• Previous Article
    A hybrid particle swarm optimization and tabu search algorithm for order planning problems of steel factories based on the Make-To-Stock and Make-To-Order management architecture
  • JIMO Home
  • This Issue
  • Next Article
    On the admission control and demand management in a two-station tandem production system
January  2011, 7(1): 19-30. doi: 10.3934/jimo.2011.7.19

A queueing analysis of multi-purpose production facility's operations

1. 

Saint Mary's University, Sobey School of Business, Department of Finance, Information Systems, and Management Science, Halifax, Nova Scotia, B3H 3C3, Canada

2. 

Western Washington University, College of Business and Economics, Department of Decision Sciences, Bellingham, WA 98225, United States

3. 

École de Technologie Supérieure, Département de Génie Électrique, Montréal, Québec, H3C 1K3, Canada

Received  July 2009 Revised  September 2010 Published  January 2011

In this paper, we study the production time allocation issue for a multi-purpose manufacturing facility. This production facility can produce different types of make-to-order and make-to-stock products. Using a vacation queueing model, we develop a set of quantitative performance measures for a two-parameter time allocation policy. Based on the renewal cycle analysis, we derive an average cost expression and propose a search algorithm to find the optimal time allocation policy that minimizes the average cost. Some numerical examples are presented to demonstrate the effectiveness of the search algorithm. The vacation model used in this paper is also a generalization of some previous vacation queueing models in the literature. The results obtained in this study are useful for production managers to design the operating policy in practice.
Citation: Lotfi Tadj, Zhe George Zhang, Chakib Tadj. A queueing analysis of multi-purpose production facility's operations. Journal of Industrial and Management Optimization, 2011, 7 (1) : 19-30. doi: 10.3934/jimo.2011.7.19
References:
[1]

L. Abolnikov and A. Dukhovny, Markov chains with transition delta-matrix: ergodicity conditions, invariant probability measures and applications, Journal of Applied Mathematics and Stochastic Analysis, 4 (1991), 335-355. doi: 10.1155/S1048953391000254.

[2]

J. R. Artalejo and G. Choudhury, Steady state analysis of an M/G/1 queue with repeated attempts and two phase service, Quality Technology and Quantitative Management, 1 (2004), 189-199.

[3]

D. Bertsimas and X. Papaconstantinou, On the steady-state solution of the M/C$_2(a,b)$/$S$ queueing system, Transportation Sciences, 22 (1988), 125-138. doi: 10.1287/trsc.22.2.125.

[4]

D. Bertsimas and X. Papaconstantinou, Analysis of the stationary $E_k$/$C_2$/S queueing system, European Journal of Operational Research, 37 (1988), 272-282. doi: 10.1016/0377-2217(88)90336-0.

[5]

G. Choudhury, Some aspects of an M/G/1 queueing system with optional second service, TOP, 11 (2003), 141-150. doi: 10.1007/BF02578955.

[6]

G. Choudhury and K. C. Madan, A two-phase batch arrival queueing system with a vacation time under Bernoulli schedule, Applied Mathematics and Computation, 149 (2004), 337-349. doi: 10.1016/S0096-3003(03)00138-3.

[7]

G. Choudhury and K. C. Madan, A two-stage arrival queueing system with a modified Bernoulli schedule vacation under N-policy, Mathematical and Computer Modelling, 42 (2005), 71-85. doi: 10.1016/j.mcm.2005.04.003.

[8]

G. Choudhury and M. Paul, A batch arrival queue with an additional service channel under N-policy, Applied Mathematics and Computation, 156 (2004), 115-130. doi: 10.1016/j.amc.2003.07.006.

[9]

G. Choudhury and M. Paul, Analysis of a two phases batch arrival queueing model with Bernoulli vacation schedule, Revista Investigatión Operacional, 25 (2004), 217-228.

[10]

B. T. Doshi, Queueing systems with vacations: A survey, Queueing Systems, 1 (1986), 29-66. doi: 10.1007/BF01149327.

[11]

B. T. Doshi, Single-server queues with vacations, in "Stochastic Analysis of Computer and Communication Systems" (eds. H. Takagi), Noth-Holland, Amsterdam, (1990), 217-265.

[12]

B. T. Doshi, Analysis of a two-phase queueing system with general service times, Operations Research Letters, 10 (1991), 265-272. doi: 10.1016/0167-6377(91)90012-E.

[13]

A. Federgruen and K. C. So, Optimality of threshold policies in single server queueing system with vacations, Advances in Applied Probability, 23 (1991), 388-405. doi: 10.2307/1427755.

[14]

O. Kella, The threshold policy in the M/G/1 queue with server vacations, Naval Research Logistics, 36 (1989), 111-123. doi: 10.1002/1520-6750(198902)36:1<111::AID-NAV3220360109>3.0.CO;2-3.

[15]

T. S. Kim and K. C. Chae, Two-phase queueing system with generalized vacation, Journal of the Korean Institute of Industrial Engineers, 22 (1996), 95-104.

[16]

T. S. Kim and A. Q. Park, Cycle analysis of a two-phase queueing model with threshold, European Journal of Operational Research, 144 (2003), 157-165.

[17]

C. M. Krishna and Y. H. Lee, A study of two-phase service, Operations Research Letters, 9 (1990), 91-97. doi: 10.1016/0167-6377(90)90047-9.

[18]

H. W. Lee, S. S. Lee, J. O. Park and K. C. Chae, Analysis of M$^x$/G/1 queue with N policy and multiple vacations, Journal of Applied Probability, 31 (1994), 467-496. doi: 10.2307/3215040.

[19]

K. C. Madan, A cyclic queueing system with three servers and optional two-way feedback, Microelectron. Rel., 28 (1988), 873-875. doi: 10.1016/0026-2714(88)90285-5.

[20]

K. C. Madan, An M/G/1 queue with second optional service, Queueing Systems, 34 (2000), 37-46. doi: 10.1023/A:1019144716929.

[21]

K. C. Madan, On a single server queue with two stage general heterogeneous service and binomial schedule server vacations, The Egyptian Statistical Journal, 44 (2000), 39-55.

[22]

K. C. Madan, On a single server queue with two stage general heterogeneous service and deterministic schedule server vacations, International Journal of System Science, 32 (2001), 837-844. doi: 10.1080/00207720121488.

[23]

K. C. Madan and M. Al-Rawwash, On the M$^x$/G/1 queue with feedback and optional server vacations based on a single vacation policy, Applied Mathematics and Computation, 160 (2005), 909-919.

[24]

K. C. Madan and A. Z. Abu Al-Rub, On a single server queue with optional phase type server vacations based on exhaustive deterministic service and a single vacation policy, Applied Mathematics and Computation, 149 (2004), 723-734. doi: 10.1016/S0096-3003(03)00174-7.

[25]

K. C. Madan, A. D. Al-Nasser and A. Q. Al-Masri, On M$^x$/(G1,G2)/1 queue with optional re-service, Applied Mathematics and Computation, 152 (2004), 71-88. doi: 10.1016/S0096-3003(03)00545-9.

[26]

J. Medhi, A single server Poisson input queue with a second optional channel, Queueing Systems, 42 (2002), 239-242. doi: 10.1023/A:1020519830116.

[27]

D. D. Selvam and V. Sivasankaran, A two-phase queueing system with server vacations, Operations Research Letters, 15 (1994), 163-168. doi: 10.1016/0167-6377(94)90052-3.

[28]

L. Tadj and G. Choudhury, Optimal design and control of queues, TOP, 13 (2005), 359-414. doi: 10.1007/BF02579061.

[29]

L. Tadj and J-.C. Ke, Control policy of a hysteretic queueing system, Mathematical Methods of Operations Research, 57 (2003), 367-376.

[30]

L. Tadj and J-.C. Ke, Control policy of a hysteretic bulk queueing system, Mathematical and Computer Modelling, 5 (2004), 571-579.

[31]

H. Takagi, "Queueing Analysis - A Foundation of Performance Evaluation," Vol. 1, Elsevier, Amsterdam, 1991.

[32]

N. Tian and Z. G. Zhang, "Vacation Queueing Models - Theory and Applications," Springer-Verlag, New York, 2006.

[33]

Z. G. Zhang, R. G. Vickson and M. J. A. van Eenige, Optimal two threshold policies in an M/G/1 queue with two vacation types, Performance Evaluation, 29 (1997), 63-80. doi: 10.1016/S0166-5316(96)00005-3.

[34]

J. Wang, An M/G/1 queue with second optional service and server breakdowns, Computers and Mathematics with Applications, 47 (2004), 1713-1723. doi: 10.1016/j.camwa.2004.06.024.

show all references

References:
[1]

L. Abolnikov and A. Dukhovny, Markov chains with transition delta-matrix: ergodicity conditions, invariant probability measures and applications, Journal of Applied Mathematics and Stochastic Analysis, 4 (1991), 335-355. doi: 10.1155/S1048953391000254.

[2]

J. R. Artalejo and G. Choudhury, Steady state analysis of an M/G/1 queue with repeated attempts and two phase service, Quality Technology and Quantitative Management, 1 (2004), 189-199.

[3]

D. Bertsimas and X. Papaconstantinou, On the steady-state solution of the M/C$_2(a,b)$/$S$ queueing system, Transportation Sciences, 22 (1988), 125-138. doi: 10.1287/trsc.22.2.125.

[4]

D. Bertsimas and X. Papaconstantinou, Analysis of the stationary $E_k$/$C_2$/S queueing system, European Journal of Operational Research, 37 (1988), 272-282. doi: 10.1016/0377-2217(88)90336-0.

[5]

G. Choudhury, Some aspects of an M/G/1 queueing system with optional second service, TOP, 11 (2003), 141-150. doi: 10.1007/BF02578955.

[6]

G. Choudhury and K. C. Madan, A two-phase batch arrival queueing system with a vacation time under Bernoulli schedule, Applied Mathematics and Computation, 149 (2004), 337-349. doi: 10.1016/S0096-3003(03)00138-3.

[7]

G. Choudhury and K. C. Madan, A two-stage arrival queueing system with a modified Bernoulli schedule vacation under N-policy, Mathematical and Computer Modelling, 42 (2005), 71-85. doi: 10.1016/j.mcm.2005.04.003.

[8]

G. Choudhury and M. Paul, A batch arrival queue with an additional service channel under N-policy, Applied Mathematics and Computation, 156 (2004), 115-130. doi: 10.1016/j.amc.2003.07.006.

[9]

G. Choudhury and M. Paul, Analysis of a two phases batch arrival queueing model with Bernoulli vacation schedule, Revista Investigatión Operacional, 25 (2004), 217-228.

[10]

B. T. Doshi, Queueing systems with vacations: A survey, Queueing Systems, 1 (1986), 29-66. doi: 10.1007/BF01149327.

[11]

B. T. Doshi, Single-server queues with vacations, in "Stochastic Analysis of Computer and Communication Systems" (eds. H. Takagi), Noth-Holland, Amsterdam, (1990), 217-265.

[12]

B. T. Doshi, Analysis of a two-phase queueing system with general service times, Operations Research Letters, 10 (1991), 265-272. doi: 10.1016/0167-6377(91)90012-E.

[13]

A. Federgruen and K. C. So, Optimality of threshold policies in single server queueing system with vacations, Advances in Applied Probability, 23 (1991), 388-405. doi: 10.2307/1427755.

[14]

O. Kella, The threshold policy in the M/G/1 queue with server vacations, Naval Research Logistics, 36 (1989), 111-123. doi: 10.1002/1520-6750(198902)36:1<111::AID-NAV3220360109>3.0.CO;2-3.

[15]

T. S. Kim and K. C. Chae, Two-phase queueing system with generalized vacation, Journal of the Korean Institute of Industrial Engineers, 22 (1996), 95-104.

[16]

T. S. Kim and A. Q. Park, Cycle analysis of a two-phase queueing model with threshold, European Journal of Operational Research, 144 (2003), 157-165.

[17]

C. M. Krishna and Y. H. Lee, A study of two-phase service, Operations Research Letters, 9 (1990), 91-97. doi: 10.1016/0167-6377(90)90047-9.

[18]

H. W. Lee, S. S. Lee, J. O. Park and K. C. Chae, Analysis of M$^x$/G/1 queue with N policy and multiple vacations, Journal of Applied Probability, 31 (1994), 467-496. doi: 10.2307/3215040.

[19]

K. C. Madan, A cyclic queueing system with three servers and optional two-way feedback, Microelectron. Rel., 28 (1988), 873-875. doi: 10.1016/0026-2714(88)90285-5.

[20]

K. C. Madan, An M/G/1 queue with second optional service, Queueing Systems, 34 (2000), 37-46. doi: 10.1023/A:1019144716929.

[21]

K. C. Madan, On a single server queue with two stage general heterogeneous service and binomial schedule server vacations, The Egyptian Statistical Journal, 44 (2000), 39-55.

[22]

K. C. Madan, On a single server queue with two stage general heterogeneous service and deterministic schedule server vacations, International Journal of System Science, 32 (2001), 837-844. doi: 10.1080/00207720121488.

[23]

K. C. Madan and M. Al-Rawwash, On the M$^x$/G/1 queue with feedback and optional server vacations based on a single vacation policy, Applied Mathematics and Computation, 160 (2005), 909-919.

[24]

K. C. Madan and A. Z. Abu Al-Rub, On a single server queue with optional phase type server vacations based on exhaustive deterministic service and a single vacation policy, Applied Mathematics and Computation, 149 (2004), 723-734. doi: 10.1016/S0096-3003(03)00174-7.

[25]

K. C. Madan, A. D. Al-Nasser and A. Q. Al-Masri, On M$^x$/(G1,G2)/1 queue with optional re-service, Applied Mathematics and Computation, 152 (2004), 71-88. doi: 10.1016/S0096-3003(03)00545-9.

[26]

J. Medhi, A single server Poisson input queue with a second optional channel, Queueing Systems, 42 (2002), 239-242. doi: 10.1023/A:1020519830116.

[27]

D. D. Selvam and V. Sivasankaran, A two-phase queueing system with server vacations, Operations Research Letters, 15 (1994), 163-168. doi: 10.1016/0167-6377(94)90052-3.

[28]

L. Tadj and G. Choudhury, Optimal design and control of queues, TOP, 13 (2005), 359-414. doi: 10.1007/BF02579061.

[29]

L. Tadj and J-.C. Ke, Control policy of a hysteretic queueing system, Mathematical Methods of Operations Research, 57 (2003), 367-376.

[30]

L. Tadj and J-.C. Ke, Control policy of a hysteretic bulk queueing system, Mathematical and Computer Modelling, 5 (2004), 571-579.

[31]

H. Takagi, "Queueing Analysis - A Foundation of Performance Evaluation," Vol. 1, Elsevier, Amsterdam, 1991.

[32]

N. Tian and Z. G. Zhang, "Vacation Queueing Models - Theory and Applications," Springer-Verlag, New York, 2006.

[33]

Z. G. Zhang, R. G. Vickson and M. J. A. van Eenige, Optimal two threshold policies in an M/G/1 queue with two vacation types, Performance Evaluation, 29 (1997), 63-80. doi: 10.1016/S0166-5316(96)00005-3.

[34]

J. Wang, An M/G/1 queue with second optional service and server breakdowns, Computers and Mathematics with Applications, 47 (2004), 1713-1723. doi: 10.1016/j.camwa.2004.06.024.

