Metode Mehar Untuk Solusi Optimal Fuzzy Dan Analisa Sensitivitas Program Linier Dengan Variabel Fuzzy Bilangan Triangular

. Fuzzy linear programming problems containing closely with uncertainty about the parameters. Changes in the value of the parameters without changing the optimal solution or change the optimal solution is called sensitivity analysis. Sensitivity analysis is a basic for studying the effect of the changes that occur to the optimal solution. Linear programming with fuzzy variable is a form of fuzzy linear program is not fully because there are objective function coefficients and coefficients of constraints that are crisp numbers. Resolving the problem of linear programming with fuzzy variables by using mehar method will get solutions and optimal fuzzy value and solutions and optimal crisp value. To solve the problem of linear program with fuzzy variable is using mehar, must be converted beforehand in the form of crisp linear programming. This thesis explores mehar method to solve linear programming problems with fuzzy variables with triangular number and a sensitivity analysis on the optimum solution FVLP so that when there is a change of data of the problem, new solution will remain optimal

Design and Implementation of a Stochastic Programming Optimizer with Recourse and Tenders

This paper serves two purposes, to which we give equal emphasis. First, it describes an optimization system for solving large-scale stochastic linear programs with simple (i.e. decision-free in the second stage) recourse and stochastic right-hand-side elements. Second, it is a study of the means whereby large-scale Mathematical Programming Systems may be readily extended to handle certain forms of uncertainty, through post-optimal options akin to sensitivity on parametric analysis, which we term "recourse analysis". This latter theme (implicit throughout the paper) is explored in a proselytizing manner, in the concluding section

An Extented Sensitivity Analysis in Linear Programming Problems

When a real world problem is formulated as a linear programming model, we are often faced with difficulties in the parameter specification. We might know the plausible values or the possible ranges of parameters, but there still remains uncertainty. The parameter values could be obtained more exactly by experiments, investigations and/or inspections. However, to make such an experiment, investigation or inspection, expenses would be necessary. Because of capital limitations, we cannot invest in all possible experiments, investigations and inspections. Thus, we have a selection problem, which uncertainty reduction is the most profitable. In this paper, we discuss an analytic approach to the problem. Because of the difficulty of the global analysis, we make a local analysis around appropriate values of parameters. We focus on giving the decision maker useful information for the selection. First, sensitivity analyses with respect to the uncertain parameters are developed. The sensitivities are available only for the marginal domain without changing the optimal basis. The domain is obtained as an interval. The difficulty of the sensitivity analysis is in the cases of degeneracy and multiplicity of the optimal solutions. A treatment of such difficult cases is proposed. Finally, a numerical example is given for illustrating the proposed approach

Fuzzy Inventory Model with Shortages in Man Power Planning

In this paper, an EOQ (Economical Order Quitting) model with shortages (of employees) can be studied. The cost due to decrease in real wage and the cost involved in moving to a new job are considered, with a constraint that, the decrease in the real income over a period of time is limited. In real life, these costs are uncertain to a certain extent. This uncertainty has been discussed by utilizing the concept of fuzzy set theory. Fuzzy non-linear programming technique using Lagrange multipliers is used to solve the problems in this model. The application of this model in man power planning is illustrated by means of a numerical example. The variations of the results with those of the crisp model have been compared. Further the sensitivity analysis is also presented. Keywords: Inventory, Economical Order Quitting, Real Wage, Fuzzy Sets, Man Power Planning, Membership Function, Sensitivity Analysis

Modeling, simulation, and control of the spacecraft attitude dynamics

Based on the three-dimensional dynamics of a rigid body and Newton’s laws, the simplified dynamics of a spacecraft is studied and described through the systematical representation, mathematical modeling and also by a block diagram representation, to finally simulates the spacecraft dynamics in the Matlab programming environment called Simulink. It is paramount to be able to identify and recognize the attitude (often represented with the Euler angles) and position variables like the degrees of freedom (DOF) of the system and also the linear behavior. All this to conclude up about the non-linear behavior presented by the accelerations, velocities, positions and Euler angles (attitude) when those mentioned are plotted against time. In addition to this, the linearized system is found in order to facilitate the control analysis and stability analysis, at using linear analysis tools of Simulink and concepts like controllability and observability, reaching the point of determining under the previous concepts to proceed with the control design phase. Lastly, an uncertainty and sensitivity analysis is realized, by means the Monte-Carlo and the Linear regression method (in Simulink too), to find the torque like critical model input, since it has the greatest effect on the response variables in the system; and thus finally, to implement the Linear Quadratic Regulator (LQR) controller, at using the lqr Matlab functio

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part I: template-based generic programming

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering