Optimal block replacement policies with multiple choice at failure

1992 ◽  
Vol 29 (1) ◽  
pp. 129-141 ◽  
Author(s):  
Shey-Huei Sheu
Keyword(s):  
Operating System ◽  
Mathematical Model ◽  
Multiple Choice ◽  
Replacement Policy ◽  
Minimal Repair ◽  
Analytical Results ◽  
The Cost ◽  
Random Part ◽  
The Mathematical Model

A generalization of the block replacement policy (BRP) is proposed and analysed. Under such a policy, an operating system is preventively replaced at times kT (k = 1, 2, 3, ···), independently of its failure history. At failure an operating system is either replaced by a new or a used one or minimally repaired or remains inactive until the next planned replacement. The cost of the ith minimal repair of the new subsystem at age y depends on the random part C(y) and the deterministic part ci(y). The mathematical model is defined and general analytical results are obtained.

Optimal block replacement policies with multiple choice at failure

1992 ◽  
Vol 29 (01) ◽  
pp. 129-141 ◽  
Author(s):  
Shey-Huei Sheu
Keyword(s):  
Operating System ◽  
Mathematical Model ◽  
Multiple Choice ◽  
Replacement Policy ◽  
Minimal Repair ◽  
Analytical Results ◽  
The Cost ◽  
Random Part ◽  
The Mathematical Model

A generalization of the block replacement policy (BRP) is proposed and analysed. Under such a policy, an operating system is preventively replaced at times kT (k = 1, 2, 3, ···), independently of its failure history. At failure an operating system is either replaced by a new or a used one or minimally repaired or remains inactive until the next planned replacement. The cost of the ith minimal repair of the new subsystem at age y depends on the random part C(y) and the deterministic part ci (y). The mathematical model is defined and general analytical results are obtained.

A modified block replacement policy with two variables and general random minimal repair cost

1996 ◽  
Vol 33 (2) ◽  
pp. 557-572 ◽  
Author(s):  
Shey-Huei Sheu
Keyword(s):  
Operating System ◽  
Replacement Policy ◽  
Repair Cost ◽  
Minimal Repair ◽  
Expected Cost ◽  
Cost Rate ◽  
Age Dependent ◽  
Modified Block ◽  
The Cost ◽  
Random Part

This paper considers a modified block replacement with two variables and general random minimal repair cost. Under such a policy, an operating system is preventively replaced by new ones at times kT (k= 1, 2, ···) independently of its failure history. If the system fails in [(k − 1)T, (k − 1)T+ T0) it is either replaced by a new one or minimally repaired, and if in [(k − 1) T + T0, kT) it is either minimally repaired or remains inactive until the next planned replacement. The choice of these two possible actions is based on some random mechanism which is age-dependent. The cost of the ith minimal repair of the system at age y depends on the random part C(y) and the deterministic part ci (y). The expected cost rate is obtained, using the results of renewal reward theory. The model with two variables is transformed into a model with one variable and the optimum policy is discussed.

A modified block replacement policy with two variables and general random minimal repair cost

1996 ◽  
Vol 33 (02) ◽  
pp. 557-572 ◽  
Author(s):  
Shey-Huei Sheu
Keyword(s):  
Operating System ◽  
Replacement Policy ◽  
Repair Cost ◽  
Minimal Repair ◽  
Expected Cost ◽  
Cost Rate ◽  
Age Dependent ◽  
Modified Block ◽  
The Cost ◽  
Random Part

This paper considers a modified block replacement with two variables and general random minimal repair cost. Under such a policy, an operating system is preventively replaced by new ones at timeskT(k=1, 2, ···) independently of its failure history. If the system fails in [(k − 1)T,(k− 1)T+T0) it is either replaced by a new one or minimally repaired, and if in [(k− 1)T+T0, kT) it is either minimally repaired or remains inactive until the next planned replacement. The choice of these two possible actions is based on some random mechanism which is age-dependent. The cost of theith minimal repair of the system at ageydepends on the random partC(y) and the deterministic partci(y). The expected cost rate is obtained, using the results of renewal reward theory. The model with two variables is transformed into a model with one variable and the optimum policy is discussed.

scholarly journals An Optimized Mathematical Model for Items Supplies Planning of a Logistic System

