Optimization of a condition-based duration-varying preventive maintenance policy for the stockless production system based on queueing model

Jianyu Cao; Weixin Xie

doi:10.3934/jimo.2018085

Previous Article
Performance analysis of a cooperative flow game algorithm in ad hoc networks and a comparison to Dijkstra's algorithm
JIMO Home
This Issue
Next Article
Global and local advertising strategies: A dynamic multi-market optimal control model

July 2019, 15(3): 1049-1083. doi: 10.3934/jimo.2018085

Optimization of a condition-based duration-varying preventive maintenance policy for the stockless production system based on queueing model

Jianyu Cao ^, and Weixin Xie

College of information engineering, Shenzhen University, Shenzhen 518060, China

^* Corresponding author: Jianyu Cao

Received April 2016 Revised March 2018 Published July 2018

Fund Project: This work is supported by the National Natural Science Foundations of China (Grant Nos. 61401286, 61702341 and 61771319) and the Research Project of Shenzhen Technology University (Grant No. 201727).

A stockless production system is considered, in which the products are not produced until the orders are accepted. Due to this character, the duration of the preventive maintenance has an influence on the lead time. In addition, in this stockless production system, the cost of the preventive maintenance depends on its duration; if the lead time exceeds to the quoted lead time, some penalty cost should be considered; and the non-conforming products can still be sold by a discount. A condition-based duration-varying preventive maintenance policy is designed for the stockless production system, by making a tradeoff among the duration of the preventive maintenance, the time for the machine continuously producing, and the lead time of the order. According to the characters of the stockless production system with the designed preventive maintenance policy, it can be modeled by a BMAP/G/1 infinite-buffer queueing model with gated service and queue-length dependent vacation. Based on this queueing model, the stationary probability distributions of four performance measures for the stockless production system are analyzed, including, the number of the products produced in a production cycle, the number of the unfulfilled orders at arbitrary time, the time required to fulfill the tasks present at arbitrary time, and the lead time of the order accepted at arbitrary time. Moreover, based on some information of these performance measures, a profit function, which represents the average profit of the manufacture in a production cycle, is constructed to optimize the designed preventive maintenance policy according to specific conditions. Finally, given an example with the purchasers having different sensitivities to the lead time, some numerical experiments are carried out; and from the numerical experiments, some general results can be inferred for the stockless production system with the designed preventive maintenance policy.

Keywords: Preventive maintenance, stockless production system, queueing model, batch Markovian arrival process, gated service.

Mathematics Subject Classification: Primary: 90B30, 60K25; Secondary: 68M20.

Citation: Jianyu Cao, Weixin Xie. Optimization of a condition-based duration-varying preventive maintenance policy for the stockless production system based on queueing model. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1049-1083. doi: 10.3934/jimo.2018085

References:

