A sequential solution procedure to stochastic capital budgeting models

1988 ◽  
Vol 14 (4) ◽  
pp. 371-380
Author(s):  
Reuven R. Levary
Keyword(s):  
Capital Budgeting ◽  
Solution Procedure ◽  
Sequential Solution

Capital Budgeting with Multiple Criteria and Multiple Decision Makers: A Fuzzy Approach

2001 ◽  
Vol 5 (3) ◽  
pp. 139-148
Author(s):  
Yong Shi ◽  
◽  
Wikil Kwak ◽  
Heeseok Lee ◽  
Cheng-few Lee ◽  
...  
Keyword(s):  
Capital Budgeting ◽  
Solution Procedure ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Optimal Selection ◽  
Fuzzy Approach ◽  
Strategic Investment ◽  
Multiple Decision Makers ◽  
Compromise Value ◽  
Selection Of

A capital budgeting model with multiple criteria and multiple decision makers (MCMDM) is more likely to provide realistic solutions than linear or goal programming models. This paper adopts a fuzzy approach to solve MCMDM capital budgeting problems. This approach is based on two fundamental human cognitive processes: (i) all decision makers who are involved in the capital budgeting problem have goal setting and compromise behavior for seeking multiple criteria, and (ii) each decision maker has a preference for the budget availability level. A solution procedure is proposed to systematically identify a fuzzy optimal selection of possible projects that can not only reach the best compromise value for the multiple criteria, but also use the best budget availability level according to the multiple decision makers’ preferences. The optimal selection can help the firm make a realistic decision regarding its strategic investment. A comparison study of the fuzzy approach with other approaches shows the advantages of using the fuzzy approach.

scholarly journals Planning service assets deployment based on information about dynamics of IT services use

2020 ◽  
Vol 63 (5) ◽  
pp. 373-378
Author(s):  
A. V. Zimin ◽  
I. A. Zolin ◽  
I. V. Burkova ◽  
V. V. Zimin
Keyword(s):  
Traditional Approach ◽  
Solution Procedure ◽  
It Services ◽  
Service Failures ◽  
Sequential Solution ◽  
Metallurgical Company ◽  
Deployment Time ◽  
Time Information ◽  
Services Use

Deployment of new service assets in operational IT environment is associated with the risk of disruption of the assets of its “basic” condition. Such disruptions cause failures of functioning services. To reduce the risk of disruption, the deploying service assets are divided by releases – sub-sets of service assets that will be embedded in the IT environment in one period. The traditional approach to formation and deployment of releases uses information on services structural properties to predict the number of failures due to the deployment of each service asset, each release and each application for deployment. As a result, the task of managing deployment of service assets is reduced to a sequential solution of three tasks: determining number of releases; determining composition of releases; building a release deployment schedule. The approach is based on the assumption that incorrect deployment of releases is manifested through the failure of services immediately after deployment. In practice, as a rule, this assumption is usually not fulfilled, because the use of various services by users who detect service failures is cyclical (daily, weekly, monthly, quarterly, annual). Many service failures can be detected by users in periods of time that are quite remote from the deployment time of the corresponding IT assets. The article contains the case where the managing process of IT provider configurations of the metallurgical company is well developed, i.e. its configuration database contains information on frequency of various services use at different periods of time. Information on dynamics of services application by users is used to predict time sequence of operating services failures due to deployment of each application. As a result, the task of forming and scheduling deployment of releases is formalized in the form of a discrete nonlinear programming task, the solution procedure of which allows simultaneous determination of number of releases, their composition and schedule for their deployment.

A Parallel Coupled Ordinates Method for Rarefied Gas Dynamics Simulations

2012 ◽  
Author(s):  
Shankhadeep Das ◽  
Battalgazi Yildirim ◽  
Sanjay R. Mathur ◽  
Alina Alexeenko ◽  
Jayathi Y. Murthy
Keyword(s):  
Rf Mems ◽  
Parallel Implementation ◽  
Real Life ◽  
Numerical Procedure ◽  
Solution Procedure ◽  
Distribution Functions ◽  
Velocity Space ◽  
Mems Switches ◽  
Rf Mems Switches ◽  
Sequential Solution

