Browsing by Author "Wu, Chia-Huang"

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A heuristic algorithm for the optimization of a retrial system with Bernoulli vacation
(2013-03-01)
Ke, Jau-Chuan
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Wu, Chia-Huang
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Pearn, Wen Lea
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工業工程與管理學系
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Department of Industrial Engineering and Management
In this study, we consider an M/M/c retrial queue with Bernoulli vacation under a single vacation policy. When an arrived customer finds a free server, the customer receives the service immediately; otherwise the customer would enter into an orbit. After the server completes the service, the server may go on a vacation or become idle (waiting for the next arriving, retrying customer). The retrial system is analysed as a quasi-birth-and-death process. The sufficient and necessary condition of system equilibrium is obtained. The formulae for computing the rate matrix and stationary probabilities are derived. The explicit close forms for system performance measures are developed. A cost model is constructed to determine the optimal values of the number of servers, service rate, and vacation rate for minimizing the total expected cost per unit time. Numerical examples are given to demonstrate this optimization approach. The effects of various parameters in the cost model on system performance are investigated.
A HEURISTIC ALGORITHM FOR THE OPTIMIZATION OF M/M/s QUEUE WITH MULTIPLE WORKING VACATIONS
(2012-02-01)
Wu, Chia-Huang
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Wang, Kuo-Hsiung
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Ke, Jau-Chuan
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Ke, Jyh-Bin
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工業工程與管理學系
This paper focuses on an M/M/s queue with multiple working vacations such that the server works with different service rates rather than no service during the vacation period. We show that this is a generalization of an M/M/1 queue with working vacations in the literature. Service times during vacation period, or during service period and vacation times are all exponentially distributed. We obtain the useful formula for the rate matrix R through matrix-geometric method. A cost function is formulated to determine the optimal number of servers subject to the stability conditions. We apply the direct search algorithm and Newton-Quasi algorithm to heuristically find an approximate solution to the constrained optimization problem. Numerical results are provided to illustrate the effectiveness of the computational algorithm.
A Note on a Multi-server Queue with Vacations of Multiple Groups of Servers
(2013-12-01)
Kei, Jau-Chuan
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Wu, Chia-Huang
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Zhang, Zhe George
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工業工程與管理學系
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Department of Industrial Engineering and Management
We study a Markovian queueing system with unreliable servers and two possible groups of servers taking two different types of vacations. Once the number of idle of servers reaches one of the two critical numbers in the system, a group of servers will take a single synchronous vacation (or leave for doing a secondary job). After taking the vacation, the servers return to attend the queue (or stay idle for the next arriving customer). Therefore, there can be a maximum of two groups of servers taking two different types of vacations at a time (doing some secondary jobs). The servers are subject to failure when attending the queue. The stability condition for the system and the stationary performance measures are developed by using the matrix-analytical method. A cost model is constructed to determine the optimal vacation policy and the optimal service rate of each server. Some numerical results are presented to illustrate the optimization procedures.
Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule
(2011-05-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper considers an infinite-capacity M/M/c queueing system with modified Bernoulli vacation under a single vacation policy. At each service completion of a server, the server may go for a vacation or may continue to serve the next customer, if any in the queue. The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. The explicit closed-form of the rate matrix is derived and the useful formula for computing stationary probabilities is developed by using matrix analytic approach. System performance measures are explicitly developed in terms of computable forms. A cost model is derived to determine the optimal values of the number of servers, service rate and vacation rate simultaneously at the minimum total expected cost per unit time. Illustrative numerical examples demonstrate the optimization approach as well as the effect of various parameters on system performance measures. (c) 2010 Elsevier Inc. All rights reserved.
An effective powerful test for one-sided supplier selection problem with multiple independent characteristics
(2016)
Pearn, W. L.
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Wu, Chia-Huang
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Chuang, Ching-Ching
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工業工程與管理學系
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Department of Industrial Engineering and Management
In this paper, we use the CT PU index to investigate the supplier selection problem for one-sided processes with multiple independent characteristics. We first review the existing approach, which we refer to as the division method, then develop a new exact approach called the subtraction method. A two-stage selection procedure is developed based on the subtraction method for practical applications. We then compared the two methods with regard to selection power. The results show that the subtraction method we propose is indeed more powerful than the existing division method. A thin-film transistor type liquid-crystal display (TFT-LCD) application example is provided to illustrate the testing procedure.
