On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT 

Year 2010, Volume: 39 Issue: 4, 599 - 611, 01.04.2010

Tahir Khaniyev  kumru Didem Atalay

https://izlik.org/JA78XB26PX

Keywords

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References

• Alsmeyer, G. Some relations between harmonic renewal measure and certain first passage times, Statistics & Probability Letters 12 (1), 19–27, 1991.
• Aras, G. and Woodroofe, M. Asymptotic expansions for the moments of a randomly stopped average, Annals of Statistics 21, 503–519, 1993.
• Beyer, D., Sethi, S. P. and Taksar, M. Inventory models with Markovian demands and cost functions of polynomial growth, Journal of Optimization Theory and Application 98 (2), 281–323, 1998.
• Borovkov, A. A. Stochastic Processes in Queuing Theory (Spinger-Verlag, New York, 1976). [5] Brown, M. and Ross, S. M. Asymptotic properties of cumulative process, Journal of Applied Mathematics 22 (1), 93–105, 1972.
• Brown, M. and Solomon, H. A. Second-order approximation for the variance of a renewal- reward process, Stochastic Processes and their Applications 3, 301–314, 1975.
• Chen, F. and Zheng, Y. Waiting time distribution in (T, S) inventory systems, Operations Research Letters 12, 145–151, 1992.
• Federyuk, M. V. Asymptotics for Integrals and Series (Nauka, Moscow, 1984).
• Feller, W. Introduction to Probability Theory and Its Applications II (John Wiley, New York, 1971).
• Gavirneni, S. An efficient heuristic for inventory control when the customer is using a (s; S) policy, Operations Research Letters 28 , 187-192, 2001.
• Gihman, I.I. and Skorohod, A.V. Theory of Stochastic Processes II, (Springer, Berlin, 1975). [12] Janssen, F., Heuts, Y. and Kok, T. On the (R, s, Q) inventory model when demand is modeled as a compound Bernoulli process, European Journal of Operational Research 104, 423–436, 1998.
• Johansen, S. G. J. and Thorstenson, A. Optimal and approximate (Q, r) inventory policies with lost sales and gamma-distributed lead time, International Journal of Production Eco- nomics 30, 179–194, 1993.
• Khaniev, T. A., Ozdemir, H. and Maden, S. Calculating probability characteristics of a boundary functional of a semi-continuous random process with reflecting and delaying screens, Applied Stochastic Models and Data Analysis 18, 117–123, 1998.
• Khaniev, T. A., Unver, I. and Maden, S. On the semi-Markovian random walk with two reflecting barriers, Stochastic Analysis and Applications 19 (5), 799–819, 2001.
• Khaniyev, T. A. and Kucuk, Z. Asymptotic expansions for the moments of the Gaussian random walk with two barriers, Statistics & Probability Letters 69 (1), 91–103, 2004.
• Khaniyev, T. A. and Mammadova, Z. On the stationary characteristics of the extended model of type(s, S) with Gaussian distribution of summands, Journal of Statistical Computation and Simulation 76 (10), 861–874, 2006.
• Khaniyev, T. A., Kesemen, T., Aliyev, R. T. and Kokang¨ul, A. Asymptotic expansions for the moments of a semi-Markovian random walk with exponentional distributed interference of chance, Statistics & Probability Letters 78 (6), 785–793, 2008.
• Lotov, V. I. On some boundary crossing problems for Gaussian random walks, Annals of Probability 24 (4), 2154–2171, 1996.
• Prabhu, N. U. Stochastic Storage Processes (Springer-Verlag, New York, 1981).
• Ross, S. M. Introduction to Probability Models (Academic Press INC., Boston, 1989).
• Sahin, I. On the continuous-review (s, S) inventory model under compound renewal demand and random lead times, Journal of Applied Probability 20, 213–219, 1983.
• Sethi, S. P. and Cheng, F. Optimality of (s, S) policies in inventory models with markovian demand, Operations Research 45 (6), 931–939, 1997.
• Smith, W. L. Renewal theory and its ramification, Journal of the Royal Statistical Society - Series B (Methodological) 20 (2), 243–302, 1958.
• Tijms, H. C. Stochastic Models: An Algorithmic Approach (Wiley, New York, 1994).
• Zheng, Y. S. and Federgruen, A. Computing an optimal (s, S) policy is as easy as a single evaluation of the cost function, Operations Research 39, 654–665, 1991.