On the continuous-review (s, S) inventory model under compound renewal demand and random lead times

Izzet Sahin

doi:10.2307/3213739

Abstract

Binomial moments of the time-dependent and limiting distributions of inventory deficit are derived for a continuous-review (s, S) inventory system under the assumption that interarrival times, demand sizes, and lead times are independent sequences of independent, identically distributed random variables. Explicit expressions for the limiting distribution are also given in some special cases of practical interest. The approach used follows that of Finch [2] who investigated the system under the additional assumption of unit demands.

Footnotes

Research supported by the National Science Foundation under Grant No. ECS-8011916.

References

[1] Coleman, R. (1981) The moments of forward recurrence time. Department of Mathematics, Imperial College.Google Scholar

[2] Finch, P. D. (1961) Some probability theorems in inventory control. Publ. Math. Debrecen. 8, 241–261.CrossRef Google Scholar

[3] Sahin, I. (1979) On the stationary analysis of continuous review (s, S) inventory systems with constant lead times. Operat. Res. 27, 717–729.CrossRef Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Zipkin, Paul 1986. Stochastic leadtimes in continuous‐time inventory models. Naval Research Logistics Quarterly, Vol. 33, Issue. 4, p. 763.

Kalpakam, S. and Arivarignan, G. 1990. Inventory system with random supply quantity. OR Spektrum, Vol. 12, Issue. 3, p. 139.

Azoury, Katy S. and Brill, Percy H. 1992. Analysis of net inventory in continuous review models with random lead time. European Journal of Operational Research, Vol. 59, Issue. 3, p. 383.

Janssen, Fred Heuts, Ruud and de Kok, Ton 1998. On the (R, s, Q) inventory model when demand is modelled as a compound Bernoulli process. European Journal of Operational Research, Vol. 104, Issue. 3, p. 423.

Krishnamoorthy, A. and Islam, Mohammad Ekramol 2004. (s,S) Inventory System with Postponed Demands. Stochastic Analysis and Applications, Vol. 22, Issue. 3, p. 827.

Bensoussan, Alain Liu, R. H. and Sethi, Suresh P. 2005. Optimality of an $(s, S)$ Policy with Compound Poisson and Diffusion Demands: A Quasi-variational Inequalities Approach. SIAM Journal on Control and Optimization, Vol. 44, Issue. 5, p. 1650.

Araman, Victor F. and Glynn, Peter W. 2006. Tail asymptotics for the maximum of perturbed random walk. The Annals of Applied Probability, Vol. 16, Issue. 3,

Artalejo, J. R. Krishnamoorthy, A. and Lopez-Herrero, M. J. 2006. Numerical analysis of(s, S) inventory systems with repeated attempts. Annals of Operations Research, Vol. 141, Issue. 1, p. 67.

Presman, Ernst and Sethi, Suresh P. 2006. Inventory Models with Continuous and Poisson Demands and Discounted and Average Costs. Production and Operations Management, Vol. 15, Issue. 2, p. 279.

Aliyev, R. T. and Khaniyev, T. A. 2012. On the rate of convergence of the asymptotic expansion for the ergodic distribution of a semi-Markov (s, S) inventory model. Cybernetics and Systems Analysis, Vol. 48, Issue. 1, p. 117.

Khaniyev, Tahir Kokangul, Ali and Aliyev, Rovshan 2013. An asymptotic approach for a semi‐Markovian inventory model of type (s, S). Applied Stochastic Models in Business and Industry, Vol. 29, Issue. 5, p. 439.

Ang, Marcus Sigman, Karl Song, Jeannette and Zhang, Hanqin 2014. Closed-Form Approximations for Optimal (r,q) and (S,T) Policies in a Parallel Processing Environment. SSRN Electronic Journal,

Federgruen, Awi and Wang, Min 2015. A CONTINUOUS REVIEW MODEL WITH GENERAL SHELF AGE AND DELAY-DEPENDENT INVENTORY COSTS. Probability in the Engineering and Informational Sciences, Vol. 29, Issue. 4, p. 507.

Aliyev, Rovshan 2017. On a stochastic process with a heavy-tailed distributed component describing inventory model type of (s, S). Communications in Statistics - Theory and Methods, Vol. 46, Issue. 5, p. 2571.

Gökpınar, Esra Khaniyev, Tahir Gamgam, Hamza and Gökpinar, Fikri 2018. Estimators of the Moments for the Inventory Model of Type (s, S). Iranian Journal of Science and Technology, Transactions A: Science, Vol. 42, Issue. 1, p. 5.

Perera, Sandun Janakiraman, Ganesh and Niu, Shun‐Chen 2018. Optimality of (s, S) Inventory Policies under Renewal Demand and General Cost Structures. Production and Operations Management, Vol. 27, Issue. 2, p. 368.

Barron, Y. 2019. A state-dependent perishability (s, S) inventory model with random batch demands. Annals of Operations Research, Vol. 280, Issue. 1-2, p. 65.

Bektaş Kamışlık, Aslı Kesemen, Tülay and Khaniyev, Tahir 2019. Inventory model of type $(s,S)$ under heavy tailed demand with infinite variance. Brazilian Journal of Probability and Statistics, Vol. 33, Issue. 1,

Badía, F. G. Sangüesa, C. and Federgruen, A. 2021. LOG-CONCAVITY OF COMPOUND DISTRIBUTIONS WITH APPLICATIONS IN OPERATIONAL AND ACTUARIAL MODELS. Probability in the Engineering and Informational Sciences, Vol. 35, Issue. 2, p. 210.

Katehakis, Michael N. Melamed, Benjamin and Shi, Jim Junmin 2022. Optimal replenishment rate for inventory systems with compound Poisson demands and lost sales: a direct treatment of time-average cost. Annals of Operations Research, Vol. 317, Issue. 2, p. 665.

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On the continuous-review (s, S) inventory model under compound renewal demand and random lead times

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

On the continuous-review (s, S) inventory model under compound renewal demand and random lead times

Abstract

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