An optimum approach of profit analysis on the machine repair system with heterogeneous repairmen
(2015-02-15)
Ke, Jau-Chuan
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Liu, Tzu-Hsin
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Wu, Chia-Huang
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工業工程與管理學系
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Department of Industrial Engineering and Management
We consider a machine repair problem with queue-dependent heterogeneous repairmen. The stationary probability distribution of the number of failed machines in the system is derived. A profit model is developed to determine the optimal values of threshold to assign/add one more repairman for increasing the total service rate where the service rate is assumed adjustable. The probabilistic global search Lausanne (PGSL) method is employed to find an initial trial solution. Based on this initial solution, a direct search method is applied to obtain the optimal values of the threshold and, then, the Quasi-Newton method is implemented to adjust the corresponding service rates. Some numerical experiments are performed to justify the efficiency of the optimum approach. (C) 2015 Elsevier Inc. All rights reserved.
Analysis of an infinite multi-server queue with an optional service
(2013-06-01)
Ke, Jau-Chuan
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Wu, Chia-Huang
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Pearn, Wen Lea
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工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper deals with an infinite-capacity multi-server queueing system with a second optional service (SOS) channel. The inter-arrival times of arriving customers, the service times of the first essential service (FES) and the SOS channel are all exponentially distributed. A customer may leave the system after the FES channel with a probability (1 - theta), or the completion of the FES may immediately require a SOS with a probability theta (0 <= theta <= 1). The formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is developed to simultaneously determine the optimal values of the number of servers and the two service rates at the minimal total expected cost per unit time. Quasi-Newton method and Particle Swarm Optimization (PSO) method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided from which several system performance measures are calculated based on the assumed numerical values of the system parameters. (c) 2013 Elsevier Ltd. All rights reserved.
Analysis of the Machine Repair Models With Multi-Threshold Synchronous Vacations
(2013-05-01)
Wu, Chia-Huang
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Ke, Jau-Chuan
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Choudhury, Gautam
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工業工程與管理學系
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Department of Industrial Engineering and Management
In this paper, we present an analysis of a machine repair problem with M operating machines and S standbys, in which c repairmen are responsible for supervising these machines and follow a multi-threshold, synchronous vacation policy. With such a policy, at a repair completion instant, if the number of the failed machines in the system is less than a preset threshold value, partial idle servers together take a single vacation (or leave for a random amount of time doing other secondary job). At the end of a vacation, they return to repair the failed machines (or waits for the arrival). The steady-state probabilities are solved by using the matrix-analytic method, and formulae of system performance measures are thereby obtained. A cost model is then developed to formulate an optimization problem to find the minimum cost. The direct search and quasi-Newton methods are implemented to determine the optimal number of servers, the optimal threshold policy and the optimal repair rate.
Computational algorithm and parameter optimization for a multi-server system with unreliable servers and impatient customers
(2010-12-01)
Wu, Chia-Huang
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Ke, Jau-Chuan
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工業工程與管理學系
;
Department of Industrial Engineering and Management
We consider an infinite capacity M/M/c queueing system with c unreliable servers, in which the customers may balk (do not enter) and renege (leave the queue after entering). The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. System performance measures are explicitly derived in terms of computable forms. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is derived to determine the optimal values of the number of servers, service rate and repair rate simultaneously at the minimal total expected cost per unit time. The parameter optimization is illustrated numerically by the Quasi-Newton method. (C) 2010 Elsevier B.V. All rights reserved.
