A note on the upper bound for the optimal work size

2004 ◽  
Vol 41 (1) ◽  
pp. 277-280 ◽  
Author(s):  
Ji Hwan Cha
Keyword(s):  
Upper Bound ◽  
Optimization Problem ◽  
Replacement Policy ◽  
Two Dimensional ◽  
Age Replacement ◽  
Work Size ◽  
Dimensional Optimization

Mi (2002) recently considered a two-dimensional optimization problem for the optimal age-replacement policy and the optimal work size. In order to find (y∗,T∗), Mi (2002) found the optimal age-replacement policy T∗(y) for each fixed work size y, and then searched for the optimal work size y∗. When applying this approach, for each fixed work size y, Mi (2002) obtained the bounds for T∗(y). However, no bound for the optimal work size y∗ was derived. In this note, the results on the upper bound for the optimal work size y∗ are given.

A note on the upper bound for the optimal work size

2004 ◽  
Vol 41 (01) ◽  
pp. 277-280
Author(s):  
Ji Hwan Cha
Keyword(s):  
Upper Bound ◽  
Optimization Problem ◽  
Replacement Policy ◽  
Two Dimensional ◽  
Age Replacement ◽  
Work Size ◽  
Dimensional Optimization

Mi (2002) recently considered a two-dimensional optimization problem for the optimal age-replacement policy and the optimal work size. In order to find (y ∗,T ∗), Mi (2002) found the optimal age-replacement policy T ∗(y) for each fixed work size y, and then searched for the optimal work size y ∗. When applying this approach, for each fixed work size y, Mi (2002) obtained the bounds for T ∗(y). However, no bound for the optimal work size y ∗ was derived. In this note, the results on the upper bound for the optimal work size y ∗ are given.

Age-replacement policy and optimal work size

2002 ◽  
Vol 39 (2) ◽  
pp. 296-311 ◽  
Author(s):  
Jie Mi
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Repair Time ◽  
Replacement Policy ◽  
Average Amount ◽  
Failure Time Distribution ◽  
Long Run ◽  
Random Failure ◽  
Age Replacement ◽  
Work Size

Suppose that there is a sequence of programs or jobs that are scheduled to be executed one after another on a computer. A program may terminate its execution because of the failure of the computer, which will obliterate all work the computer has accomplished, and the program has to be run all over again. Hence, it is common to save the work just completed after the computer has been working for a certain amount of time, say y units. It is assumed that it takes a certain time to perform a save. During the saving process, the computer is still subject to random failure. No matter when the computer failure occurs, it is assumed that the computer will be repaired completely and the repair time will be negligible. If saving is successful, then the computer will continue working from the end of the last saved work; if the computer fails during the saving process, then only unsaved work needs to be repeated. This paper discusses the optimal work size y under which the long-run average amount of work saved is maximized. In particular, the case of an exponential failure time distribution is studied in detail. The properties of the optimal age-replacement policy are also derived when the work size y is fixed.

Age-replacement policy and optimal work size

2002 ◽  
Vol 39 (02) ◽  
pp. 296-311 ◽  
Author(s):  
Jie Mi
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Repair Time ◽  
Replacement Policy ◽  
Average Amount ◽  
Failure Time Distribution ◽  
Long Run ◽  
Random Failure ◽  
Age Replacement ◽  
Work Size

Suppose that there is a sequence of programs or jobs that are scheduled to be executed one after another on a computer. A program may terminate its execution because of the failure of the computer, which will obliterate all work the computer has accomplished, and the program has to be run all over again. Hence, it is common to save the work just completed after the computer has been working for a certain amount of time, say y units. It is assumed that it takes a certain time to perform a save. During the saving process, the computer is still subject to random failure. No matter when the computer failure occurs, it is assumed that the computer will be repaired completely and the repair time will be negligible. If saving is successful, then the computer will continue working from the end of the last saved work; if the computer fails during the saving process, then only unsaved work needs to be repeated. This paper discusses the optimal work size y under which the long-run average amount of work saved is maximized. In particular, the case of an exponential failure time distribution is studied in detail. The properties of the optimal age-replacement policy are also derived when the work size y is fixed.

scholarly journals Two-dimensional optimization problem of plant location

2001 ◽  
Vol 23 (3) ◽  
pp. 149-158
Author(s):  
Tran Gia Linh ◽  
Phan Ngoc Vinh
Keyword(s):  
Numerical Experiments ◽  
Optimization Problem ◽  
Adjoint Problem ◽  
Plant Location ◽  
Propagation Problem ◽  
Pollution Level ◽  
Two Dimensional ◽  
Typical Problem ◽  
Dimensional Optimization

In this paper, the following matters are presented: the adjoint problem of the two-dimensional matter propagation problem; the algorithm for determination of a domain in which a plant can be located so that the values of the pollution-level reflecting functional does not exceed a given value at considered sensitive areas; application of this algorithm for numerical experiments to a typical problem.

