Abstract
In this article, we present a continuous review (s, S) inventory system with a service facility consisting of finite buffer (capacity N) and a single server. The customers arrive according to a Poisson process. The individual customer’s unit demand is satisfied after a random time of service, which is assumed to be exponential. When the inventory level drops to s an order for Q(= S − s) items is placed. The lead time of reorder is assumed to be exponential distribution. An arriving customer, who finds the buffer is full, enters into the pool of infinite size or leaves the system according to a Bernolli trial. At the time of service completion, if the buffer size drops to a preassigned level L (1 < L < N) or below and the inventory level is above s, we select the customers from the pool according to two different policy: in first policy, with probability p(0 < p < 1) we select the customer from the head of the pool and we place the customer at the end of the buffer; in the second policy, with p(0 < p < 1) the customer from the pool is transferred to the buffer for immediate service and after completion of his service we provide service to the customer who is in the buffer with probability one. If at a service completion epoch the buffer turns out to be empty, there is at least one customer in the pool and the inventory level is positive, then the one ahead of all waiting in the pool gets transferred to the buffer, and his service starts immediately. The joint probability distribution of the number of customers in the pool, number of customers in the buffer and the inventory level is obtained in the steady-state case. Various stationary system performance measures are computed and total expected cost rate is calculated. A comparative result of two models is illustrate numerically.
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References
G. Arivarignan, V. S. S. Yadavalli, and Sivakumar (2008). A perishable inventory system with multi-server service facility and retrial customers. Management Science and Practice, ed. N. Ravichandran, Allied Publishers pvt. Ltd., New Delhi, pages 3–27
O. Berman and E. Kim (1999). Stochastic inventory policies for inventory management of service facilities, stochastic models. Stochastic Models, 15: 695–718
O Berman, Kaplan E. H., and Shimshak D. G. (1993). Deterministic approximations for inventory management at service facilities. IIE Transactions, 25: 98–104
M. Bijvank and I. F. A. Vis (2011). Lost-sales inventory theory: A review. European Journal of Operational Research, 215:1–13
D.P. Gaver, P.A. Jacobs, and G. Latouche (1984). Finite birth-and-death models in randomly changing environments. Advances in Applied Probability, 16: 715–731
S. K. Goyal and B. C. Giri (2001).Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 34: 1–16
Q-M He, E. M. Jewkes, and J. Buzacott (1998). An efficient algorithm for computing the optimal replenishment policy for an inventory-production system. in: A. Alfa and S. Chakravarthy (ed.), Advances in Matrix Analytic Methods for Stochastic Models, Notable Publications, New Jersey, USA, pages 381–402
A. Krishnamoorthy and M. E. Islam (2004). (s, S) inventory system with postponed demands. Stochastic Analysis and Application, 22(3): 827–842
A. Krishnamoorthy, B. Lakshmy, and R. Manikandan (2011). A survey on inventory models with positive service time. OPSEARCH, 48(2): 153–169
S. Nahmias (1982). Perishable inventory theory: A review. Operations Research, 30:680–708
M.F. Neuts (1994). Matrix-geometric Solutions in Stochastic Models: an Algorithmic Approach. Dover Publication Inc. New York
B. Paul Manuel, and Sivakumar and G. Arivarignan (2007). Perishable inventory system with postponed demands and negative customers. Journal of Applied Mathematics and Decision Sciences, 2007: 1–12
F. Raafat (1991). A survey of literature on continuously deteriorating inventory models. Journal of Operational Research Society, 42:27–37
M. Schwarz, C. Sauer, H. Daduna, R. Kulik, and R. Szekli (2006). M/m/1 queueing systems with inventory. Queueing Systems, 54:55–78
N. H. Shah and Y. K. Shah (2000). Literature survey on inventory models for deteriorating items. Ekonomski anali, 44: 221–237
B. Sivakumar and G. Arivarignan (2008). An inventory system with postponed demands. Stochastic Analysis and Applications, 22(3):827–842
B. Sivakumar and G. Arivarignan (2009). A stochastic inventory system with postponed demands. Performance Evaluation, 66:47–58
V. S. S. Yadavalli, B. Sivakumar, G. Arivarignan, and Olufemi Adetunji (2011). A multi-server perishable inventory system with negative customer. Computers & Industrial Engineering, 61(2): 254–273
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The research is supported by the INSPIRE fellowship, New Delhi, research award No. DST/INSPIRE fellowship/2010/[168], Reg. No. IF1020.
The research is supported by the Council of Scientific and Industrial Research (CSIR) — India for their financial support (No. 25 (0813)/10/EMR-II)
J. Sebastian Arockia Jenifer is a Research Scholar in the School of Mathematics at Madurai Kamaraj University, Madurai, Tamil Nadu, India. She received her MSc (2009) and MPhil (2010) degrees from School of Mathematics, Madurai Kamaraj University, Madurai, India. Her research interests include inventory control and management, Production inventory system.
B. Sivakumar received his MSc in Mathematics and PhD from School of Mathematics, Madurai Kamaraj University, India. He has received the Young Scientist Award from DST — SERC Fast Track Scheme in 2008. He has numerous publications in various reputed journals of mathematics and operation research such as European Journal of Operational Research, Computers and Industrial Engineering International Journal of Production Economics, Journal of System Science and System Engineering, etc. Currently, he is working as an Assistant Professor of Mathematics in Madurai Kamaraj University, Tamilnadu, India.
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Jenifer, J.S.A., Sivakumar, B. A comparative study of the inventory system with service facility and postponed demands. J. Syst. Sci. Syst. Eng. 23, 176–195 (2014). https://doi.org/10.1007/s11518-014-5242-0
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DOI: https://doi.org/10.1007/s11518-014-5242-0