Cost Analysis of a vacation machine repair model
(2011-01-01)
Ke, Jau-Chuan
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Wu, Chia-Huang
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Liou, Cheng-Hwai
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Wang, Tsung-Yin
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工業工程與管理學系
This paper investigates a machine repair problem with homogeneous machines and standbys available, in which multiple technicians are responsible for supervising these machines and operate a (R, V, K) synchronous vacation policy. With such a policy, if any V idle technicians exist in the system, these V (V < R) technicians would take a synchronous vacation. Upon returning from vacation, they would take another vacation if there is no broken machine waiting in the queue. This pattern continues until at least one failed machine arrives. It is assumed that the number of teams/groups on vacation is less than or equal to K (0 <= KV < R). The matrix analytical method is employed to obtain a steady-state probability and the closed-form expression of the system performance measures. Efficient approaches are performed to deal with the optimization problem of the discrete / continuous variables while maintaining the system availability at a specified acceptable level. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Asia Pacific Business Innovation and Technology Management Society
Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns
(2015-04-01)
Yang, Dong-Yuh
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Wu, Chia-Huang
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工業工程與管理學系
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Department of Industrial Engineering and Management
This paper investigates the N-policy M/M/1 queueing system with working vacation and server breakdowns. As soon as the system becomes empty, the server begins a working vacation. The server works at a lower service rate rather than completely stopping service during a vacation period. The server may break down with different breakdown rates during the idle, working vacation, and normal busy periods. It is assumed that service times, vacation times, and repair times are all exponentially distributed. We analyze this queueing model as a quasi-birth-death process. Furthermore, the equilibrium condition of the system is derived for the steady state. Using the matrix-geometric method, we find the matrix-form expressions for the stationary probability distribution of the number of customers in the system and system performance measures. The expected cost function per unit time is constructed to determine the optimal values of the system decision variables, including the threshold N and mean service rates. We employ the particle swarm optimization algorithm to solve the optimization problem. Finally, numerical results are provided, and an application example is given to demonstrate the applicability of the queueing model. (C) 2015 Elsevier Ltd. All rights reserved.
Dynamic Control of a Machine Repair Problem with Switching Failure and Unreliable Repairmen
(1970-01-01)
Wu, Chia-Huang
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Yang, Dong-Yuh
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工業工程與管理學系
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Department of Industrial Engineering and Management
This study examines the dynamic control of an M/M/2 machine repair system with R operating machines, S standbys, and two unreliable repairmen, wherein standbys are subject to switching failures. We apply the matrix analytic method to derive explicit expressions of the stationary probability distributions as well as matrix expressions of the system performance measures. We construct a cost model and determine the optimal dynamic operating policy to minimize the expected cost function per unit time. Sensitivity analysis is conducted using numerical examples. The results of sensitivity analysis indicate that the optimal thresholds and corresponding minimum expected cost increase as the number of operating machines or standbys increases. Moreover, the minimum expected cost is sensitive to the mean arrival and repair rates. The results provide managers with decision reference for productivity improvement and cost reduction.
Modelling and optimisation of a two-server queue with multiple vacations and working breakdowns
(1970-01-01)
Yang, Dong-Yuh
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Chen, Yi-Hsuan
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Wu, Chia-Huang
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工業工程與管理學系
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Department of Industrial Engineering and Management
This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and may leave for a vacation when the system becomes empty. Sever 2 is unreliable and may break down while serving customers. When a breakdown occurs, Server 2 reduces the service rate rather than halting service. We formulate this queueing model as a quasi birth-and-death (QBD) process, using the matrix geometric method to compute the stationary distribution of system size. We also develop several measures to evaluate the performance of the system. A cost model based on system performance measures is formulated as a heuristic cost optimisation problem subject to stability conditions. A canonical particle swarm optimisation algorithm is used to obtain numerical solutions for the approximate optimal service rates of Server 1 and Server 2. Moreover, we present numerical results showing the effects of various parameters on the approximate optimal service rates as well as a practical example illustrating the application of the proposed model.
Modified processes capability assessment with dynamic mean shift
(1970-01-01)
Wu, Chia-Huang
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工業工程與管理學系
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Department of Industrial Engineering and Management
Rapid advancements in manufacturing technology have seen electronic products becoming lighter and thinner. This has led to production yield requirements of sawing processes in the semiconductor industry becoming increasingly strict. For sawing processes requiring a very low fraction of defective, the process capability index C-pk is widely applied for production yield measurement under the assumption of process stability. However, in practice, even when the typical control charts are implemented, dynamic and unobserved natures of the actual process mean shift may occur. Since the trial control limits are established with reference to random samples, the associated performances are also with uncertainty because of sampling error. In this paper, we investigate the effects of parameter estimation error on the development of the phase I control chart and further compare three methods with various estimators for the process standard deviation. Then, we tabulate the modified adjustment magnitudes for the dynamic C-pk under various subgroup sizes and sample sizes. On the basis of the simulation results, the proposed method can avoid overestimating the true process capability and make more trustworthy decisions. Finally, for demonstration purposes, an application of process capability measures for a sawing process is presented.
