Abstract
In this article, we consider a finite capacity queueing-inventory system in which the service rate is subject to control. We assume that the customers arrive according to a Poisson process. The customer who arrives to the service station, when the waiting hall is full, is considered to be lost. The inventory attached with the service facility is replenished according to a (s, Q) policy and the lead times are exponentially distributed. We calculate the optimal service rates to be employed at each service completion epoch so that the long-run expected cost rate is minimized for fixed maximum inventory level, reorder point and capacity of the waiting hall. This problem is modelled as a semi-Markov decision problem. The stationary optimal policy is obtained using linear programming algorithm and the results are illustrated numerically.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Al-Hamadi, H. M., Sangeetha, N., & Sivakumar, B. (2015). Optimal control of service parameter for a perishable inventory system maintained at service facility with impatient customers. Annals of Operations Research, 233(1), 3–23.
Berman, O., & Kim, E. (1999). Stochastic inventory policies for inventory management of service facilities. Stochastic Models, 15, 695–718.
Berman, O., & Kim, E. (2004). Dynamic inventory strategies for profit maximization in a service facility with stochastic service, demand and lead time. Mathematical Methods of Operations Research, 60(3), 497–521.
Berman, O., & Sapna, K. P. (2001). Optimal control of service for facilities holding inventory. Computers and Operations Research, 28, 429–441.
Berman, O., & Sapna, K. P. (2002). Optimal service rates of a service facility with perishable inventory items. Naval Research Logistics, 49, 464–482.
Berman, O. Kaplan., E. H., and Shimshak D.G. (1993). Deterministic approximations for inventory management at service facilities. IIE Transactions, 25, 98–104.
Çinlar, E. (1975). Introduction to Stochastic Processes.
Dantzig, G. B., & Wolfe, P. (1962). Linear programming in a Markov chain. Operational Research, 10(5), 702–710.
Dunning, I., Huchette, J., & Lubin, M. (2017). JuMP: A modeling language for mathematical optimization. SIAM Review, 59(2), 295–320.
Jenifer, J. S. A., Sangeetha, N., & Sivakumar, B. (2014). Optimal control of service parameter for a perishable inventory system with service facility, postponed demands and finite waiting hall. International Journal of Information and Management Sciences, 25(4), 349–370.
Keerthana, M., Saranya, N., & Sivakumar, B. (2020). A stochastic queueing inventory system with renewal demands and positive lead time. European Journal of Industrial Engineering, 14(4), 443–484.
Kim, E. (2005). Optimal inventory replenishment policy for a queueing system with finite waiting room capacity. European Journal of Operational Research, 161(1), 256–274.
Kim, E., Park, C. K., & Shin, K. (2004). Dynamic supplier-managed inventory control and the beneficial effect of information sharing. Journal of the Korean Operations Research and Management Science Society, 29(3), 63–78.
Kitaev, M. Y. and Rykov, V. V. (1995) . Controlled queueing systems. CRC Press.
Krishnamoorthy, A., Shajin, D., & Narayanan, V. C. (2020). Inventory with positive service time: A survey. In V. Anisimov & N. Limnios (Eds.), Advanced Trends in Queueing Theory: series of books Mathematics and Statistics, Sciences. ISTE & J. Wiley: London.
Melikov, A. Z., & Molchanov, A. A. (1992). Stock optimization in transportation/storage systems. Cybernetics and Systems Analysis, 28(3), 484–487.
Mine, H., & Osaki, S. (1970). Markovian decision processes.
Osaki, S., & Mine, H. (1968). Linear programming algorithms for semi-Markovian decision processes. Journal of Mathematical Analysis and Applications, 22, 356–381.
Rykov, V. (1975). Controllable queueing systems. Itogi nauki i techniki. teoria verojatn. matem. statist. teoretich. kibern. (In Russian), 12: 45 – 152.
Rykov, V. (2017). Controllable queueing systems: from the very beginning up to nowadays. Reliability: Theory and Applications, 12(2), 39–61.
Sangeetha, N., & Sivakumar, B. (2020). Optimal service rates of a perishable inventory system with service facility. International Journal of Mathematics in Operational Research, 16(4), 515–550.
Sathees Kumar, R., & Elango, C. (2012). Markov decision processes in service facilities holding perishable inventory. Opsearch, 49(4), 348–365.
Sigman, K., & Simchi-Levi, D. (1992). Light traffic heuristic for an M/G/1 queue with limited inventory. Annals of Operations Research, 40(1), 371–380.
Wang, K., Jiang, Z., Li, G., and Cao, J. (2013). Integrated capacity allocation policies for a production service system with two-class customers and items. In 2013 IEEE International Conference on Automation Science and Engineering (CASE), pp. 83–88.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The research is supported by the UGC BSR Research Fellowship, University Grants Commission, India, F.25-1/2014-15 (BSR)/5-66/2007 (BSR)
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Keerthana, M., Sangeetha, N. & Sivakumar, B. Optimal service rates of a queueing inventory system with finite waiting hall, arbitrary service times and positive lead times. Ann Oper Res 331, 739–762 (2023). https://doi.org/10.1007/s10479-022-04901-2
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-022-04901-2