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An $(s,S)$ inventory model with level-dependent $G/M/1$-Type structure
1. | Department of Industrial Engineering, Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul, 143-701, South Korea |
2. | Department of Industrial Engineering, Chosun University, 309 Pilmun-daero, Dong-gu, Gwangju, 501-759, South Korea, South Korea |
References:
[1] |
E. Altman and A. A. Borovkov, On the stability of retrial queues, Queueing Syst., 26 (1997), 343-363.
doi: 10.1023/A:1019193527040. |
[2] |
S. Asmussen, Applied Probability and Queues, John Wiley & Sons, 1987. |
[3] |
A. Brandt and M. Brandt, On the M(n)/M(n)/s queue with impatient calls, Perform. Eval., 35 (1999), 1-18. |
[4] |
A. Brandt and M. Brandt, Asymptotic results and a markovian approximation for the M(n)/M(n)/s+GI system, Queueing Syst., 41 (2002), 73-94.
doi: 10.1023/A:1015781818360. |
[5] |
L. Bright and P. G. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Commun. Statist. - Stochastic Models, 11 (1995), 497-525.
doi: 10.1080/15326349508807357. |
[6] |
S. Charkravarthy and J. Daniel, A markovian inventory system with random shelf time and back orders, Computers and Industrial Engineering, 47 (2004), 315-337. |
[7] |
G. I. Falin, On sufficient conditions for ergodicity of multichannel queueing systems with repeated calls, Adv. Appl. Prob., 16 (1984), 447-448.
doi: 10.2307/1427079. |
[8] |
Qi-Ming He, E. M. Jewkes and J. Buzacott, The value of information used in inventory control of a make-to-order inventory-production system, IIE Transactions, 34 (2002), 999-1013.
doi: 10.1080/07408170208928929. |
[9] |
S. Ioannidis, O. Jouini, A. A. Economopoulos and V. S. Kouikoglou, Control policies for single-stage production systems with perishable inventory and customer impatience, Annals of Operations Research, (2012), 1-24.
doi: 10.1007/s10479-012-1058-9. |
[10] |
S. Kalpakam and K. P. Sapna, Continuous review $(s,S)$ inventory system with random lifetimes and positive leadtimes, Operations Research Letters, 16 (1994), 115-119.
doi: 10.1016/0167-6377(94)90066-3. |
[11] |
S. Kalpakam and K. P. Sapna, $(S-1,S)$ perishable systems with stochastic lead times, Mathematical and Computer Modelling, 21 (1995), 95-104.
doi: 10.1016/0895-7177(95)00026-X. |
[12] |
I. Karaesmen, A. Scheller-Wolf and B. Deniz, Managing perishable and aging invetories: Review and future research directions, In Planning Production and Inventories in the Extended Enterprise, Springer, (2011), 393-438. |
[13] |
A. Krishnamoorthy, K. P. Jose and V. C. Narayanan, Numerical investigation of a PH/PH/1 inventory system with positive service time and shortage, Neural Parallel & Scientific Comp., 16 (2008), 579-591. |
[14] |
S. Kumaraswamy and E. Sankarasubramanian, A continuous review of $(S-s)$ inventory systems in which depletion is due to demand and failure of units, Journal of Operational Research Society, 32 (1981), 997-1001. |
[15] |
G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM series on statistics and applied probability, 1999.
doi: 10.1137/1.9780898719734. |
[16] |
L. Liu, $(s,S)$ continous review models for inventory with random lifetimes, Operations Research Letters, 9 (1990), 161-167.
doi: 10.1016/0167-6377(90)90014-V. |
[17] |
L. Liu and T. Yang, An $(s,S)$ random lifetime inventory model with a positive lead time, European Journal of Operational Research, 112 (1999), 52-63.
doi: 10.1016/S0377-2217(97)00426-8. |
[18] |
S. Nahmias, Perishable inventory theory: A review, Operational Research, 30 (1982), 680-708.
doi: 10.1287/opre.30.4.680. |
[19] |
M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, MD., 1981. |
[20] |
M. F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications, Marcel Dekker, Inc., 1989. |
[21] |
D. Perry and W. Stadje, Perishable inventory systems with impatient demands, Math. Meth. of OR, 50, (1999), 77-90. |
[22] |
G. P. Prestacos, Blood inventory management, Management Science, 30 (1984), 777-801. |
[23] |
M. Raafat, Survey of literature on continuously deteriorating inventory models, Journal of Operational Research Society, 42 (1991), 27-37. |
[24] |
N. Ravichandran, Stochastic analysis of a continous review perishable inventory system with positive lead time and Poisson demand, European Journal of Operational Research, 84 (1995), 444-457. |
[25] |
C. P. Schmidt and S. Nahmias, $(S-1,S)$ policies for perishable inventory, Management Science, 31 (1985), 719-728.
doi: 10.1287/mnsc.31.6.719. |
[26] |
A. R. Ward and P. W. Glynn, A diffusion approximation for a markovian queue with reneging, Queueing Syst., 43 (2003), 103-128.
doi: 10.1023/A:1021804515162. |
[27] |
S. Zeltyn and A. Mandelbaum, Call centers with impatient customers: Many-server asymptotics of the M/M/n + G queue, Queueing Syst., 51 (2005), 361-402.
