A nonhomogeneous quasi-birth-death process approach for an <inline-formula><tex-math id="M1">\begin{document} (s, S) \end{document}</tex-math></inline-formula> policy for a perishable inventory system with retrial demands

Previous Article
Vector-valued separation functions and constrained vector optimization problems: optimality and saddle points
JIMO Home
This Issue
Next Article
Convergence analysis of a new iterative algorithm for solving split variational inclusion problems

doi: 10.3934/jimo.2019009

A nonhomogeneous quasi-birth-death process approach for an $ (s, S) $ policy for a perishable inventory system with retrial demands

Sung-Seok Ko

Department of Industrial Engineering, Konkuk University, Seoul, Korea

Received March 2018 Revised October 2018 Published March 2019

In this paper, an $ (s, S) $ continuous inventory model with perishable items and retrial demands is proposed. In addition, replenishment lead times that are independent and identically distributed according to phase-type distribution are implemented. The proposed system is modeled as a three-dimensional Markov process using a level-dependent quasi-birth-death (QBD) process. The ergodicity of the modeled Markov system is demonstrated and the best method for efficiently approximating the steady-state distribution at the inventory level is determined. This paper also provides performance measure formulas based on the steady-state distribution of the proposed approximation method. Furthermore, in order to minimize the system cost, the optimum values of $ s $ and $ S $ are determined numerically and sensitivity analysis is performed on the main parameters.

Keywords: Inventory, perishable item, retrial demand, level-dependent QBD process.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation: Sung-Seok Ko. A nonhomogeneous quasi-birth-death process approach for an $ (s, S) $ policy for a perishable inventory system with retrial demands. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019009

References:

[1]	M. Alizadeh, H. Eskandari and S. M. Sajadifar, A modified $(S-1, S)$ inventory system for deteriorating items with Poisson demand and non-zero lead time, Applied Mathematical Modelling, 38 (2014), 699-711. doi: 10.1016/j.apm.2013.07.014. Google Scholar
[2]	W. J. Anderson, Continuous-time Markov Chains: An Applications-oriented Approach, Springer-Verlag, New York, 1991. doi: 10.1007/978-1-4612-3038-0. Google Scholar
[3]	J. R. Artalejo, Accessible bibliography on retrial queues, Mathematical and Computer Modelling, 51 (2010), 1071-1081. doi: 10.1016/j.mcm.2009.12.011. Google Scholar
[4]	J. Artalejo and G. Falin, Standard and retrial queueing systems: A comparative analysis, Revista Matematica Complutense, 15 (2002), 101-129. doi: 10.5209/rev_REMA.2002.v15.n1.16950. Google Scholar
[5]	J. R. Artalejo, A. Krishnamoorthy and M. J. Lopez-Herrero, Numerical analysis of $(s, S)$ inventory systems with repeated attempts, Annals of Operations Research, 141 (2006), 67-83. doi: 10.1007/s10479-006-5294-8. Google Scholar
[6]	J. R. Artalejo and M. J. Lopez-Herrero, A simulation study of a discrete-time multiserver retrial queue with finite population, Journal of Statistical Planning and Inference, 137 (2007), 2536-2542. doi: 10.1016/j.jspi.2006.04.018. Google Scholar
[7]	O. Baron, O. Berman and D. Perry, Continuous review inventory models for perishable items ordered in batches, Mathematical Methods of Operations Research, 72 (2010), 217-247. doi: 10.1007/s00186-010-0318-1. Google Scholar
[8]	L. Bright and P. G. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Stochastic Models, 11 (1995), 497-525. doi: 10.1080/15326349508807357. Google Scholar
[9]	B. D. Choi and B. Kim, Non-ergodicity criteria for denumerable continuous time Markov processes, Operations Research Letters, 32 (2004), 574-580. doi: 10.1016/j.orl.2004.03.001. Google Scholar
[10]	G. Falin and J. G. Templeton, Retrial Queues (Vol. 75). CRC Press, 1997.Google Scholar
[11]	A. Gómez-Corral, A bibliographical guide to the analysis of retrial queues through matrix analytic techniques, Annals of Operations Research, 141 (2006), 163-191. doi: 10.1007/s10479-006-5298-4. Google Scholar
[12]	Ü. Gürler and B. Y. Özkaya, Analysis of the $(s, S)$ policy for perishables with a random shelf life, IIE Transactions, 40 (2008), 759-781. Google Scholar
[13]	S. Kalpakam and G. Arivarignan, A continuous review perishable inventory model, Statistics, 19 (1988), 389-398. doi: 10.1080/02331888808802112. Google Scholar
[14]	S. Kalpakam and G. Arivarignan, Inventory system with random supply quantity, Operations Research Spektrum, 12 (1990), 139-145. doi: 10.1007/BF01719709. Google Scholar
[15]	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. Google Scholar
[16]	S. Kalpakam and K. P. Sapna, $(S-1, S)$ Perishable systems with stochastic leadtimes, Mathematical and Computer Modelling, 21 (1995), 95-104. doi: 10.1016/0895-7177(95)00026-X. Google Scholar
[17]	T. Karthick, B. Sivakumar and G. Arivarignan, An inventory system with two types of customers and retrial demands, International Journal of Systems Science: Operations & Logistics, 2 (2015), 90-112. Google Scholar
[18]	C. Kouki, E. Sahin, Z. Jemai and Y. Dallery, Periodic Review Inventory Policy for Perishables with Random Lifetime, In Eighth International Conference of Modeling and Simulation, 2010.Google Scholar
[19]	A. Krishnamoorthy and P. V. Ushakumari, Reliability of a k-out-of-n system with repair and retrial of failed units, Top, 7 (1999), 293-304. doi: 10.1007/BF02564728. Google Scholar
[20]	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 the Operational Research Society, 32 (1981), 997-1001. Google Scholar
[21]	G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, Society for Industrial and Applied Mathematics, 1999. doi: 10.1137/1.9780898719734. Google Scholar
[22]	A. S. Lawrence, B. Sivakumar and G. Arivarignan, A perishable inventory system with service facility and finite source, Applied Mathematical Modelling, 37 (2013), 4771-4786. doi: 10.1016/j.apm.2012.09.018. Google Scholar