[1]	E.-H. Aghezzaf, A. Khatab and P. L. Tam, Optimizing production and imperfect preventive maintenance planning's integration in failure-prone manufacturing systems, Reliability Engineering & System Safety, 145 (2016), 190-198. doi: 10.1016/j.ress.2015.09.017. Google Scholar
[2]	A. Arreola-Risa and M. F. Keblis, Design of stockless production systems, Production and Operations Management, 22 (2013), 203-215. doi: 10.1111/j.1937-5956.2012.01343.x. Google Scholar
[3]	J.-B. Bacot and J. H. Dshalalow, A bulk input queueing system with batch gated service and multiple vacation policy, Mathematical and Computer Modelling, 34 (2001), 873-886. doi: 10.1016/S0895-7177(01)00106-6. Google Scholar
[4]	A. D. Banik, The infinite-buffer single server queue with a variant of multiple vacation policy and batch {M}arkovian arrival process, Applied Mathematical Modelling, 33 (2009), 3025-3039. doi: 10.1016/j.apm.2008.10.021. Google Scholar
[5]	A. D. Banik and S. K. Samanta, Controlling packet loss of bursty and correlated traffics in a variant of multiple vacation policy, in 2013 International Conference on Distributed Computing and Internet Technology (ICDCIT), Vol. 7753 of Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2013,208-219. doi: 10.1007/978-3-642-36071-8_16. Google Scholar
[6]	R. Bellman, Introduction to Matrix Analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. Google Scholar
[7]	F. Berthaut, A. Gharbi, J.-P. Kenné and J.-F. Boulet, Improved joint preventive maintenance and hedging point policy, International Journal of Production Economics, 127 (2010), 60-72. doi: 10.1016/j.ijpe.2010.04.030. Google Scholar
[8]	B. Bouslah, A. Gharbi and R. Pellerin, Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint, Omega, 61 (2016), 110-126. doi: 10.1016/j.omega.2015.07.012. Google Scholar
[9]	B. Bouslah, A. Gharbi and R. Pellerin, Joint economic design of production, continuous sampling inspection and preventive maintenance of a deteriorating production system, International Journal of Production Economics, 173 (2016), 184-198. doi: 10.1016/j.ijpe.2015.12.016. Google Scholar
[10]	L. Breuer and D. Baum, An Introduction to Queueing Theory and Matrix-Analytic Methods, Springer, Dordrecht, 2005. Google Scholar
[11]	J. Cao and W. Xie, Stability of a two-queue cyclic polling system with BMAPs under gated service and state-dependent time-limited service disciplines, Queueing Systems, 85 (2017), 117-147. doi: 10.1007/s11134-016-9504-z. Google Scholar
[12]	A. Chelbi and N. Rezg, Analysis of a production/inventory system with randomly failing production unit subjected to a minimum required availability level, International Journal of Production Economics, 99 (2006), 131-143. doi: 10.1016/j.ijpe.2004.12.012. Google Scholar
[13]	A. Chelbi, N. Rezg and M. Radhoui, Simultaneous determination of production lot size and preventive maintenance schedule for unreliable production system, Journal of Quality in Maintenance Engineering, 14 (2008), 161-176. doi: 10.1108/13552510810877665. Google Scholar
[14]	E. Çinlar, Markov renewal theory, Advances in Applied Probability, 1 (1969), 123-187. doi: 10.2307/1426216. Google Scholar
[15]	E. Çinlar, Introduction to Stochastic Processes, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1975. Google Scholar
[16]	D. Das, A. Roy and S. Kar, A volume flexible economic production lot-sizing problem with imperfect quality and random machine failure in fuzzy-stochastic environment, Computers & Mathematics with Applications, 61 (2011), 2388-2400. doi: 10.1016/j.camwa.2011.02.015. Google Scholar
[17]	K. Dhouib, A. Gharbi and M. N. Ben Aziza, Joint optimal production control/preventive maintenance policy for imperfect process manufacturing cell, International Journal of Production Economics, 137 (2012), 126-136. doi: 10.1016/j.ijpe.2012.01.023. Google Scholar
[18]	L. Doyen, Semi-parametric estimation of Brown-Proschan preventive maintenance effects and intrinsic wear-out, Computational Statistics & Data Analysis, 77 (2014), 206-222. doi: 10.1016/j.csda.2014.02.022. Google Scholar
[19]	D. Gibson and E. Seneta, Monotone infinite stochastic matrices and their augmented truncations, Stochastic Processes and their Applications, 24 (1987), 287-292. doi: 10.1016/0304-4149(87)90019-6. Google Scholar
[20]	W. K. Grassmann, M. I. Taksar and D. P. Heyman, Regenerative analysis and steady state distributions for Markov chains, Operations Research, 33 (1985), 1107-1116. doi: 10.1287/opre.33.5.1107. Google Scholar
[21]	D. Gupta and S. Benjaafar, Make-to-order, make-to-stock, or delay product differentiation? A common framework for modeling and analysis, IIE Transactions, 36 (2004), 529-546. doi: 10.1080/07408170490438519. Google Scholar
[22]	E. M. Jewkes and A. S. Alfa, A queueing model of delayed product differentiation, European Journal of Operational Research, 199 (2009), 734-743. doi: 10.1016/j.ejor.2008.08.001. Google Scholar
[23]	Y. -L. Jin, Multi-objective optimization of flexible period preventive maintenance on a single machine, in 2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (ICQR2MSE), Chengdu, China, 2012,475-479. doi: 10.1109/ICQR2MSE.2012.6246277. Google Scholar
[24]	V. V. Krivtsov, Recent advances in theory and applications of stochastic point process models in reliability engineering, Reliability Engineering & System Safety, 92 (2007), 549-551. doi: 10.1016/j.ress.2006.05.001. Google Scholar
[25]	G.-L. Liao, Production and maintenance policies for an {EPQ} model with perfect repair, rework, free-repair warranty, and preventive maintenance, IEEE Transactions on Systems, Man, Cybernetics: Systems, 46 (2016), 1129-1139. doi: 10.1109/TSMC.2015.2465961. Google Scholar
[26]	J. D. C. Little, A proof for the queuing formula: L = λW, Operations Research, 9 (1961), 383-387. doi: 10.1287/opre.9.3.383. Google Scholar
[27]	C. Liu, Y. Fan, C. Zhao and J. Wang, Multiple common due-dates assignment and optimal maintenance activity scheduling with linear deteriorating jobs, Journal of Industrial & Management Optimization, 13 (2017), 713-720. doi: 10.3934/jimo.2016042. Google Scholar
[28]	D. M. Lucantoni, New results on the single server queue with a bath Markovian arrival process, Stochastic Models, 7 (1991), 1-46. doi: 10.1080/15326349108807174. Google Scholar
[29]	D. M. Lucantoni, K. S. Meier-Hellstern and M. F. Neuts, A single-server queue with server vacations and a class of non-renewal arrival processes, Advances in Applied Probability, 22 (1990), 676-705. doi: 10.2307/1427464. Google Scholar
[30]	L. Mann, A. Saxena and G. M. Knapp, Statistical-based or condition-based preventive maintenance?, Journal of Quality in Maintenance Engineering, 1 (1995), 46-59. doi: 10.1108/13552519510083156. Google Scholar
[31]	R. Mehdi, R. Nidhal and C. Anis, Integrated maintenance and control policy based on quality control, Computers & Industrial Engineering, 58 (2010), 443-451. doi: 10.1016/j.cie.2009.11.002. Google Scholar
[32]	T. Nakagawa, Periodic and sequential preventive maintenance policies, Journal of Applied Probability, 23 (1986), 536-542. doi: 10.2307/3214197. Google Scholar
[33]	M. F. Neuts, Matrix-geometric Solutions in Stochastic Models. An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, 1981. Google Scholar
[34]	M. Radhoui, N. Rezg and A. Chelbi, Integrated model of preventive maintenance, quality control and buffer sizing for unreliable and imperfect production systems, International Journal of Production Research, 47 (2009), 389-402. doi: 10.1080/00207540802426201. Google Scholar
[35]	V. Ramaswami, The N/G/1 queue and its detailed analysis, Advances in Applied Probability, 12 (1980), 222-261. doi: 10.2307/1426503. Google Scholar
[36]	J. Schutz, N. Rezg and J.-B. Léger, Periodic and sequential preventive maintenance policies over a finite planning horizon with a dynamic failure law, Journal of Intelligent Manufacturing, 22 (2011), 523-532. doi: 10.1007/s10845-009-0313-7. Google Scholar
[37]	M. Shahriari, N. Shoja, A. E. Zade, S. Barak and M. Sharifi, JIT single machine scheduling problem with periodic preventive maintenance, Journal of Industrial Engineering International, 12 (2016), 299-310. doi: 10.1007/s40092-016-0147-9. Google Scholar
[38]	O. Tang, R. W. Grubbström and S. Zanoni, Planned lead time determination in a make-to-order remanufacturing system, International Journal of Production Economics, 108 (2007), 426-435. doi: 10.1016/j.ijpe.2006.12.034. Google Scholar
[39]	V. M. Vishnevsky, A. N. Dudin, O. V. Semenova and V. I. Klimenok, Performance analysis of the BMAP/G/1 queue with gated servicing and adaptive vacations, Performance Evaluation, 68 (2011), 446-462. doi: 10.1016/j.peva.2011.02.003. Google Scholar
[40]	H.-M. Wee, W.-T. Wang and P.-C. Yang, A production quantity model for imperfect quality items with shortage and screening constraint, International Journal of Production Research, 51 (2013), 1869-1884. doi: 10.1080/00207543.2012.718453. Google Scholar
[41]	L. Xiao, S. Song, X. Chen and D. W. Coit, Joint optimization of production scheduling and machine group preventive maintenance, Reliability Engineering & System Safety, 146 (2016), 68-78. doi: 10.1016/j.ress.2015.10.013. Google Scholar
[42]	K.-C. Ying, C.-C. Lu and J.-C. Chen, Exact algorithms for single-machine scheduling problems with a variable maintenance, Computers & Industrial Engineering, 98 (2016), 427-433. doi: 10.1016/j.cie.2016.05.037. Google Scholar
[43]	W. Zhou, R. Zhang and Y. Zhou, A queuing model on supply chain with the form postponement strategy, Computers & Industrial Engineering, 66 (2013), 643-652. doi: 10.1016/j.cie.2013.09.022. Google Scholar

show all references

References:

[1]	E.-H. Aghezzaf, A. Khatab and P. L. Tam, Optimizing production and imperfect preventive maintenance planning's integration in failure-prone manufacturing systems, Reliability Engineering & System Safety, 145 (2016), 190-198. doi: 10.1016/j.ress.2015.09.017. Google Scholar
[2]	A. Arreola-Risa and M. F. Keblis, Design of stockless production systems, Production and Operations Management, 22 (2013), 203-215. doi: 10.1111/j.1937-5956.2012.01343.x. Google Scholar
[3]	J.-B. Bacot and J. H. Dshalalow, A bulk input queueing system with batch gated service and multiple vacation policy, Mathematical and Computer Modelling, 34 (2001), 873-886. doi: 10.1016/S0895-7177(01)00106-6. Google Scholar
[4]	A. D. Banik, The infinite-buffer single server queue with a variant of multiple vacation policy and batch {M}arkovian arrival process, Applied Mathematical Modelling, 33 (2009), 3025-3039. doi: 10.1016/j.apm.2008.10.021. Google Scholar
[5]	A. D. Banik and S. K. Samanta, Controlling packet loss of bursty and correlated traffics in a variant of multiple vacation policy, in 2013 International Conference on Distributed Computing and Internet Technology (ICDCIT), Vol. 7753 of Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2013,208-219. doi: 10.1007/978-3-642-36071-8_16. Google Scholar
[6]	R. Bellman, Introduction to Matrix Analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. Google Scholar
[7]	F. Berthaut, A. Gharbi, J.-P. Kenné and J.-F. Boulet, Improved joint preventive maintenance and hedging point policy, International Journal of Production Economics, 127 (2010), 60-72. doi: 10.1016/j.ijpe.2010.04.030. Google Scholar
[8]	B. Bouslah, A. Gharbi and R. Pellerin, Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint, Omega, 61 (2016), 110-126. doi: 10.1016/j.omega.2015.07.012. Google Scholar
[9]	B. Bouslah, A. Gharbi and R. Pellerin, Joint economic design of production, continuous sampling inspection and preventive maintenance of a deteriorating production system, International Journal of Production Economics, 173 (2016), 184-198. doi: 10.1016/j.ijpe.2015.12.016. Google Scholar
[10]	L. Breuer and D. Baum, An Introduction to Queueing Theory and Matrix-Analytic Methods, Springer, Dordrecht, 2005. Google Scholar
[11]	J. Cao and W. Xie, Stability of a two-queue cyclic polling system with BMAPs under gated service and state-dependent time-limited service disciplines, Queueing Systems, 85 (2017), 117-147. doi: 10.1007/s11134-016-9504-z. Google Scholar
[12]	A. Chelbi and N. Rezg, Analysis of a production/inventory system with randomly failing production unit subjected to a minimum required availability level, International Journal of Production Economics, 99 (2006), 131-143. doi: 10.1016/j.ijpe.2004.12.012. Google Scholar
[13]	A. Chelbi, N. Rezg and M. Radhoui, Simultaneous determination of production lot size and preventive maintenance schedule for unreliable production system, Journal of Quality in Maintenance Engineering, 14 (2008), 161-176. doi: 10.1108/13552510810877665. Google Scholar
[14]	E. Çinlar, Markov renewal theory, Advances in Applied Probability, 1 (1969), 123-187. doi: 10.2307/1426216. Google Scholar
[15]	E. Çinlar, Introduction to Stochastic Processes, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1975. Google Scholar
[16]	D. Das, A. Roy and S. Kar, A volume flexible economic production lot-sizing problem with imperfect quality and random machine failure in fuzzy-stochastic environment, Computers & Mathematics with Applications, 61 (2011), 2388-2400. doi: 10.1016/j.camwa.2011.02.015. Google Scholar
[17]	K. Dhouib, A. Gharbi and M. N. Ben Aziza, Joint optimal production control/preventive maintenance policy for imperfect process manufacturing cell, International Journal of Production Economics, 137 (2012), 126-136. doi: 10.1016/j.ijpe.2012.01.023. Google Scholar
[18]	L. Doyen, Semi-parametric estimation of Brown-Proschan preventive maintenance effects and intrinsic wear-out, Computational Statistics & Data Analysis, 77 (2014), 206-222. doi: 10.1016/j.csda.2014.02.022. Google Scholar
[19]	D. Gibson and E. Seneta, Monotone infinite stochastic matrices and their augmented truncations, Stochastic Processes and their Applications, 24 (1987), 287-292. doi: 10.1016/0304-4149(87)90019-6. Google Scholar
[20]	W. K. Grassmann, M. I. Taksar and D. P. Heyman, Regenerative analysis and steady state distributions for Markov chains, Operations Research, 33 (1985), 1107-1116. doi: 10.1287/opre.33.5.1107. Google Scholar
[21]	D. Gupta and S. Benjaafar, Make-to-order, make-to-stock, or delay product differentiation? A common framework for modeling and analysis, IIE Transactions, 36 (2004), 529-546. doi: 10.1080/07408170490438519. Google Scholar
[22]	E. M. Jewkes and A. S. Alfa, A queueing model of delayed product differentiation, European Journal of Operational Research, 199 (2009), 734-743. doi: 10.1016/j.ejor.2008.08.001. Google Scholar
[23]	Y. -L. Jin, Multi-objective optimization of flexible period preventive maintenance on a single machine, in 2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (ICQR2MSE), Chengdu, China, 2012,475-479. doi: 10.1109/ICQR2MSE.2012.6246277. Google Scholar
[24]	V. V. Krivtsov, Recent advances in theory and applications of stochastic point process models in reliability engineering, Reliability Engineering & System Safety, 92 (2007), 549-551. doi: 10.1016/j.ress.2006.05.001. Google Scholar
[25]	G.-L. Liao, Production and maintenance policies for an {EPQ} model with perfect repair, rework, free-repair warranty, and preventive maintenance, IEEE Transactions on Systems, Man, Cybernetics: Systems, 46 (2016), 1129-1139. doi: 10.1109/TSMC.2015.2465961. Google Scholar
[26]	J. D. C. Little, A proof for the queuing formula: L = λW, Operations Research, 9 (1961), 383-387. doi: 10.1287/opre.9.3.383. Google Scholar
[27]	C. Liu, Y. Fan, C. Zhao and J. Wang, Multiple common due-dates assignment and optimal maintenance activity scheduling with linear deteriorating jobs, Journal of Industrial & Management Optimization, 13 (2017), 713-720. doi: 10.3934/jimo.2016042. Google Scholar
[28]	D. M. Lucantoni, New results on the single server queue with a bath Markovian arrival process, Stochastic Models, 7 (1991), 1-46. doi: 10.1080/15326349108807174. Google Scholar
[29]	D. M. Lucantoni, K. S. Meier-Hellstern and M. F. Neuts, A single-server queue with server vacations and a class of non-renewal arrival processes, Advances in Applied Probability, 22 (1990), 676-705. doi: 10.2307/1427464. Google Scholar
[30]	L. Mann, A. Saxena and G. M. Knapp, Statistical-based or condition-based preventive maintenance?, Journal of Quality in Maintenance Engineering, 1 (1995), 46-59. doi: 10.1108/13552519510083156. Google Scholar
[31]	R. Mehdi, R. Nidhal and C. Anis, Integrated maintenance and control policy based on quality control, Computers & Industrial Engineering, 58 (2010), 443-451. doi: 10.1016/j.cie.2009.11.002. Google Scholar
[32]	T. Nakagawa, Periodic and sequential preventive maintenance policies, Journal of Applied Probability, 23 (1986), 536-542. doi: 10.2307/3214197. Google Scholar
[33]	M. F. Neuts, Matrix-geometric Solutions in Stochastic Models. An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, 1981. Google Scholar
[34]	M. Radhoui, N. Rezg and A. Chelbi, Integrated model of preventive maintenance, quality control and buffer sizing for unreliable and imperfect production systems, International Journal of Production Research, 47 (2009), 389-402. doi: 10.1080/00207540802426201. Google Scholar
[35]	V. Ramaswami, The N/G/1 queue and its detailed analysis, Advances in Applied Probability, 12 (1980), 222-261. doi: 10.2307/1426503. Google Scholar
[36]	J. Schutz, N. Rezg and J.-B. Léger, Periodic and sequential preventive maintenance policies over a finite planning horizon with a dynamic failure law, Journal of Intelligent Manufacturing, 22 (2011), 523-532. doi: 10.1007/s10845-009-0313-7. Google Scholar
[37]	M. Shahriari, N. Shoja, A. E. Zade, S. Barak and M. Sharifi, JIT single machine scheduling problem with periodic preventive maintenance, Journal of Industrial Engineering International, 12 (2016), 299-310. doi: 10.1007/s40092-016-0147-9. Google Scholar
[38]	O. Tang, R. W. Grubbström and S. Zanoni, Planned lead time determination in a make-to-order remanufacturing system, International Journal of Production Economics, 108 (2007), 426-435. doi: 10.1016/j.ijpe.2006.12.034. Google Scholar
[39]	V. M. Vishnevsky, A. N. Dudin, O. V. Semenova and V. I. Klimenok, Performance analysis of the BMAP/G/1 queue with gated servicing and adaptive vacations, Performance Evaluation, 68 (2011), 446-462. doi: 10.1016/j.peva.2011.02.003. Google Scholar
[40]	H.-M. Wee, W.-T. Wang and P.-C. Yang, A production quantity model for imperfect quality items with shortage and screening constraint, International Journal of Production Research, 51 (2013), 1869-1884. doi: 10.1080/00207543.2012.718453. Google Scholar
[41]	L. Xiao, S. Song, X. Chen and D. W. Coit, Joint optimization of production scheduling and machine group preventive maintenance, Reliability Engineering & System Safety, 146 (2016), 68-78. doi: 10.1016/j.ress.2015.10.013. Google Scholar
[42]	K.-C. Ying, C.-C. Lu and J.-C. Chen, Exact algorithms for single-machine scheduling problems with a variable maintenance, Computers & Industrial Engineering, 98 (2016), 427-433. doi: 10.1016/j.cie.2016.05.037. Google Scholar
[43]	W. Zhou, R. Zhang and Y. Zhou, A queuing model on supply chain with the form postponement strategy, Computers & Industrial Engineering, 66 (2013), 643-652. doi: 10.1016/j.cie.2013.09.022. Google Scholar

Figure 1. ${{K''}_t}\left\{ {\left. {\left( {i,v} \right) \times [0,x]} \right|\left( {{i_0},{v_0}} \right)} \right\}$ for ${{i}_{0}} = 0$, provided that at time $t$ $\left( t<{{T}_{1}} \right)$, a virtual customer arrives at the queue, while the server does not attend to the queue.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2. ${{K''}_t}\left\{ {\left. {\left( {i,v} \right) \times [0,x]} \right|\left( {{i_0},{v_0}} \right)} \right\}$ for ${{i}_{0}}\ge 1$, provided that at time $t$ $\left( t<{{T}_{1}} \right)$, a virtual customer arrives at the queue, while the server does not attend to the queue.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3. ${K''_t}\left\{ {\left. {\left( {i,v} \right) \times [0,x]} \right|\left( {{i_0},{v_0}} \right)} \right\}$ for $1\le {{i}_{0}}\le i$, provided that at time $t$ $\left( t<{{T}_{1}} \right)$, a virtual customer arrives at the queue, while the server is attending to the queue.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4. ${K''_t}\left\{ {\left. {\left( {i,v} \right) \times [0,x]} \right|\left( {{i_0},{v_0}} \right)} \right\}$ for ${{i}_{0}}\ge 2$ and ${{i}_{0}}>i>0$, provided that at time $t$ $\left( t<{{T}_{1}} \right)$, a virtual customer arrives at the queue, while the server is attending to the queue.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5. Schematic diagrams of ${\varphi }(n)$, ${M_{c}}(x)$ and ${W_{c}}(x)$.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6. $\eta(q)$ vs. $q$ for the purchasers with different sensitivities to the lead time.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 7. ${{\sigma }_{m}}$ vs. $q$.

Figure Options

Download full-size image

Download as PowerPoint slide

Table 1. The correspondence between performance measures of the stockless production system and the queueing model

The stockless production system	The queueing model
The number of the products produced in a production cycle	The queue length just after the server travels to the queue
The number of the unfulfilled orders at arbitrary time	The queue length (including the customer in service) at arbitrary time
The time required to fulfill the tasks ¹ present at arbitrary time	The virtual waiting time² at arbitrary time
The lead time of the order accepted at arbitrary time	The actual waiting time³ at arbitrary time
¹ The tasks contain the future or remaining machine set-up, machine close-down as well as PM (or the idle period) in the current production cycle, and the present unfulfilled orders. ² The definition of the virtual waiting time is given in Section 5. ³ The definition of the actual waiting time is given in Section 6.

Table Options

Download as excel

The stockless production system	The queueing model
The number of the products produced in a production cycle	The queue length just after the server travels to the queue
The number of the unfulfilled orders at arbitrary time	The queue length (including the customer in service) at arbitrary time
The time required to fulfill the tasks ¹ present at arbitrary time	The virtual waiting time² at arbitrary time
The lead time of the order accepted at arbitrary time	The actual waiting time³ at arbitrary time
¹ The tasks contain the future or remaining machine set-up, machine close-down as well as PM (or the idle period) in the current production cycle, and the present unfulfilled orders. ² The definition of the virtual waiting time is given in Section 5. ³ The definition of the actual waiting time is given in Section 6.

[1]	Pikkala Vijaya Laxmi, Obsie Mussa Yesuf. Analysis of a finite buffer general input queue with Markovian service process and accessible and non-accessible batch service. Journal of Industrial & Management Optimization, 2010, 6 (4) : 929-944. doi: 10.3934/jimo.2010.6.929
[2]	A. Azhagappan, T. Deepa. Transient analysis of N-policy queue with system disaster repair preventive maintenance re-service balking closedown and setup times. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-14. doi: 10.3934/jimo.2019083
[3]	Tien-Yu Lin. Effect of warranty and quantity discounts on a deteriorating production system with a Markovian production process and allowable shortages. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2020013
[4]	Zsolt Saffer, Wuyi Yue. A dual tandem queueing system with GI service time at the first queue. Journal of Industrial & Management Optimization, 2014, 10 (1) : 167-192. doi: 10.3934/jimo.2014.10.167
[5]	Javad Taheri-Tolgari, Mohammad Mohammadi, Bahman Naderi, Alireza Arshadi-Khamseh, Abolfazl Mirzazadeh. An inventory model with imperfect item, inspection errors, preventive maintenance and partial backlogging in uncertainty environment. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1317-1344. doi: 10.3934/jimo.2018097
[6]	Zsolt Saffer, Miklós Telek. Analysis of globally gated Markovian limited cyclic polling model and its application to uplink traffic in the IEEE 802.16 network. Journal of Industrial & Management Optimization, 2011, 7 (3) : 677-697. doi: 10.3934/jimo.2011.7.677
[7]	Tao Jiang, Liwei Liu. Analysis of a batch service multi-server polling system with dynamic service control. Journal of Industrial & Management Optimization, 2018, 14 (2) : 743-757. doi: 10.3934/jimo.2017073
[8]	Wai-Ki Ching, Sin-Man Choi, Min Huang. Optimal service capacity in a multiple-server queueing system: A game theory approach. Journal of Industrial & Management Optimization, 2010, 6 (1) : 73-102. doi: 10.3934/jimo.2010.6.73
[9]	Willem Mélange, Herwig Bruneel, Bart Steyaert, Dieter Claeys, Joris Walraevens. A continuous-time queueing model with class clustering and global FCFS service discipline. Journal of Industrial & Management Optimization, 2014, 10 (1) : 193-206. doi: 10.3934/jimo.2014.10.193
[10]	Volker Rehbock, Iztok Livk. Optimal control of a batch crystallization process. Journal of Industrial & Management Optimization, 2007, 3 (3) : 585-596. doi: 10.3934/jimo.2007.3.585
[11]	Rongfei Liu, Dingcheng Wang, Jiangyan Peng. Infinite-time ruin probability of a renewal risk model with exponential Levy process investment and dependent claims and inter-arrival times. Journal of Industrial & Management Optimization, 2017, 13 (2) : 995-1007. doi: 10.3934/jimo.2016058
[12]	Yoshiaki Inoue, Tetsuya Takine. The FIFO single-server queue with disasters and multiple Markovian arrival streams. Journal of Industrial & Management Optimization, 2014, 10 (1) : 57-87. doi: 10.3934/jimo.2014.10.57
[13]	Gábor Horváth, Zsolt Saffer, Miklós Telek. Queue length analysis of a Markov-modulated vacation queue with dependent arrival and service processes and exhaustive service policy. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1365-1381. doi: 10.3934/jimo.2016077
[14]	Simone Göttlich, Stephan Knapp. Semi-Markovian capacities in production network models. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3235-3258. doi: 10.3934/dcdsb.2017090
[15]	Ellina Grigorieva, Evgenii Khailov. A nonlinear controlled system of differential equations describing the process of production and sales of a consumer good. Conference Publications, 2003, 2003 (Special) : 359-364. doi: 10.3934/proc.2003.2003.359
[16]	Le Thi Hoai An, Tran Duc Quynh, Kondo Hloindo Adjallah. A difference of convex functions algorithm for optimal scheduling and real-time assignment of preventive maintenance jobs on parallel processors. Journal of Industrial & Management Optimization, 2014, 10 (1) : 243-258. doi: 10.3934/jimo.2014.10.243
[17]	Masoud Ebrahimi, Seyyed Mohammad Taghi Fatemi Ghomi, Behrooz Karimi. Application of the preventive maintenance scheduling to increase the equipment reliability: Case study- bag filters in cement factory. Journal of Industrial & Management Optimization, 2020, 16 (1) : 189-205. doi: 10.3934/jimo.2018146
[18]	Jian Zhang, Tony T. Lee, Tong Ye, Liang Huang. An approximate mean queue length formula for queueing systems with varying service rate. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019106
[19]	Veena Goswami, Pikkala Vijaya Laxmi. Analysis of renewal input bulk arrival queue with single working vacation and partial batch rejection. Journal of Industrial & Management Optimization, 2010, 6 (4) : 911-927. doi: 10.3934/jimo.2010.6.911
[20]	Lotfi Tadj, Zhe George Zhang, Chakib Tadj. A queueing analysis of multi-purpose production facility's operations. Journal of Industrial & Management Optimization, 2011, 7 (1) : 19-30. doi: 10.3934/jimo.2011.7.19

2018 Impact Factor: 1.025

Tools

Metrics

Tools

Article outline

Figures and Tables

2018 Impact Factor: 1.025

Tools

Figures and Tables

2018 Impact Factor: 1.025

American Institute of Mathematical Sciences

Optimization of a condition-based duration-varying preventive maintenance policy for the stockless production system based on queueing model

References:

References:

Tools

Metrics

Other articles
by authors

Tools

Tools

Tools

Metrics

Other articles
by authors

American Institute of Mathematical Sciences

Optimization of a condition-based duration-varying preventive maintenance policy for the stockless production system based on queueing model

References:

References:

Tools

Metrics

Other articlesby authors

Tools

Tools

Tools

Metrics

Other articlesby authors

Other articles
by authors

Other articles
by authors