2016 ◽  
Vol 10 (10) ◽  
pp. 133
Author(s):  
Mohammad Ali Nasiri Khalili ◽  
Mostafa Kafaei Razavi ◽  
Morteza Kafaee Razavi
Keyword(s):  
Mathematical Model ◽  
Mixed Integer ◽  
Logistics System ◽  
Proposed Model ◽  
Multiple Objective Decision Making ◽  
System Requirements ◽  
Purchasing Logistics ◽  
The Cost ◽  
The Mathematical Model ◽  
First Time

Items supplies planning of a logistic system is one of the major issue in operations research. In this article the aim is to determine how much of each item per month from each supplier logistics system requirements must be provided. To do this, a novel multi objective mixed integer programming mathematical model is offered for the first time. Since in logistics system, delivery on time is very important, the first objective is minimization of time in delivery on time costs (including lack and maintenance costs) and the cost of purchasing logistics system. The second objective function is minimization of the transportation supplier costs. Solving the mathematical model shows how to use the Multiple Objective Decision Making (MODM) can provide the ensuring policy and transportation logistics needed items. This model is solved with CPLEX and computational results show the effectiveness of the proposed model.

MATHEMATICAL MODELLING FOR FISH FEED FORMULATION OF MYSTUS NEMURUS SP. CATFISH: OPTIMIZING GROWTH AND NUTRIENTS REQUIREMENTS

2018 ◽  
Vol 80 (6) ◽  
Author(s):  
Nur Aidya Hanum Aizam ◽  
Rabiatul Adawiyah Ibrahim ◽  
Raphael Lee Kuok Lung ◽  
Pang Yen Ling ◽  
Aidilla Mubarak
Keyword(s):  
Mathematical Model ◽  
Nutrient Composition ◽  
Future Research ◽  
Fish Feed ◽  
Research Directions ◽  
Feed Formulation ◽  
Future Research Directions ◽  
The Cost ◽  
The Mathematical Model ◽  
Mystus Nemurus

This study integrates mathematical model in the plan of producing a fish feed formulation by reducing the total cost without neglecting the nutrient requirements. This study focuses on producing the perfect combination of fish feed for Mystus nemurus sp. catfish in different stages of life. The mathematical model developed will consider their required nutrients in each stage, the cost of each ingredient and the amount of nutrients to be consumed (nutrient composition of fish feed ingredients). This research employs AIMMS mathematical software to assist with the computation. The results from this study obtain a much better combination of different ingredients compared to available commercial pellets in terms of nutrient composition and production cost. The combinations yield much cheaper costs yet boosts up the nutrient consumptions, which is an eye-opener for independent local fish farmers. Thorough discussion on utilizing the results with future research directions will also be included.

Performance Analysis of Parallel Feed LT-MED Desalination System with Thermal Vapor Compressor

2011 ◽  
Vol 347-353 ◽  
pp. 3058-3063 ◽  
Author(s):  
Xiao Hua Liu ◽  
Guo Jian Cao ◽  
Sheng Qiang Shen ◽  
Guang Bin Zhao
Keyword(s):  
Mathematical Model ◽  
Flow Resistance ◽  
Tube Bundle ◽  
Steam Temperature ◽  
Heating Steam ◽  
Temperature Loss ◽  
Output Ratio ◽  
Actual Operation ◽  
The Cost ◽  
The Mathematical Model

This paper presents a theoretical analysis on parallel feed LT-MED desalination system with thermal vapor compressor which is helpful to the design and operation of such kind of seawater desalination plant. The mathematical model of a parallel feed LT-MED desalination system with thermal vapor compressor (TVC) is developed on the basis of the mass and energy conservation equations. In the model, the temperature loss is considered caused by the boiling point elevation (BPE) of seawater and the steam flow resistance is also included caused by flowing through tube bundle demisters and pipelines between adjacent evaporators. The property parameters of seawater are taken as the functions of temperature and concentration. A computer program is drawn up to solve the mathematical model. The calculation is based on the system with rated water production 3000 t/d. Taking actual operation into account, the influence of heating steam temperature of the first effect and entrained steam position of TVC on system performance are analyzed. The results show that when other relative parameters are fixed, the gained output ratio (GOR) and the total area of evaporators change slightly with the increasing of the heating steam temperature of first effect under the calculation condition of this paper. The results also demonstrate that there exist suitable entrained steam positions of TVC for the cost of water.

