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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

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.

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

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.
There are 24 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Tahir Khaniyev This is me

 kumru Didem Atalay This is me

Publication Date April 1, 2010
Published in Issue Year 2010 Volume: 39 Issue: 4

Cite

APA Khaniyev, T., & Atalay, .D. (2010). On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics, 39(4), 599-611.
AMA Khaniyev T, Atalay D. On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. April 2010;39(4):599-611.
Chicago Khaniyev, Tahir, and  kumru Didem Atalay. “On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 39, no. 4 (April 2010): 599-611.
EndNote Khaniyev T, Atalay D (April 1, 2010) On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics 39 4 599–611.
IEEE T. Khaniyev and  . D. Atalay, “On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT ”, Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 4, pp. 599–611, 2010.
ISNAD Khaniyev, Tahir - Atalay, kumruDidem. “On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 39/4 (April 2010), 599-611.
JAMA Khaniyev T, Atalay D. On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2010;39:599–611.
MLA Khaniyev, Tahir and  kumru Didem Atalay. “On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 4, 2010, pp. 599-11.
Vancouver Khaniyev T, Atalay D. On the Weak Convergence of the Ergodic Distribution for an Inventory Model of Type (s,S)  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2010;39(4):599-611.