[23]	P. Vijaya Laxmi and M. L. Soujanya, Perishable inventory system with service interruptions, retrial demands and negative customers, Applied Mathematics and Computation, 262 (2015), 102-110. doi: 10.1016/j.amc.2015.04.013. Google Scholar
[24]	Z. Lian and L. Liu, Continuous review perishable inventory systems: Models and heuristics, IIE Transactions, 33 (2001), 809-822. Google Scholar
[25]	L. Liu, (s, S) Continuous Review Models for Inventory with Random Lifetimes, Operations Research Letters, 9 (1990), 161-167. doi: 10.1016/0167-6377(90)90014-V. Google Scholar
[26]	L. Liu and D. H. Shi, An $(s, S)$ model for inventory with exponential lifetimes and renewal demands, Naval Research Logistics, 46 (1999), 39-56. doi: 10.1002/(SICI)1520-6750(199902)46:1<39::AID-NAV3>3.0.CO;2-G. Google Scholar
[27]	L. Liu and T. Yang, An $(s, S)$ random lifetime inventory model with a positive lead time, European Journal of Operational Research, 113 (1999), 52-63. doi: 10.1016/0167-6377(90)90014-V. Google Scholar
[28]	E. Mohebbi and M. J. Posner, A continuous review inventory system with lost sales and variable lead time, Naval Research Logistics, 45 (1998), 259-278. doi: 10.1002/(SICI)1520-6750(199804)45:3<259::AID-NAV2>3.0.CO;2-6. Google Scholar
[29]	S. Nahmias, Perishable inventory theory: A review, Operations Research, 30 (1982), 680-708. Google Scholar
[30]	S. Nahmias, Perishable Inventory Systems, Springer Science & Business Media, 2011.Google Scholar
[31]	M. F. Neuts, Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach, Courier Corporation, 1981. Google Scholar
[32]	F. Olsson and P. Tydesjö, Inventory problems with perishable items: Fixed lifetimes and backlogging, European Journal of Operational Research, 202 (2010), 131-137. doi: 10.1016/j.ejor.2009.05.010. Google Scholar
[33]	C. Periyasamy, A finite source perishable inventory system with retrial demands and multiple server vacation, International Journal of Engineering Research and Technology, 2 (2013), 3802-3815. Google Scholar
[34]	G. P. Prastacos, Blood inventory management: An overview of theory and practice, Management Science, 30 (1984), 777-800. doi: 10.1287/mnsc.30.7.777. Google Scholar
[35]	F. Raafat, Survey of literature on continuously deteriorating inventory models, Journal of the Operational Research society, 42 (1991), 27-37. Google Scholar
[36]	N. Ravichandran, Stochastic analysis of a continuous review perishable inventory system with positive lead time and Poisson demand, European Journal of Operational Research, 84 (1995), 444-457. Google Scholar
[37]	G. E. H. Reuter, Competition processes, In Proc. 4th Berkeley Symp. Math. Statist. Prob, 2 (1961), 421–430. Google Scholar
[38]	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. Google Scholar
[39]	L. I. Sennott, P. A. Humblet and R. L. Tweedie, Mean drifts and the non-ergodicity of Markov chains, Operations Research, 31 (1983), 783-789. doi: 10.1287/opre.31.4.783. Google Scholar
[40]	B. Sivakumar, Two-commodity inventory system with retrial demand, European Journal of Operational Research, 187 (2008), 70-83. doi: 10.1016/j.ejor.2007.02.036. Google Scholar
[41]	B. Sivakumar, A perishable inventory system with retrial demands and a finite population, Journal of Computational and Applied Mathematics, 224 (2009), 29-38. doi: 10.1016/j.cam.2008.03.041. Google Scholar
[42]	R. L. Tweedie, Criteria for ergodicity, exponential ergodicity and strong ergodicity of Markov processes, Journal of Applied Probability, 18 (1981), 122-130. doi: 10.2307/3213172. Google Scholar
[43]	P. V. Ushakumari, On $(s, S)$ inventory system with random lead time and repeated demands, International Journal of Stochastic Analysis, 2006 (2006), Art. ID 81508, 22 pp. doi: 10.1155/JAMSA/2006/81508. Google Scholar
[44]	H. J. Weiss, Optimal ordering policies for continuous review perishable inventory models, Operations Research, 28 (1980), 365-374. doi: 10.1287/opre.28.2.365. Google Scholar

