INAR implementation of newsvendor model for serially dependent demand counts

References

• Abdulwahab, U., and M. I. M. Wahab. 2014. “Approximate Dynamic Programming Modeling for a Typical Blood Platelet Bank.” Computers & Industrial Engineering 78: 259–270.
   Web of Science ®Google Scholar
• Ali, M. M., and J. E. Boylan. 2012. “On the Effect of Non-optimal Forecasting Methods on Supply Chain Downstream Demand.” IMA Journal of Management Mathematics 23 (1): 81–98.
   Web of Science ®Google Scholar
• Al-Osh, M. A., and A. A. Alzaid. 1987. “First-order Integer-valued Autoregressive (INAR(1)) Process.” Journal of Time Series Analysis 8 (3): 261–275.
   Google Scholar
• Alwan, L. C., J. J. Liu, and D. Q. Yao. 2003. “Stochastic Characterization of Upstream Demand Processes in a Supply Chain.” IIE Transactions 35 (3): 207–219.
   Web of Science ®Google Scholar
• Alwan, L. C., J. J. Liu, and D. Q. Yao. 2008. “Forecast Facilitated Lot-for-lot Ordering in the Presence of Autocorrelated Demand.” Computers & Industrial Engineering 54 (4): 840–850.
   Web of Science ®Google Scholar
• Alwan, L. C., M. Xu, D. Q. Yao, and X. Yue. 2016. “The Dynamic Newsvendor Model with Correlated Demand.” Decision Sciences 47 (1): 11–30.
   Web of Science ®Google Scholar
• Aviv, Y. 2003. “A Time-series Framework for Supply-chain Inventory Management.” Operations Research 51 (2): 210–227.
   Web of Science ®Google Scholar
• Babai, M. Z., M. M. Ali, J. E. Boylan, and A. A. Syntetos. 2013. “Forecasting and Inventory Performance in a Two-stages Supply Chain with ARIMA(0,1,1) Demand: Theory and Empirical Analysis.” International Journal of Production Economics 143 (2): 462–471.
   Web of Science ®Google Scholar
• Böckenholt, U. 1999. “Mixed INAR(1) Poisson Regression Models: Analyzing Heterogeneity and Serial Dependencies in Longitudinal Count Data.” Journal of Econometrics 89 (1–2): 317–338.
   Web of Science ®Google Scholar
• Cachon, G. P., and M. Fisher. 2000. “Supply Chain Inventory Management and the Value of Shared Information.” Management Science 46 (8): 1032–1048.
   Web of Science ®Google Scholar
• Chen, F. Z., Z. Drezner, J. K. Ryan, and D. Simchi-Levi. 2000. “Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information.” Management Science 46 (3): 436–443.
   Web of Science ®Google Scholar
• Chen, F., J. K. Ryan, and D. Simchi-Levi. 2000. “The Impact of Exponential Smoothing Forecasts on the Bullwhip Effect.” Naval Research Logistics 47 (4): 269–286.
   Web of Science ®Google Scholar
• Cox, D. R. 1981. “Statistical Analysis of Time Series: Some Recent Developments.” Scandinavian Journal of Statistics 8: 93–115.
   Web of Science ®Google Scholar
• Erkip, N., W. H. Hausman, and S. Nahmias. 1990. “Optimal Centralized Ordering Policies in Multi-Echelon Inventory Systems with Correlated Demands.” Management Science 36 (3): 381–392.
   Web of Science ®Google Scholar
• Fotopoulos, S., M. C. Wang, and S. S. Rao. 1988. “Safety Stock Determination with Correlated Demands and Arbitrary Lead Times.” European Journal of Operational Research 35 (2): 172–181.
   Web of Science ®Google Scholar
• Franke, J., and T. Seligmann. 1993. “Conditional Maximum Likelihood Estimates for INAR(1) Processes and their Application to Modelling Epileptic Seizure Counts”. In Developments in Time Series Analysis, edited by T. Subba Rao, 310–330. London: Chapman & Hall.
   Google Scholar
• Freeland, R. K., and B. P. M. McCabe. 2004a. “Analysis of Low Count Time Series Data by Poisson Autoregression.” Journal of Time Series Analysis 25 (5): 701–722.
   Web of Science ®Google Scholar
• Freeland, R. K., and B. P. M. McCabe. 2004b. “Forecasting Discrete Valued Low Count Time Series.” International Journal of Forecasting 20 (3): 427–434.
   Web of Science ®Google Scholar
• Gilbert, K. 2005. “An ARIMA Supply Chain Model.” Management Science 51 (2): 305–310.
   Web of Science ®Google Scholar
• Giloni, A., C. Hurvich, and S. Seshadri. 2014. “Forecasting and Information Sharing in Supply Chains under ARMA Demand.” IIE Transactions 46 (1): 35–54.
   Web of Science ®Google Scholar
• Graves, S. C. 1999. “A Single-item Inventory Model for a Nonstationary Demand Process.” Manufacturing and Service Operations Management 1 (1): 50–61.