Lapping Aspheric Workpiece Using Bending Method

2013 ◽  
Vol 331 ◽  
pp. 595-599
Author(s):  
Chun Min Shang ◽  
Dong Mei Zhang ◽  
Jian Dong Yang
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
New Method ◽  
Aspheric Surface ◽  
Shape Precision ◽  
Tool Shape ◽  
Forming Precision ◽  
Surface Precision ◽  
The Cost ◽  
The Mathematical Model

A new method is proposed that high speed lapping aspheric surface workpiece using lapping tool by means of bending because there processing difficult, In this study, the principle of high speed lapping has been presented, the mathematical model for the lapping tool has been established, and the equidistance curve error of the lapping tool has been analyzed. The results of the experiment indicate that the forming precision of the lapping tool is high using this method, the surface precision of the workpiece reaches micron grade, furthermore, the aspheric surface workpiece can been machined using this method in lapping, and that it can meet the need of medium precision of machining the aspheric surface workpiece. The experiment result indicates that the the lapping tool shape precision is high, the lapping error of the workpiece is 0.0108mm, and lapping efficiency is high and the cost is low. This aspheric lapping method has incomparable superiority of other processing methods.

Modeling the Multiobjective Optimization of Electricity Consumption for Residential Consumers

2013 ◽  
Vol 748 ◽  
pp. 493-497 ◽  
Author(s):  
José L. Bernal-Agustín ◽  
Tomás Cortés-Arcos ◽  
Rodolfo Dufo-López ◽  
Juan M. Lujano-Rojas ◽  
Cláudio Monteiro
Keyword(s):  
Mathematical Model ◽  
Multiobjective Optimization ◽  
Smart Grid ◽  
Evolutionary Algorithm ◽  
Pareto Optimality ◽  
Electricity Consumption ◽  
Cost Of Electricity ◽  
Multiobjective Evolutionary Algorithm ◽  
The Cost ◽  
The Mathematical Model

This paper presents a mathematical model to simultaneously optimize the cost of electricity and the satisfaction of a residential consumer using the communication infrastructure of a smart grid. For this task the concept of Pareto optimality has been used. It is possible to consider the satisfaction of the consumer as an independent objective to be maximized, and simultaneously, to minimize the cost of the electrical bill. In future works a multiobjective evolutionary algorithm will be applied along with the mathematical model presented in this paper.

scholarly journals A Probabilistic Analysis of Path Duration Using Routing Protocol in VANETs

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ram Shringar Rao ◽  
Sanjay Kumar Soni ◽  
Nanhay Singh ◽  
Omprakash Kaiwartya
Keyword(s):  
Mathematical Model ◽  
Routing Protocol ◽  
Delivery Ratio ◽  
Estimation Model ◽  
Routing Metrics ◽  
Analytical Results ◽  
Path Duration ◽  
Result Analysis ◽  
Duration Estimation ◽  
The Mathematical Model

In recent years, various routing metrics such as throughput, end-to-end delay, packet delivery ratio, path duration, and so forth have been used to evaluate the performance of routing protocols in VANETs. Among these routing metrics, path duration is one of the most influential metrics. Highly mobile vehicles cause frequent topology change in vehicular network environment that ultimately affects the path duration. In this paper, we have derived a mathematical model to estimate path duration using border node-based most forward progress within radius (B-MFR), a position based routing protocol. The mathematical model for estimation of path duration consists of probability of finding next-hop node in forwarding region, estimation of expected number of hops, probability distribution of velocity of nodes, and link duration between each intermediate pair of nodes. The analytical results for the path duration estimation model have been obtained using MATLAB. The model for path duration estimation has been simulated in NS2. Each of the analytical results has been verified through respective simulation results. The result analysis clearly reveals that path duration increases with the increase in transmission range and node density and decreases with the increase in the number of hops in the path and velocity of the nodes.

scholarly journals Mathematical analysis of tuberculosis control model using nonsingular kernel type Caputo derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Saeed Ahmad ◽  
Rafi Ullah ◽  
Dumitru Baleanu
Keyword(s):  
Mathematical Model ◽  
Research Work ◽  
Control Model ◽  
Tuberculosis Control ◽  
Fixed Point Approach ◽  
Analytical Results ◽  
Adomian Decomposition ◽  
The Mathematical Model ◽  
Tuberculosis Disease ◽  
Kernel Type

AbstractThis research work investigates some theoretical and semi-analytical results for the mathematical model of tuberculosis disease via derivative due to Caputo and Fabrizio. The concerned derivative involves exponential kernel and very recently it has been adapted for various applied problems. The required results are established by using some fixed point approach of Krasnoselskii and Banach. Further, by the use of iterative tools of Adomian decomposition and Laplace, the semi-analytical results are studied. Some graphical results are given with discussion.

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