scholarly journals Asymptotic normality of the optimal solution in multiresponse surface mathematical programming

2015 ◽  
Vol 12 (1) ◽  
Author(s):  
José Díaz-García ◽  
Francisco Caro-Lopera
Keyword(s):  
Sensitivity Analysis ◽  
Mathematical Programming ◽  
Asymptotic Normality ◽  
Critical Point ◽  
Explicit Form ◽  
Optimal Solution ◽  
Regression Coefficients ◽  
Standard Methods ◽  
The Matrix ◽  
Perturbation Effect

An explicit form for the perturbation effect on the matrix of regression coefficients on the optimal solution in multiresponse surface methodology is obtained in this paper. Then, the sensitivity analysis of the optimal solution is studied and the critical point characterisation of the convex program, associated with the optimum of a multiresponse surface, is also analysed. Finally, the asymptotic normality of the optimal solution is derived by the standard methods.

Aplikasi Metode Hungarian Dalam Optimalisasi Waktu Penugasan Karyawan dan Keuntungan Produksi Home Industry

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Empya Charlie ◽  
Siti Rusdiana ◽  
Rini Oktavia
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Optimal Scheduling ◽  
Total Work ◽  
Work Time ◽  
Hungarian Method ◽  
Total Work Time

Penelitian ini bertujuan untuk mengoptimalkan penjadwalan karyawan di CV. Karya Indah Bordir dalam melakukan tugas-tugas tertentu menggunakan metode Hungaria, serta menganalisis sensitivitas solusi optimal jika ada pengurangan waktu karyawan untuk menyelesaikan tugas-tugas. Metode Hongaria diterapkan pada proses bordir yang melibatkan 11 karyawan dan 10 tugas. Hasil penjadwalan yang optimal meminimalkan waktu produksi bordir perusahaan. Hasil penjadwalan optimal yang ditemukan adalah: karyawan 1 mengerjakan tas Mambo, karyawan 2 mengerjakan tas Elli, karyawan 3 mengerjakan tas Lonjong, karyawan 4 mengerjakan tas Tampang bunga, karyawan 6 mengerjakan tas Ransel, karyawan 7 mengerjakan tas Tima, karyawan 8 mengerjakan tas Keong, karyawan 9 mengerjakan tas Alexa, karyawan 10 mengerjakan tas Luna, dan karyawan 11 mengerjakan tas Mikha, dengan total waktu kerja adalah 13,7 jam. Setelah metode Hongaria diterapkan, CV. Karya Indah Bordir mendapat peningkatan pendapatan sebanyak 9,09%. Analisis sensitivitas dilakukan dengan mengurangi waktu karyawan dalam menyulam tas. Hasil analisis sensitivitas adalah beberapa batasan untuk variabel basis dan non basis untuk mempertahankan solusi optimal.   This research has a purpose to optimize the scheduling of employees in CV. Karya Indah Bordir in doing certain tasks using Hungarian method, as well as analyzing the sensitivity of the optimal solution if there is a reduction on the employees time to finish the tasks. The Hungarian method was applied on the embroidery process involving 11 employees and 10 tasks. The optimal scheduling result minimize the time of the embroidery production of the company. The optimal scheduling result found is: employee 1 does the Mambo bag, employee 2 does the Elli bag, employee 3 does the Lonjong bag, employee 4 does the Tampang bunga bag, employee 6 does the Ransel, employee 7 does the Tima bag, employee 8 does the Keong bag, employee 9 does the Alexa bag, employees 10 does the Luna bag, and employee 11 does the Mikha bag, with the total work time is 13,7 hours. After the Hungarian method was applied, CV. Karya Indah Bordir got the increasing revenue as much as 9,09 %. The sensitivity analysis was conducted by reducing the time of the employees take in embroidery the bags. The results of the sensitivity analysis are some boundaries for basis and non basis variables to maintain the optimal solution. 

scholarly journals 99 Breed authentication of five lines comparing Structure, Admixture, and an allele frequency method

2020 ◽  
Vol 98 (Supplement_3) ◽  
pp. 25-25
Author(s):  
Austin M Putz ◽  
Patrick Charagu ◽  
Abe Huisman
Keyword(s):  
Population Structure ◽  
Allele Frequency ◽  
Regression Coefficients ◽  
Frequency Method ◽  
Large White ◽  
Reference Allele ◽  
Software Packages ◽  
The Matrix ◽  
Snp Panel ◽  
Compare And Contrast

Abstract Two commonly used population structure software packages are freely available for breed authentication, Structure and Admixture. Structure uses a Bayesian approach to model population structure, while Admixture uses a frequentist approach. More recently, an allele frequency method has been updated to use quadratic programming to constrain the multiple linear regression coefficients of the regression of genotype count (divided by two) on the matrix of allele frequencies for each known breed or line. This constraint forced coefficients to sum to one and be greater than or equal to 0 and less than or equal to 1. The goal of this research was to compare and contrast these three methods to determine the breed/line authenticity for each of the five genetic lines. These five lines included Large White, Landrace, a lean Duroc, a meat quality Duroc, and a Pietrain line. Only animals with a 50K SNP panel were used in this analysis. Analyses were run five times for Structure and Admixture to check repeatability. The allele frequency method did not need to be repeated because it remains the same as long as the reference allele frequency matrix stays constant. For Structure, results of breed composition were inconsistent across replicates. Structure separated at least one of the maternal lines in three out of the five replicates with only 500 animals and kept the Duroc lines together as one population. Only 500 animals could be utilized in each run of Structure due to computational restraints. Admixture was very consistent across runs for each animal, but also failed to separate the two Duroc lines, instead splitting one of the two maternal lines. Finally, the allele frequency method split all five lines correctly and was 100% reproducible as long as the reference allele frequency matrix stays the same across runs.

