeness coefficients are calculated. In addition, the alternatives are ranked by the relative closeness coefficient of the alternatives. Finally, an illustrative example with the interval number is given to demonstrate the steps and the effectiveness of the proposed method. Full article
Open AccessArticle
Optimal Lot Sizing with Scrap and Random Breakdown Occurring in Backorder Replenishing Period
Math. Comput. Appl. 2011, 16(2), 329-339; https://doi.org/10.3390/mca16020329 - 01 Aug 2011
Cited by 9 | Viewed by 683
Abstract
This paper is concerned with determination of optimal lot size for an economic production quantity model with scrap and random breakdown occurring in backorder replenishing period. In most real-life manufacturing systems, generation of defective items and random breakdown of production equipment are inevitable. [...] Read more.
This paper is concerned with determination of optimal lot size for an economic production quantity model with scrap and random breakdown occurring in backorder replenishing period. In most real-life manufacturing systems, generation of defective items and random breakdown of production equipment are inevitable. To deal with the stochastic machine failures, production planners practically calculate the mean time between failures (MTBF) and establish the robust plan accordingly, in terms of optimal lot size that minimizes total production-inventory costs for such an unreliable system. Random scrap rate is considered in this study, and breakdown is assumed to occur in the backorder filling period. Mathematical modeling and analysis is used and the renewal reward theorem is employed to cope with the variable cycle length. An optimal manufacturing lot size that minimizes the long-run average costs for such an imperfect system is derived. Numerical example is provided to demonstrate its practical usages. Full article
Open AccessArticle
Joint Determination of the Production Lot Size and Number of Shipments for EPQ Model with Rework
Math. Comput. Appl. 2011, 16(2), 317-328; https://doi.org/10.3390/mca16020317 - 01 Aug 2011
Cited by 8 | Viewed by 674
Abstract
This paper is concerned with joint determination of the optimal lot size and optimal number of shipments for an economic production quantity (EPQ) model with the reworking of random defective items produced. The classic EPQ model assumes a continuous issuing policy for satisfying [...] Read more.
This paper is concerned with joint determination of the optimal lot size and optimal number of shipments for an economic production quantity (EPQ) model with the reworking of random defective items produced. The classic EPQ model assumes a continuous issuing policy for satisfying product demand and perfect quality production for all items produced. However, in a real life vendor-buyer integrated-productioninventory system, a multi-delivery policy is used practically in lieu of the continuous issuing policy, and it is inevitable to generate defective items during a production run. In this study, all nonconforming items produced are considered to be repairable and are reworked in each cycle after the end of a production run. The fixed-quantity multiple installments of the finished batch can only be delivered to customers if the whole lot is quality assured at the end of the rework. Mathematical modeling is used and the longrun average integrated cost per unit time is derived. Convexity of the cost function is proved by the use of the Hessian matrix equations. A closed-form optimal productionshipment policy to the problem is obtained. A special case to the model is discussed. Finally, a numerical example is provided to demonstrate the model’s practical usage. Full article
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