doi: 10.1007/s11134-005-3699-8. |
show all references
References:
[1] |
E. Altman and A. A. Borovkov, On the stability of retrial queues, Queueing Syst., 26 (1997), 343-363.
doi: 10.1023/A:1019193527040. |
[2] |
S. Asmussen, Applied Probability and Queues, John Wiley & Sons, 1987. |
[3] |
A. Brandt and M. Brandt, On the M(n)/M(n)/s queue with impatient calls, Perform. Eval., 35 (1999), 1-18. |
[4] |
A. Brandt and M. Brandt, Asymptotic results and a markovian approximation for the M(n)/M(n)/s+GI system, Queueing Syst., 41 (2002), 73-94.
doi: 10.1023/A:1015781818360. |
[5] |
L. Bright and P. G. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Commun. Statist. - Stochastic Models, 11 (1995), 497-525.
doi: 10.1080/15326349508807357. |
[6] |
S. Charkravarthy and J. Daniel, A markovian inventory system with random shelf time and back orders, Computers and Industrial Engineering, 47 (2004), 315-337. |
[7] |
G. I. Falin, On sufficient conditions for ergodicity of multichannel queueing systems with repeated calls, Adv. Appl. Prob., 16 (1984), 447-448.
doi: 10.2307/1427079. |
[8] |
Qi-Ming He, E. M. Jewkes and J. Buzacott, The value of information used in inventory control of a make-to-order inventory-production system, IIE Transactions, 34 (2002), 999-1013.
doi: 10.1080/07408170208928929. |
[9] |
S. Ioannidis, O. Jouini, A. A. Economopoulos and V. S. Kouikoglou, Control policies for single-stage production systems with perishable inventory and customer impatience, Annals of Operations Research, (2012), 1-24.
doi: 10.1007/s10479-012-1058-9. |
[10] |
S. Kalpakam and K. P. Sapna, Continuous review $(s,S)$ inventory system with random lifetimes and positive leadtimes, Operations Research Letters, 16 (1994), 115-119.
doi: 10.1016/0167-6377(94)90066-3. |
[11] |
S. Kalpakam and K. P. Sapna, $(S-1,S)$ perishable systems with stochastic lead times, Mathematical and Computer Modelling, 21 (1995), 95-104.
doi: 10.1016/0895-7177(95)00026-X. |
[12] |
I. Karaesmen, A. Scheller-Wolf and B. Deniz, Managing perishable and aging invetories: Review and future research directions, In Planning Production and Inventories in the Extended Enterprise, Springer, (2011), 393-438. |
[13] |
A. Krishnamoorthy, K. P. Jose and V. C. Narayanan, Numerical investigation of a PH/PH/1 inventory system with positive service time and shortage, Neural Parallel & Scientific Comp., 16 (2008), 579-591. |
[14] |
S. Kumaraswamy and E. Sankarasubramanian, A continuous review of $(S-s)$ inventory systems in which depletion is due to demand and failure of units, Journal of Operational Research Society, 32 (1981), 997-1001. |
[15] |
G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM series on statistics and applied probability, 1999.
doi: 10.1137/1.9780898719734. |
[16] |
L. Liu, $(s,S)$ continous review models for inventory with random lifetimes, Operations Research Letters, 9 (1990), 161-167.
doi: 10.1016/0167-6377(90)90014-V. |
[17] |
L. Liu and T. Yang, An $(s,S)$ random lifetime inventory model with a positive lead time, European Journal of Operational Research, 112 (1999), 52-63.
doi: 10.1016/S0377-2217(97)00426-8. |
[18] |
S. Nahmias, Perishable inventory theory: A review, Operational Research, 30 (1982), 680-708.
doi: 10.1287/opre.30.4.680. |
[19] |
M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, MD., 1981. |
[20] |
M. F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications, Marcel Dekker, Inc., 1989. |
[21] |
D. Perry and W. Stadje, Perishable inventory systems with impatient demands, Math. Meth. of OR, 50, (1999), 77-90. |
[22] |
G. P. Prestacos, Blood inventory management, Management Science, 30 (1984), 777-801. |
[23] |
M. Raafat, Survey of literature on continuously deteriorating inventory models, Journal of Operational Research Society, 42 (1991), 27-37. |
[24] |
N. Ravichandran, Stochastic analysis of a continous review perishable inventory system with positive lead time and Poisson demand, European Journal of Operational Research, 84 (1995), 444-457. |
[25] |
C. P. Schmidt and S. Nahmias, $(S-1,S)$ policies for perishable inventory, Management Science, 31 (1985), 719-728.
doi: 10.1287/mnsc.31.6.719. |
[26] |
A. R. Ward and P. W. Glynn, A diffusion approximation for a markovian queue with reneging, Queueing Syst., 43 (2003), 103-128.
doi: 10.1023/A:1021804515162. |
[27] |
S. Zeltyn and A. Mandelbaum, Call centers with impatient customers: Many-server asymptotics of the M/M/n + G queue, Queueing Syst., 51 (2005), 361-402.
doi: 10.1007/s11134-005-3699-8. |
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