A Sensitivity Analysis Based Method for Robot Calibration

1992 ◽  
Author(s):  
S. Kaizerman ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
G. Zak
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Model ◽  
Calibration Procedure ◽  
Inverse Kinematic ◽  
Model Parameters ◽  
Robot Calibration ◽  
Adjoint Sensitivity ◽  
Analysis Methods ◽  
The Matrix ◽  
Direct Sensitivity

Abstract A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two degree of freedom revolute-joint planar manipulator.

Predictive Search for Capacitated Multi-Item Lot Sizing Problems

2021 ◽  
Author(s):  
Tao Wu
Keyword(s):  
Mathematical Programming ◽  
Heuristic Search ◽  
Lot Sizing ◽  
Optimal Solution ◽  
Solution Space ◽  
Search Method ◽  
Benchmark Problems ◽  
Solution Quality ◽  
Programming Technique ◽  
Advanced Analytics

For capacitated multi-item lot sizing problems, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework. Advanced analytics can predict the probability that an event will happen and has been applied to pressing industry issues, such as credit scoring, risk management, and default management. Although little research has applied such technique for lot sizing problems, we observe that advanced analytics can uncover optimal patterns of setup variables given properties associated with the problems, such as problem attributes, and solution values yielded by linear programming relaxation, column generation, and Lagrangian relaxation. We, therefore, build advanced analytics models that yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to partition the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. The discussion is followed by computational tests, where comparisons with other methods indicate that our approach can obtain better results for the benchmark problems than other state-of-the-art methods. Summary of Contribution: In this study, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems. The advanced analytics models are used to yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to divide the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. Through computational tests based on benchmark problems, we observe that the proposed approach can obtain better results than other state-of-the-art methods.

scholarly journals Higher-order Darboux transformations for two-dimensional Dirac systems with diagonal matrix potential

2021 ◽  
Vol 2090 (1) ◽  
pp. 012038
Author(s):  
A Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Explicit Form ◽  
Higher Order ◽  
Diagonal Matrix ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Systems ◽  
Matrix Potential ◽  
De Vries ◽  
The Matrix

Abstract We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

scholarly journals Two – Warehouse Inventory System Model for Deteriorating Items Considering Partial Upstream Trade Credit Financing

2021 ◽  
pp. 69-80
Author(s):  
Z. H. Aliyu ◽  
B. Sani
Keyword(s):  
Sensitivity Analysis ◽  
Credit Risk ◽  
Trade Credit ◽  
Optimal Solution ◽  
Inventory System ◽  
System Model ◽  
Credit Period ◽  
Business Transaction ◽  
Credit Financing ◽  
Relevant Cost

In this study, we developed an inventory system model under two – level trade credit where the supplier considers the retailer as credit risk but the retailer considers the customers as credit worthy. Therefore, the retailer is given a trade credit period on  proportion of the goods ordered whenever he/she pays for proportion of the goods immediately after delivery. In the same vein, the retailer passes the same grace to the customers but without attaching any condition as the customers are assumed credit worthy. This partial upstream trade credit is offered to reduce the risk of failure in payment on the business transaction especially that most retailers are involved in bulk orders. The relevant cost functions are determined and a numerical example is given. Sensitivity analysis was carried out to see the effect of changes in parameters on the optimal solution of the model.

Multi-Objecitve Control of Dynamical Systems

1995 ◽  
Author(s):  
Petros Voulgaris
Keyword(s):  
Exact Solution ◽  
Duality Theory ◽  
Closed Loop ◽  
Finite Impulse Response ◽  
Optimal Solution ◽  
Standard Methods ◽  
Continuity Properties ◽  
Step Procedure ◽  
Quadratic Programming Problems ◽  
Finite Step

Abstract In this paper we consider the problem of minimizing the H2-norm of the closed loop map while maintaining its ℓ1-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed loop maps. Utilizing duality theory, it is shown that the optimal solution is unique and has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the ℓ1-constraint are established.

scholarly journals Sensitivity Analysis of Road Freight Transportation of a Mega Non-Alcoholic Beverage Industry

2020 ◽  
Vol 24 (3) ◽  
pp. 449-454
Author(s):  
T. Latunde ◽  
J.O. Richard ◽  
O.O. Esan ◽  
O.O. Dare
Keyword(s):  
Sensitivity Analysis ◽  
Alcoholic Beverage ◽  
Optimal Solution ◽  
Transportation Cost ◽  
Demand And Supply ◽  
North West ◽  
The North ◽  
Beverage Industry ◽  
Road Freight ◽  
Road Freight Transportation

Re-optimization can be very costly for gathering and obtaining more data for a particular problem, to curb this very expensive investment.  Sensitivity analysis has been used in this work to determine the behaviour of input parameters of the formulated problem. The main goal of the study is to respectively provide, derive, observe, compare and discuss the sensitivity analysis of data that has been optimized using different methods of the optimal solution. The best method, saving the highest percentage of transportation cost, for the formulated problem is determined to be the North-West Corner method. This was carried out by arbitrarily assigning values to the available warehouses to determine the best possible demand and supply cases rather than the initial cases. Thus, more cases are advised to be supplied to FID from the Asejire plant for the optimum reduced value of transportation cost. Keywords: Sensitivity, Parameters, Transportation Problem.

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