Multi-server machine repair model with standbys and synchronous multiple vacation
(2012-02-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper investigates a machine repair problem with homogeneous machines and standbys available, in which multiple technicians are responsible for supervising these machines and operate a (R, V, K) synchronous vacation policy. With such a policy, if any V idle technicians exist in the system, these V (V < R) technicians would take a synchronous vacation. Upon returning from vacation, they would take another vacation if there is no broken machine waiting in the queue. This pattern continues until at least one failed machine arrives. It is assumed that the number of teams/groups on vacation is less than or equal to K (0 <= KV < R). The matrix analytical method is employed to obtain a steady-state probability and the closed-form expression of the system performance measures. Efficient approaches are performed to deal with the optimization problem of the discrete/continuous variables while maintaining the system availability at a specified acceptable level. (C) 2011 Elsevier Ltd. All rights reserved.
Multi-server machine repair model with standbys and synchronous multiple vacation (vol 62, pg 296, 2012)
(2012-05-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Multi-server machine repair problems under a (V,R) synchronous single vacation policy
(2014-04-01)
Wu, Chia-Huang
;
Ke, Jau-Chuan
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper considers a machine repair problem with M operating machines and S standbys, in which R repairmen are responsible for supervising these machines and operate a (V,R) vacation policy. With such policy, if the number of the failed machines is reduced to R - V (R > V) (there exists V idle repairmen) at a service completion, these V idle servers will together take a synchronous vacation (or leave for other secondary job). Upon returning from the vacation, they do not take a vacation again and remain idle until the first arriving failed machine arrives. The steady-state probabilities are solved in terms of matrix forms and the system performance measures are obtained. Algorithmic procedures are provided to deal with the optimization problem of discrete/continuous decision variables while maintaining a minimum specified level of system availability. (C) 2013 Elsevier Inc. All rights reserved.
Multi-server retrial queue with second optional service: algorithmic computation and optimisation
(2011)
Ke, Jau-Chuan
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Wu, Chia-Huang
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Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
We consider an infinite-capacity M/M/c retrial queue with second optional service (SOS) channel. An arriving customer finds a free server would enter the service (namely, the first essential service, denoted by FES) immediately; otherwise, the customer enters into an orbit and starts generating requests for service in an exponentially distributed time interval until he finds a free server and begins receiving service. After the completion of FES, only some of them receive SOS. The retrial system is modelled by a quasi-birth-and-death process and some system performance measures are derived. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix-analytic approach. A cost model is derived to determine the optimal values of the number of servers and the two different service rates simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimisation approach as well as the effect of various parameters on system performance measures.
Multi-threshold policy for a multi-server queue with synchronous single vacation
(2013-03-01)
Wu, Chia-Huang
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Ke, Jau-Chuan
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper considers an infinite buffer M/M/c queueing system in which servers follow a multi-threshold vacation policy. With such a policy, at a service completion instant, if the number of customers in the system is less than a prefixed threshold value, part of servers together take a single vacation (or leave for a random amount of time doing other secondary job). At the vacation completion instant, they return to the system for serving the customers. Some practical production and inventory systems or call centers could be modeled as this Markovian queue with a multi-threshold vacation policy. Using the Markovian process model, we obtain the exact closed-form expression of rate matrix and the stationary distribution of the number of customers in the system. A cost model is developed to search the joint optimal values of the thresholds of vacation policy and service rate of each server, which minimizes the long-term average cost. Some numerical results are presented to illustrate the optimization procedures. (C) 2012 Elsevier Ltd. All rights reserved.
Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation
(2010-05-15)
Yang, Dong-Yuh
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Wang, Kuo-Hsiung
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Wu, Chia-Huang
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工業工程與管理學系
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Department of Industrial Engineering and Management
This paper analyzes the F-policy M/M/1/K queueing system with working vacation and an exponential startup time. The F-policy deals with the issue of controlling arrivals to a queueing system, and the server requires a startup time before allowing customers to enter the system. For the queueing systems with working vacation, the server can still provide service to customers rather than completely stop the service during a vacation period. The matrix-analytic method is applied to develop the steady-state probabilities, and then obtain several system characteristics. We construct the expected cost function and formulate an optimization problem to find the minimum cost. The direct search method and Quasi-Newton method are implemented to determine the optimal system capacity K, the optimal threshold F and the optimal service rates (mu(B), mu(V)) at the minimum cost. A sensitivity analysis is conducted to investigate the effect of changes in the system parameters on the expected cost function. Finally, numerical examples are provided for illustration purpose. (C) 2010 Elsevier B.V. All rights reserved.