On stochastic scheduling with precedence relations and switching costs

1980 ◽  
Vol 17 (4) ◽  
pp. 1016-1024 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Probability Distribution ◽  
Single Machine ◽  
Optimal Strategy ◽  
Switching Costs ◽  
Stochastic Scheduling ◽  
Random Variable ◽  
Precedence Relation ◽  
Precedence Relations

A collection of jobs is to be processed by a single machine. The amount of processing required by each job is a random variable with a known probability distribution. The jobs must be processed in a manner which is consistent with a precedence relation but the machine is free to switch from one job to another at any time; such switches are costly, however. This paper discusses conditions under which there is an optimal strategy for allocating the machine to the jobs which is given by a fixed permutation of the jobs indicating in which order they should be processed. When this is so, existing algorithms may be helpful in giving the best job ordering.

On stochastic scheduling with precedence relations and switching costs

1980 ◽  
Vol 17 (04) ◽  
pp. 1016-1024 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Probability Distribution ◽  
Single Machine ◽  
Optimal Strategy ◽  
Switching Costs ◽  
Stochastic Scheduling ◽  
Random Variable ◽  
Precedence Relation ◽  
Precedence Relations

A collection of jobs is to be processed by a single machine. The amount of processing required by each job is a random variable with a known probability distribution. The jobs must be processed in a manner which is consistent with a precedence relation but the machine is free to switch from one job to another at any time; such switches are costly, however. This paper discusses conditions under which there is an optimal strategy for allocating the machine to the jobs which is given by a fixed permutation of the jobs indicating in which order they should be processed. When this is so, existing algorithms may be helpful in giving the best job ordering.

STRUCTURAL RELIABILITY ANALYSIS BASED ON P-BOXES

2020 ◽  
Vol 92 (6) ◽  
pp. 51-58
Author(s):  
S.A. SOLOVYEV ◽  
Keyword(s):  
Probability Distribution ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Random Variable ◽  
Strength Criterion ◽  
Structural Elements ◽  
Structural Element ◽  
Limit States ◽  
Distribution Shape

The article describes a method for reliability (probability of non-failure) analysis of structural elements based on p-boxes. An algorithm for constructing two p-blocks is shown. First p-box is used in the absence of information about the probability distribution shape of a random variable. Second p-box is used for a certain probability distribution function but with inaccurate (interval) function parameters. The algorithm for reliability analysis is presented on a numerical example of the reliability analysis for a flexural wooden beam by wood strength criterion. The result of the reliability analysis is an interval of the non-failure probability boundaries. Recommendations are given for narrowing the reliability boundaries which can reduce epistemic uncertainty. On the basis of the proposed approach, particular methods for reliability analysis for any structural elements can be developed. Design equations are given for a comprehensive assessment of the structural element reliability as a system taking into account all the criteria of limit states.

On the scheduling of alternative stochastic jobs on a single machine

1987 ◽  
Vol 19 (4) ◽  
pp. 955-973 ◽  
Author(s):  
K. D. Glazebrook ◽  
N. A. Fay
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Stochastic Scheduling ◽  
Major Area ◽  
Research Planning ◽  
Stochastic Resource Allocation ◽  
Standard Models ◽  
Set Up ◽  
Area Of Application

Standard models in stochastic resource allocation concern the economic processing of all jobs in some set J. We consider a set up in which tasks in various subsets of J are deemed to be alternative to one another, in that only one member of such a subset of alternative tasks will be completed during the evolution of the process. Existing stochastic scheduling methodology for single-machine problems is developed and extended to this novel class of models. A major area of application is in research planning.

scholarly journals The impact of inclusive business on ethical values & internal control quality: an accounting perspective

2016 ◽  
Vol 5 (4) ◽  
pp. 106-113 ◽  
Author(s):  
Tamer El Nashar
Keyword(s):  
Probability Distribution ◽  
Internal Control ◽  
Random Variable ◽  
Ethical Values ◽  
Discrete Probability ◽  
Control Quality ◽  
Inclusive Business ◽  
Potential Impact ◽  
Business Approach ◽  
The Impact

The objective of this paper is to examine the impact of inclusive business on the internal ethical values and the internal control quality while conceiving the accounting perspective. I construct the hypothesis for this paper based on the potential impact on the organizations’ awareness to be directed to the inclusive business approach that will significantly impact the culture of the organizations then the ethical values and the internal control quality. I use the approach of the expected value and variance of random variable test in order to analyze the potential impact of inclusive business. I support the examination by discrete probability distribution and continuous probability distribution. I find a probability of 85.5% to have a significant potential impact of the inclusive business by 100% score on internal ethical values and internal control quality. And to help contribute to sustainability growth, reduce poverty and improve organizational culture and learning.

Method for Constructing a Confidence Interval for the Variance of a Random Variable

Vestnik NSUEM ◽  
2021 ◽  
pp. 146-155
Author(s):  
A. V. Ganicheva ◽  
A. V. Ganichev
Keyword(s):  
Probability Distribution ◽  
Confidence Interval ◽  
Random Variable ◽  
New Method ◽  
Interval Estimate ◽  
Normal Law

The problem of reducing the number of observations for constructing a confidence interval of variance with a given degree of accuracy and reliability is considered. The new method of constructing an interval estimate of variance developed in the article is formulated by three statements and justified by four proven theorems. Formulas for calculating the required number of observations depending on the accuracy and reliability of the estimate are derived. The results of the calculations are presented in the table and shown in the diagram. The universality and effectiveness of this method is shown. The universality of the method lies in the fact that it is applicable to any laws of probability distribution, and not only for the normal law. The effectiveness of the developed method is justified by comparing its performance with other known methods.

Introduction to Information Theory

2014 ◽  
Author(s):  
M. Vidyasagar
Keyword(s):  
Information Theory ◽  
Probability Distribution ◽  
Relative Entropy ◽  
Probability Distributions ◽  
Random Variables ◽  
Conditional Entropy ◽  
Random Variable ◽  
Entropy Function ◽  
Concave Functions ◽  
Leibler Divergence

This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random variable (or more precisely, the probability distribution of the random variable). When there are two or more random variables, it is worthwhile to study the conditional entropy of one random variable with respect to another. The last concept is relative entropy, also known as the Kullback–Leibler divergence, which measures the “disparity” between two probability distributions. The chapter first considers convex and concave functions before discussing the properties of the entropy function, conditional entropy, uniqueness of the entropy function, and the Kullback–Leibler divergence.

scholarly journals On the equivalence of various definitions of mixed poisson processes

2019 ◽  
Vol 69 (2) ◽  
pp. 453-468
Author(s):  
Demetrios P. Lyberopoulos ◽  
Nikolaos D. Macheras ◽  
Spyridon M. Tzaninis
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Random Variable ◽  
Poisson Processes ◽  
Counting Processes ◽  
Mixing Parameter ◽  
Mixed Poisson Process ◽  
Probability Spaces ◽  
The One

Abstract Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing probability distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of “canonical” probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions for the characterization of mixed Poisson processes in terms of disintegrations cannot be omitted.

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