[1]

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 and Management Optimization, 2020, 16 (6) : 2843-2856. doi: 10.3934/jimo.2019083

[2]

Pikkala Vijaya Laxmi, Singuluri Indira, Kanithi Jyothsna. Ant colony optimization for optimum service times in a Bernoulli schedule vacation interruption queue with balking and reneging. Journal of Industrial and Management Optimization, 2016, 12 (4) : 1199-1214. doi: 10.3934/jimo.2016.12.1199

[3]

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 and Management Optimization, 2017, 13 (3) : 1365-1381. doi: 10.3934/jimo.2016077

[4]

Andrea Bacchiocchi, Germana Giombini. An optimal control problem of monetary policy. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5769-5786. doi: 10.3934/dcdsb.2021224

[5]

Kar Hung Wong, Yu Chung Eugene Lee, Heung Wing Joseph Lee, Chi Kin Chan. Optimal production schedule in a single-supplier multi-manufacturer supply chain involving time delays in both levels. Journal of Industrial and Management Optimization, 2018, 14 (3) : 877-894. doi: 10.3934/jimo.2017080

[6]

Martin Bohner, Sabrina Streipert. Optimal harvesting policy for the Beverton--Holt model. Mathematical Biosciences & Engineering, 2016, 13 (4) : 673-695. doi: 10.3934/mbe.2016014

[7]

Jianbin Li, Ruina Yang, Niu Yu. Optimal capacity reservation policy on innovative product. Journal of Industrial and Management Optimization, 2013, 9 (4) : 799-825. doi: 10.3934/jimo.2013.9.799

[8]

Lianxia Zhao, Hui Qiao, Qi An. Optimal pre-sale policy for deteriorating items. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 109-120. doi: 10.3934/naco.2021054

[9]

Jing Shi, Tiaojun Xiao. Service investment and consumer returns policy in a vendor-managed inventory supply chain. Journal of Industrial and Management Optimization, 2015, 11 (2) : 439-459. doi: 10.3934/jimo.2015.11.439

[10]

Bart Feyaerts, Stijn De Vuyst, Herwig Bruneel, Sabine Wittevrongel. The impact of the $NT$-policy on the behaviour of a discrete-time queue with general service times. Journal of Industrial and Management Optimization, 2014, 10 (1) : 131-149. doi: 10.3934/jimo.2014.10.131

[11]

Peng Tong, Xiaogang Ma. Design of differentiated warranty coverage that considers usage rate and service option of consumers under 2D warranty policy. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1577-1591. doi: 10.3934/jimo.2020035

[12]

Ziyuan Zhang, Liying Yu. Research on optimal pricing decisions of the service supply chain oriented to strategic consumers. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022096

[13]

Xiaoming Yan, Ping Cao, Minghui Zhang, Ke Liu. The optimal production and sales policy for a new product with negative word-of-mouth. Journal of Industrial and Management Optimization, 2011, 7 (1) : 117-137. doi: 10.3934/jimo.2011.7.117

[14]

Yiling Chen, Baojun Bian. optimal investment and dividend policy in an insurance company: A varied bound for dividend rates. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 5083-5105. doi: 10.3934/dcdsb.2019044

[15]

John Leventides, Iraklis Kollias. Optimal control indicators for the assessment of the influence of government policy to business cycle shocks. Journal of Dynamics and Games, 2014, 1 (1) : 79-104. doi: 10.3934/jdg.2014.1.79

[16]

Jianxiong Zhang, Zhenyu Bai, Wansheng Tang. Optimal pricing policy for deteriorating items with preservation technology investment. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1261-1277. doi: 10.3934/jimo.2014.10.1261

[17]

Veena Goswami, Gopinath Panda. Optimal information policy in discrete-time queues with strategic customers. Journal of Industrial and Management Optimization, 2019, 15 (2) : 689-703. doi: 10.3934/jimo.2018065

[18]

Guodong Yi, Xiaohong Chen, Chunqiao Tan. Optimal pricing of perishable products with replenishment policy in the presence of strategic consumers. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1579-1597. doi: 10.3934/jimo.2018112

[19]

Yiling Chen, Baojun Bian. Optimal dividend policy in an insurance company with contagious arrivals of claims. Mathematical Control and Related Fields, 2021, 11 (1) : 1-22. doi: 10.3934/mcrf.2020024

[20]

C.E.M. Pearce, J. Piantadosi, P.G. Howlett. On an optimal control policy for stormwater management in two connected dams. Journal of Industrial and Management Optimization, 2007, 3 (2) : 313-320. doi: 10.3934/jimo.2007.3.313

2020 Impact Factor: 1.801

Metrics

  • PDF downloads (113)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]