Deterministic solution techniques for non-equilibrium rarefied flows in RF MEMS switches are frequently based on the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) form of the Boltzmann kinetic equation. These numerical schemes involve the sequential solution of the distribution function in velocity space. However, these schemes have poor convergence rates, especially at low Knudsen numbers, because of the explicit coupling of the distribution functions in velocity space. Furthermore, parallel implementation of these schemes is inefficient, making simulation of real-life devices practically impossible. In this paper we describe the parallel performance of a recently-developed numerical procedure called the coupled ordinates method (COMET) to solve ESBGK equations. In this method, the distribution functions for all velocity ordinates are strongly coupled at each physical point, resulting in an implicit solution procedure in velocity space. The coupled procedure is used as a relaxation sweep in a geometric multigrid scheme to promote spatial coupling. Results show that COMET gives excellent CPU scaling on multiple processors even for very small workload per processor. The solver is also shown to have very good strong and weak scaling characteristics. The parallel COMET solver also gives significantly faster solutions than the parallel implementation of the conventional sequential solution procedure. It is believed that the parallel COMET solver can become an efficient tool to model real-life RF MEMS switches.

A Coupled Ordinates Method for Convergence Acceleration of the Phonon Boltzmann Transport Equation

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
James M. Loy ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Transport Equation ◽  
Convergence Rates ◽  
Boltzmann Transport Equation ◽  
Physical Space ◽  
Solution Procedure ◽  
Computational Time ◽  
Boltzmann Transport ◽  
Knudsen Numbers ◽  
Numerical Solution Methods ◽  
Sequential Solution

Sequential numerical solution methods are commonly used for solving the phonon Boltzmann transport equation (BTE) because of simplicity of implementation and low storage requirements. However, they exhibit poor convergence for low Knudsen numbers. This is because sequential solution procedures couple the phonon BTEs in physical space efficiently but the coupling is inefficient in wave vector (K) space. As the Knudsen number decreases, coupling in K space becomes dominant and convergence rates fall. Since materials like silicon have K-resolved Knudsen numbers that span two to five orders of magnitude at room temperature, diffuse-limit solutions are not feasible for all K vectors. Consequently, nongray solutions of the BTE experience extremely slow convergence. In this paper, we develop a coupled-ordinates method for numerically solving the phonon BTE in the relaxation time approximation. Here, interequation coupling is treated implicitly through a point-coupled direct solution of the K-resolved BTEs at each control volume. This implicit solution is used as a relaxation sweep in a geometric multigrid method which promotes coupling in physical space. The solution procedure is benchmarked against a traditional sequential solution procedure for thermal transport in silicon. Significant acceleration in computational time, between 10 and 300 times, over the sequential procedure is found for heat conduction problems.

A Coupled Ordinates Method for Convergence Acceleration of the Phonon Boltzmann Transport Equation

2012 ◽  
Author(s):  
James M. Loy ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Transport Equation ◽  
Convergence Rates ◽  
Control Volume ◽  
Boltzmann Transport Equation ◽  
Physical Space ◽  
Convergence Acceleration ◽  
Solution Procedure ◽  
Boltzmann Transport ◽  
Knudsen Numbers ◽  
Sequential Solution

Sequential solution methods are commonly-used for solving the phonon Boltzmann transport equation (BTE) because of simplicity of implementation and low storage requirements. However, they exhibit poor convergence for low Knudsen numbers. This is because sequential solution procedures couple the phonon BTEs in physical space efficiently but the coupling is inefficient in wave-vector (K) space. As the Knudsen number decreases, coupling in K space becomes dominant and convergence rates fall. Since materials like silicon have K-resolved Knudsen numbers that span 3–4 orders of magnitude at room temperature, diffuse-limit solutions are not feasible for all K vectors. Consequently, non-gray solutions of the BTE almost always experience extremely slow convergence. In this paper, we develop a coupled-ordinates method for solving the phonon BTE in the relaxation time approximation. Here, inter-equation coupling is treated implicitly through a point-coupled direct solution of the K-resolved BTEs at each control volume. This implicit solution is used as a relaxation sweep in a geometric multigrid method. The solution procedure is benchmarked against a traditional sequential solution procedure for thermal transport in silicon. Significant acceleration, between 10 to 300 times, over the sequential procedure is found for heat conduction problems.

A Heuristic Solution Procedure to Minimize \[Tmacr] on a Single Machine

1989 ◽  
Vol 40 (3) ◽  
pp. 293-297 ◽  
Author(s):  
T D Fry ◽  
L Vicens ◽  
K Macleod ◽  
S Fernandez
Keyword(s):  
Single Machine ◽  
Solution Procedure ◽  
Heuristic Solution
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