show all references

References:

[1]	M. Alizadeh, H. Eskandari and S. M. Sajadifar, A modified $(S-1, S)$ inventory system for deteriorating items with Poisson demand and non-zero lead time, Applied Mathematical Modelling, 38 (2014), 699-711. doi: 10.1016/j.apm.2013.07.014. Google Scholar
[2]	W. J. Anderson, Continuous-time Markov Chains: An Applications-oriented Approach, Springer-Verlag, New York, 1991. doi: 10.1007/978-1-4612-3038-0. Google Scholar
[3]	J. R. Artalejo, Accessible bibliography on retrial queues, Mathematical and Computer Modelling, 51 (2010), 1071-1081. doi: 10.1016/j.mcm.2009.12.011. Google Scholar
[4]	J. Artalejo and G. Falin, Standard and retrial queueing systems: A comparative analysis, Revista Matematica Complutense, 15 (2002), 101-129. doi: 10.5209/rev_REMA.2002.v15.n1.16950. Google Scholar
[5]	J. R. Artalejo, A. Krishnamoorthy and M. J. Lopez-Herrero, Numerical analysis of $(s, S)$ inventory systems with repeated attempts, Annals of Operations Research, 141 (2006), 67-83. doi: 10.1007/s10479-006-5294-8. Google Scholar
[6]	J. R. Artalejo and M. J. Lopez-Herrero, A simulation study of a discrete-time multiserver retrial queue with finite population, Journal of Statistical Planning and Inference, 137 (2007), 2536-2542. doi: 10.1016/j.jspi.2006.04.018. Google Scholar
[7]	O. Baron, O. Berman and D. Perry, Continuous review inventory models for perishable items ordered in batches, Mathematical Methods of Operations Research, 72 (2010), 217-247. doi: 10.1007/s00186-010-0318-1. Google Scholar
[8]	L. Bright and P. G. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Stochastic Models, 11 (1995), 497-525. doi: 10.1080/15326349508807357. Google Scholar
[9]	B. D. Choi and B. Kim, Non-ergodicity criteria for denumerable continuous time Markov processes, Operations Research Letters, 32 (2004), 574-580. doi: 10.1016/j.orl.2004.03.001. Google Scholar
[10]	G. Falin and J. G. Templeton, Retrial Queues (Vol. 75). CRC Press, 1997.Google Scholar
[11]	A. Gómez-Corral, A bibliographical guide to the analysis of retrial queues through matrix analytic techniques, Annals of Operations Research, 141 (2006), 163-191. doi: 10.1007/s10479-006-5298-4. Google Scholar
[12]	Ü. Gürler and B. Y. Özkaya, Analysis of the $(s, S)$ policy for perishables with a random shelf life, IIE Transactions, 40 (2008), 759-781. Google Scholar
[13]	S. Kalpakam and G. Arivarignan, A continuous review perishable inventory model, Statistics, 19 (1988), 389-398. doi: 10.1080/02331888808802112. Google Scholar
[14]	S. Kalpakam and G. Arivarignan, Inventory system with random supply quantity, Operations Research Spektrum, 12 (1990), 139-145. doi: 10.1007/BF01719709. Google Scholar
[15]	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. Google Scholar
[16]	S. Kalpakam and K. P. Sapna, $(S-1, S)$ Perishable systems with stochastic leadtimes, Mathematical and Computer Modelling, 21 (1995), 95-104. doi: 10.1016/0895-7177(95)00026-X. Google Scholar
[17]	T. Karthick, B. Sivakumar and G. Arivarignan, An inventory system with two types of customers and retrial demands, International Journal of Systems Science: Operations & Logistics, 2 (2015), 90-112. Google Scholar
[18]	C. Kouki, E. Sahin, Z. Jemai and Y. Dallery, Periodic Review Inventory Policy for Perishables with Random Lifetime, In Eighth International Conference of Modeling and Simulation, 2010.Google Scholar
[19]	A. Krishnamoorthy and P. V. Ushakumari, Reliability of a k-out-of-n system with repair and retrial of failed units, Top, 7 (1999), 293-304. doi: 10.1007/BF02564728. Google Scholar
[20]	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 the Operational Research Society, 32 (1981), 997-1001. Google Scholar
[21]	G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, Society for Industrial and Applied Mathematics, 1999. doi: 10.1137/1.9780898719734. Google Scholar
[22]	A. S. Lawrence, B. Sivakumar and G. Arivarignan, A perishable inventory system with service facility and finite source, Applied Mathematical Modelling, 37 (2013), 4771-4786. doi: 10.1016/j.apm.2012.09.018. Google Scholar
[23]	P. Vijaya Laxmi and M. L. Soujanya, Perishable inventory system with service interruptions, retrial demands and negative customers, Applied Mathematics and Computation, 262 (2015), 102-110. doi: 10.1016/j.amc.2015.04.013. Google Scholar
[24]	Z. Lian and L. Liu, Continuous review perishable inventory systems: Models and heuristics, IIE Transactions, 33 (2001), 809-822. Google Scholar
[25]	L. Liu, (s, S) Continuous Review Models for Inventory with Random Lifetimes, Operations Research Letters, 9 (1990), 161-167. doi: 10.1016/0167-6377(90)90014-V. Google Scholar
[26]	L. Liu and D. H. Shi, An $(s, S)$ model for inventory with exponential lifetimes and renewal demands, Naval Research Logistics, 46 (1999), 39-56. doi: 10.1002/(SICI)1520-6750(199902)46:1<39::AID-NAV3>3.0.CO;2-G. Google Scholar
[27]	L. Liu and T. Yang, An $(s, S)$ random lifetime inventory model with a positive lead time, European Journal of Operational Research, 113 (1999), 52-63. doi: 10.1016/0167-6377(90)90014-V. Google Scholar
[28]	E. Mohebbi and M. J. Posner, A continuous review inventory system with lost sales and variable lead time, Naval Research Logistics, 45 (1998), 259-278. doi: 10.1002/(SICI)1520-6750(199804)45:3<259::AID-NAV2>3.0.CO;2-6. Google Scholar
[29]	S. Nahmias, Perishable inventory theory: A review, Operations Research, 30 (1982), 680-708. Google Scholar
[30]	S. Nahmias, Perishable Inventory Systems, Springer Science & Business Media, 2011.Google Scholar
[31]	M. F. Neuts, Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach, Courier Corporation, 1981. Google Scholar
[32]	F. Olsson and P. Tydesjö, Inventory problems with perishable items: Fixed lifetimes and backlogging, European Journal of Operational Research, 202 (2010), 131-137. doi: 10.1016/j.ejor.2009.05.010. Google Scholar
[33]	C. Periyasamy, A finite source perishable inventory system with retrial demands and multiple server vacation, International Journal of Engineering Research and Technology, 2 (2013), 3802-3815. Google Scholar
[34]	G. P. Prastacos, Blood inventory management: An overview of theory and practice, Management Science, 30 (1984), 777-800. doi: 10.1287/mnsc.30.7.777. Google Scholar
[35]	F. Raafat, Survey of literature on continuously deteriorating inventory models, Journal of the Operational Research society, 42 (1991), 27-37. Google Scholar
[36]	N. Ravichandran, Stochastic analysis of a continuous review perishable inventory system with positive lead time and Poisson demand, European Journal of Operational Research, 84 (1995), 444-457. Google Scholar
[37]	G. E. H. Reuter, Competition processes, In Proc. 4th Berkeley Symp. Math. Statist. Prob, 2 (1961), 421–430. Google Scholar
[38]	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. Google Scholar
[39]	L. I. Sennott, P. A. Humblet and R. L. Tweedie, Mean drifts and the non-ergodicity of Markov chains, Operations Research, 31 (1983), 783-789. doi: 10.1287/opre.31.4.783. Google Scholar
[40]	B. Sivakumar, Two-commodity inventory system with retrial demand, European Journal of Operational Research, 187 (2008), 70-83. doi: 10.1016/j.ejor.2007.02.036. Google Scholar
[41]	B. Sivakumar, A perishable inventory system with retrial demands and a finite population, Journal of Computational and Applied Mathematics, 224 (2009), 29-38. doi: 10.1016/j.cam.2008.03.041. Google Scholar
[42]	R. L. Tweedie, Criteria for ergodicity, exponential ergodicity and strong ergodicity of Markov processes, Journal of Applied Probability, 18 (1981), 122-130. doi: 10.2307/3213172. Google Scholar
[43]	P. V. Ushakumari, On $(s, S)$ inventory system with random lead time and repeated demands, International Journal of Stochastic Analysis, 2006 (2006), Art. ID 81508, 22 pp. doi: 10.1155/JAMSA/2006/81508. Google Scholar
[44]	H. J. Weiss, Optimal ordering policies for continuous review perishable inventory models, Operations Research, 28 (1980), 365-374. doi: 10.1287/opre.28.2.365. Google Scholar

Figure 1. Inventory Model

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2. Contour Plot of TCR

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3. The effect of $ \lambda $

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4. The effect of $ \mu $

Figure Options

Download full-size image

Download as PowerPoint slide

Table 1. Total Cost Rate(TCR)

$S \diagdown s$	1	2	3	4	5	6	7	8	9	10
15	367.40	363.25	361.55	362.46	366.06	372.45	381.92	394.31	409.75	429.18
16	366.82	362.49	360.49	360.94	363.82	369.16	377.05	387.83	400.29	415.71
17	366.83	362.40	360.21	360.34	362.72	367.30	374.09	383.24	394.32	407.17
18	367.32	362.86	360.56	360.46	362.49	366.53	372.52	380.51	390.68	401.73
19	368.23	363.77	361.42	361.18	362.95	366.59	372.00	379.14	388.10	398.40
20	369.49	365.07	362.70	362.38	363.97	367.32	372.29	378.80	386.87	396.60
21	371.06	366.69	364.35	363.98	365.45	368.58	373.22	379.25	386.65	395.44
22	372.88	368.60	366.29	365.91	367.30	370.27	374.65	380.32	387.20	395.29
23	374.93	370.74	368.49	368.12	369.45	372.31	376.50	381.89	388.37	395.91
24	377.18	373.09	370.91	370.56	371.87	374.65	378.69	383.85	390.02	397.14
25	379.60	375.62	373.52	373.21	374.51	377.23	381.16	386.14	392.06	398.84
26	382.17	378.31	376.29	376.03	377.34	380.02	383.86	388.71	394.42	400.93
27	384.88	381.13	379.20	379.00	380.33	382.99	386.76	391.50	397.05	403.34
28	387.71	384.07	382.24	382.10	383.46	386.10	389.83	394.48	399.91	406.01
29	390.64	387.12	385.38	385.31	386.70	389.35	393.05	397.63	402.94	408.90
30	393.66	390.27	388.62	388.62	390.05	392.71	396.39	400.91	406.14	411.98

Table Options

Download as excel

$S \diagdown s$	1	2	3	4	5	6	7	8	9	10
15	367.40	363.25	361.55	362.46	366.06	372.45	381.92	394.31	409.75	429.18
16	366.82	362.49	360.49	360.94	363.82	369.16	377.05	387.83	400.29	415.71
17	366.83	362.40	360.21	360.34	362.72	367.30	374.09	383.24	394.32	407.17
18	367.32	362.86	360.56	360.46	362.49	366.53	372.52	380.51	390.68	401.73
19	368.23	363.77	361.42	361.18	362.95	366.59	372.00	379.14	388.10	398.40
20	369.49	365.07	362.70	362.38	363.97	367.32	372.29	378.80	386.87	396.60
21	371.06	366.69	364.35	363.98	365.45	368.58	373.22	379.25	386.65	395.44
22	372.88	368.60	366.29	365.91	367.30	370.27	374.65	380.32	387.20	395.29
23	374.93	370.74	368.49	368.12	369.45	372.31	376.50	381.89	388.37	395.91
24	377.18	373.09	370.91	370.56	371.87	374.65	378.69	383.85	390.02	397.14
25	379.60	375.62	373.52	373.21	374.51	377.23	381.16	386.14	392.06	398.84
26	382.17	378.31	376.29	376.03	377.34	380.02	383.86	388.71	394.42	400.93
27	384.88	381.13	379.20	379.00	380.33	382.99	386.76	391.50	397.05	403.34
28	387.71	384.07	382.24	382.10	383.46	386.10	389.83	394.48	399.91	406.01
29	390.64	387.12	385.38	385.31	386.70	389.35	393.05	397.63	402.94	408.90
30	393.66	390.27	388.62	388.62	390.05	392.71	396.39	400.91	406.14	411.98

