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Stochastic Problems (stochastic + problem)

Distribution by Scientific Domains
Mathematics and Statistics40%

Selected Abstracts

Branch-and-Price Methods for Prescribing Profitable Upgrades of High-Technology Products with Stochastic Demands*

DECISION SCIENCES, Issue 1 2004
Purushothaman Damodaran
ABSTRACT This paper develops a model that can be used as a decision support aid, helping manufacturers make profitable decisions in upgrading the features of a family of high-technology products over its life cycle. The model integrates various organizations in the enterprise: product design, marketing, manufacturing, production planning, and supply chain management. Customer demand is assumed random and this uncertainty is addressed using scenario analysis. A branch-and-price (B&P) solution approach is devised to optimize the stochastic problem effectively. Sets of random instances are generated to evaluate the effectiveness of our solution approach in comparison with that of commercial software on the basis of run time. Computational results indicate that our approach outperforms commercial software on all of our test problems and is capable of solving practical problems in reasonable run time. We present several examples to demonstrate how managers can use our models to answer "what if" questions. [source]

Collocation methods based on radial basis functions for solving stochastic Poisson problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2007
Somchart ChantasiriwanArticle first published online: 19 JUN 200
Abstract Collocation methods based on radial basis functions can be used to provide accurate solutions to deterministic problems. For stochastic problems, accurate solutions may not be desirable if they are too sensitive to random inputs. In this paper, four methods are used to solve stochastic Poisson problems by expressing solutions in terms of source terms and boundary conditions. Comparison among the methods reveals that the method based on fundamental solutions performs better than other methods. Copyright © 2006 John Wiley & Sons, Ltd. [source]

The stochastic second-order perturbation technique in the finite difference method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2001
Marcin Kami, skiArticle first published online: 17 JUL 200
Abstract The main idea of the paper is to introduce the second-order perturbation second probabilistic moment extension of the finite difference method (FDM). The approach can be successfully applied to all these engineering analyses where FDM modelling is still useful and some structural parameters are treated as random variables or fields. The main advantage of the stochastic finite difference method (SFDM) proposed is relatively easy extension of the existing deterministic results in the classical theory of elasticity on the random or even stochastic problems. A very attractive aspect can be the usage of the SFDM in the stochastic signals processing in a conjunction with the wavelet optimized FDM. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Deterministic and stochastic scheduling with teamwork tasks

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2004
Xiaoqiang Cai
Abstract We study a class of new scheduling problems which involve types of teamwork tasks. Each teamwork task consists of several components, and requires a team of processors to complete, with each team member to process a particular component of the task. Once the processor completes its work on the task, it will be available immediately to work on the next task regardless of whether the other components of the last task have been completed or not. Thus, the processors in a team neither have to start, nor have to finish, at the same time as they process a task. A task is completed only when all of its components have been processed. The problem is to find an optimal schedule to process all tasks, under a given objective measure. We consider both deterministic and stochastic models. For the deterministic model, we find that the optimal schedule exhibits the pattern that all processors must adopt the same sequence to process the tasks, even under a general objective function GC = F(f1(C1), f2(C2), , , fn(Cn)), where fi(Ci) is a general, nondecreasing function of the completion time Ci of task i. We show that the optimal sequence to minimize the maximum cost MC = max fi(Ci) can be derived by a simple rule if there exists an order f1(t) , , , fn(t) for all t between the functions {fi(t)}. We further show that the optimal sequence to minimize the total cost TC = , fi(Ci) can be constructed by a dynamic programming algorithm. For the stochastic model, we study three optimization criteria: (A) almost sure minimization; (B) stochastic ordering; and (C) expected cost minimization. For criterion (A), we show that the results for the corresponding deterministic model can be easily generalized. However, stochastic problems with criteria (B) and (C) become quite difficult. Conditions under which the optimal solutions can be found for these two criteria are derived. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004 [source]

A Versatile Birth,Death Model Applicable to Four Distinct Problems

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2004
J. Gani
Summary This paper revisits a simple birth,death model which arises in slightly different forms in four distinct stochastic problems. These are the barbershop queue, coupon collecting, vocabulary usage and geological dating. Discrete and continuous time Markov chains are used to characterize these problems. Somewhat different questions are posed for each particular case, and practical results are derived for each process. The paper concludes with some comments on the versatility of this applied probability model. [source]