The failure probability of components in three-state networks with applications to age replacement policy

2017 ◽  
Vol 54 (4) ◽  
pp. 1051-1070 ◽  
Author(s):  
S. Ashrafi ◽  
M. Asadi
Keyword(s):  
Failure Probability ◽  
The State ◽  
Replacement Policy ◽  
Two Dimensional ◽  
Age Replacement ◽  
Stochastic Properties ◽  
Failure Probabilities

Abstract In this paper we investigate the stochastic properties of the number of failed components of a three-state network. We consider a network made up of n components which is designed for a specific purpose according to the performance of its components. The network starts operating at time t = 0 and it is assumed that, at any time t > 0, it can be in one of states up, partial performance, or down. We further suppose that the state of the network is inspected at two time instants t1 and t2 (t1 < t2). Using the notion of the two-dimensional signature, the probability of the number of failed components of the network is calculated, at t1 and t2, under several scenarios about the states of the network. Stochastic and ageing properties of the proposed failure probabilities are studied under different conditions. We present some optimal age replacement policies to show applications of the proposed criteria. Several illustrative examples are also provided.

Geometrical Description of Two-Dimensional Optimization Design Model

2012 ◽  
Vol 472-475 ◽  
pp. 831-834
Author(s):  
Hai Wen Li ◽  
Li Hong Dong
Keyword(s):  
Optimization Design ◽  
Optimization Problem ◽  
Design Model ◽  
Curved Surface ◽  
Two Dimensional ◽  
Constraint Function ◽  
Geometrical Description ◽  
Design Variables ◽  
The Given ◽  
Dimensional Optimization

The optimization problem of objective function that has two design variables can be converted into the minimum value problem of the objective function’s curved surface within the range of constraint function in the 3D coordinate system. By using the powerful data visualization capabilities of MATLAB, draw out the curved surface of objective and constraint functions in 3D coordinates system and make geometrical description of the two-dimensional optimization design model. Through the given examples of optimization design, it can be seen that to solve the optimization design problem through this method is efficient, easy and convenient.

On classes of life distributions based on the mean time to failure function

2021 ◽  
Vol 58 (2) ◽  
pp. 289-313
Author(s):  
Ruhul Ali Khan ◽  
Dhrubasish Bhattacharyya ◽  
Murari Mitra
Keyword(s):  
Damage Model ◽  
Replacement Policy ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Moment Convergence ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
The Mean ◽  
Age Replacement ◽  
Mean Time

AbstractThe performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

scholarly journals Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint

2021 ◽  
Vol 5 (1) ◽  
pp. 1-22
Author(s):  
Jing Tang ◽  
Xueyan Tang ◽  
Andrew Lim ◽  
Kai Han ◽  
Chongshou Li ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Greedy Algorithm ◽  
Branch And Bound ◽  
Upper Bound ◽  
Optimization Problem ◽  
Approximation Factor ◽  
Real World Application ◽  
Efficiency Of Algorithms ◽  
Knapsack Constraint ◽  
Submodular Maximization

Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we show that this algorithm can achieve an approximation factor of 0.405, which significantly improves the known factors of 0.357 given by Wolsey and (1-1/e)/2\approx 0.316 given by Khuller et al. More importantly, our analysis closes a gap in Khuller et al.'s proof for the extensively mentioned approximation factor of (1-1/\sqrte )\approx 0.393 in the literature to clarify a long-standing misconception on this issue. Second, we enhance the modified greedy algorithm to derive a data-dependent upper bound on the optimum. We empirically demonstrate the tightness of our upper bound with a real-world application. The bound enables us to obtain a data-dependent ratio typically much higher than 0.405 between the solution value of the modified greedy algorithm and the optimum. It can also be used to significantly improve the efficiency of algorithms such as branch and bound.

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