[1]	Sung-Seok Ko, Jangha Kang, E-Yeon Kwon. An $(s,S)$ inventory model with level-dependent $G/M/1$-Type structure. Journal of Industrial & Management Optimization, 2016, 12 (2) : 609-624. doi: 10.3934/jimo.2016.12.609
[2]	Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1345-1373. doi: 10.3934/jimo.2018098
[3]	Chih-Te Yang, Liang-Yuh Ouyang, Hsiu-Feng Yen, Kuo-Liang Lee. Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase. Journal of Industrial & Management Optimization, 2013, 9 (2) : 437-454. doi: 10.3934/jimo.2013.9.437
[4]	Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. A two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 21-50. doi: 10.3934/naco.2017002
[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]	Fuying Jing, Zirui Lan, Yang Pan. Forecast horizon of dynamic lot size model for perishable inventory with minimum order quantities. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-22. doi: 10.3934/jimo.2019010
[7]	Jia Shu, Zhengyi Li, Weijun Zhong. A market selection and inventory ordering problem under demand uncertainty. Journal of Industrial & Management Optimization, 2011, 7 (2) : 425-434. doi: 10.3934/jimo.2011.7.425
[8]	Dalila Azzam-Laouir, Fatiha Selamnia. On state-dependent sweeping process in Banach spaces. Evolution Equations & Control Theory, 2018, 7 (2) : 183-196. doi: 10.3934/eect.2018009
[9]	Shouyu Ma, Zied Jemai, Evren Sahin, Yves Dallery. Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts. Journal of Industrial & Management Optimization, 2018, 14 (3) : 931-951. doi: 10.3934/jimo.2017083
[10]	Konstantina Skouri, Ioannis Konstantaras. Two-warehouse inventory models for deteriorating products with ramp type demand rate. Journal of Industrial & Management Optimization, 2013, 9 (4) : 855-883. doi: 10.3934/jimo.2013.9.855
[11]	Wei Liu, Shiji Song, Cheng Wu. Single-period inventory model with discrete stochastic demand based on prospect theory. Journal of Industrial & Management Optimization, 2012, 8 (3) : 577-590. doi: 10.3934/jimo.2012.8.577
[12]	Yanyi Xu, Arnab Bisi, Maqbool Dada. New structural properties of inventory models with Polya frequency distributed demand and fixed setup cost. Journal of Industrial & Management Optimization, 2017, 13 (2) : 931-945. doi: 10.3934/jimo.2016054
[13]	Lizhao Yan, Fei Xu, Yongzeng Lai, Mingyong Lai. Stability strategies of manufacturing-inventory systems with unknown time-varying demand. Journal of Industrial & Management Optimization, 2017, 13 (4) : 2033-2047. doi: 10.3934/jimo.2017030
[14]	Zhijie Sasha Dong, Wei Chen, Qing Zhao, Jingquan Li. Optimal pricing and inventory strategies for introducing a new product based on demand substitution effects. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-15. doi: 10.3934/jimo.2018175
[15]	Katherinne Salas Navarro, Jaime Acevedo Chedid, Whady F. Florez, Holman Ospina Mateus, Leopoldo Eduardo Cárdenas-Barrón, Shib Sankar Sana. A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-14. doi: 10.3934/jimo.2019020
[16]	Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. Deteriorating inventory with preservation technology under price- and stock-sensitive demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-28. doi: 10.3934/jimo.2019019
[17]	Sankar Kumar Roy, Magfura Pervin, Gerhard Wilhelm Weber. Imperfection with inspection policy and variable demand under trade-credit: A deteriorating inventory model. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2019032
[18]	Jui-Jung Liao, Wei-Chun Lee, Kuo-Nan Huang, Yung-Fu Huang. Optimal ordering policy for a two-warehouse inventory model use of two-level trade credit. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1661-1683. doi: 10.3934/jimo.2017012
[19]	Tuan Phung-Duc, Hiroyuki Masuyama, Shoji Kasahara, Yutaka Takahashi. State-dependent M/M/c/c + r retrial queues with Bernoulli abandonment. Journal of Industrial & Management Optimization, 2010, 6 (3) : 517-540. doi: 10.3934/jimo.2010.6.517
[20]	Kegui Chen, Xinyu Wang, Min Huang, Wai-Ki Ching. Compensation plan, pricing and production decisions with inventory-dependent salvage value, and asymmetric risk-averse sales agent. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1397-1422. doi: 10.3934/jimo.2018013

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

A nonhomogeneous quasi-birth-death process approach for an $ (s, S) $ policy for a perishable inventory system with retrial demands

References:

References:

Tools

Metrics

Other articles
by authors

Tools

Tools

Tools

Metrics

Other articles
by authors

American Institute of Mathematical Sciences

A nonhomogeneous quasi-birth-death process approach for an $ (s, S) $ policy for a perishable inventory system with retrial demands

References:

References:

Tools

Metrics

Other articlesby authors

Tools

Tools

Tools

Metrics

Other articlesby authors

Other articles
by authors

Other articles
by authors