   Google Scholar
• Graves, S. C., and S. P. Willems. 2000. “Optimizing Strategic Safety Stock Placement in Supply Chains.” Manufacturing and Service Operations Management 2 (1): 68–83.
   Google Scholar
• Jazi, M. A., G. Jones, and C.-D. Lai. 2012. “First-order Integer Valued AR Processes with Zero Inflated Poisson Innovations.” Journal of Time Series Analysis 33 (6): 954–963.
   Web of Science ®Google Scholar
• Johnson, G. D., and H. E. Thompson. 1975. “Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes.” Management Science 21 (11): 1303–1307.
   Web of Science ®Google Scholar
• Kahn, J. 1987. “Inventories and the Volatility of Production.” The American Economic Review 77 (4): 667–679.
   Web of Science ®Google Scholar
• Karlin, S., and H. Scarf. 1958. “Inventory Models and Related Stochastic Processes.” In Studies in the Mathematical Theory of Inventory and Production, edited by K. J. Arrow, S. Karlin and H. Scarf, 319–336. Stanford, CA: Stanford University Press.
   Google Scholar
• Lee, H. L., P. Padmanabhan, and S. Whang. 1997. “Information Distortion in a Supply Chain: The Bullwhip Effect.” Management Science 43 (4): 546–558.
   Web of Science ®Google Scholar
• Lee, H. L., K. C. So, and C. S. Tang. 2000. “The Value of Information Sharing in a Two-level Supply Chain.” Management Science 46 (5): 626–643.
   Web of Science ®Google Scholar
• Marmorstein, H., and W. Zinn. 1993. “A Conditional Effect of Autocorrelated Demand on Safety Stock Determination.” European Journal of Operational Research 68 (1): 139–142.
   Web of Science ®Google Scholar
• McKenzie, E. 1985. “Some Simple Models for Discrete Variate Time Series.” Water Resources Bulletin 21 (4): 645–650.
   Google Scholar
• Mohammadipour, M., and J. E. Boylan. 2012. “Forecast Horizon Aggregation in Integer Autoregressive Moving Average (INARMA) Models.” Omega 40 (6): 703–712.
   Web of Science ®Google Scholar
• Pavlopoulos, H., and D. Karlis. 2008. “INAR(1) Modeling of Overdispersed Count Series with an Environmental Application.” Environmetrics 19 (4): 369–393.
   Web of Science ®Google Scholar
• Presman, E., and S. P. Sethi. 2006. “Inventory Models with Continuous and Poisson Demands and Discounted and Average Costs.” Production and Operations Management 15 (2): 279–293.
   Web of Science ®Google Scholar
• Qin, Y., R. Wang, A. J. Vakharia, Y. Chen, and M. H. Seref. 2011. “The Newsvendor Problem: Review and Directions for Future Research.” European Journal Of Operational Research 213 (2): 361–374.
   Web of Science ®Google Scholar
• Quddus, M. A. 2008. “Time Series Count Data Models: An Empirical Application to Traffic Accidents.” Accident Analysis and Prevention 40 (5): 1732–1741.
   PubMed Web of Science ®Google Scholar
• Raghunathan, S. 2001. “Information Sharing in a Supply Chain: A Note in its Value When Demand is Non-stationary.” Management Science 21 (11): 605–610.
   Web of Science ®Google Scholar
• R Core Team. 2014. R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing. http://www.R-project.org/.
   Google Scholar
• Scarf, H. 1958. “Stationary Operating Characteristics of An Inventory Model with Time Lag.” In Studies in the Mathematical Theory of Inventory and Production, edited by K. J. Arrow, S. Karlin and H. Scarf, 298–319. Stanford, CA: Stanford University Press.
   Google Scholar
• Schweer, S., and C. H. Weiß. 2014. “Compound Poisson INAR(1) Processes: Stochastic Properties and Testing for Overdispersion.” Computational Statistics and Data Analysis 77: 267–284.
   Web of Science ®Google Scholar
• Song, J., and P. Zipkin. 1993. “Inventory Control in a Fluctuating Demand Environment.” Operations Research 41 (2): 351–370.
   Web of Science ®Google Scholar
• Steutel, F. W., and K. van Harn. 1979. “Discrete Analogues of Self-decomposability and Stability.” Annals of Probability 7 (5): 893–899.
   Web of Science ®Google Scholar
• Syntetos, A. A., J. E. Boylan, and S. M. Disney. 2009. “Forecasting for Inventory Planning: A 50-year Reveiw.” Journal of Operational Research Society 60: 149–160.
   Web of Science ®Google Scholar
• Vazifedan, T., and M. Shitan. 2012. “Modeling Polio Data using the First Order Non-negative Integer-valued Autoregressive, INAR(1), Model.” International Journal of Modern Physics: Conference Series 9: 232–239.
   Google Scholar
• Weiß, C. H. 2007. “Controlling Correlated Processes of Poisson Counts.” Quality and Reliability Engineering International 23 (6): 741–754.
   Web of Science ®Google Scholar
• Weiß, C. H. 2008. “Thinning Operations for Modeling Time Series of Counts - A Survey.” Advances in Statistical Analysis 92 (3): 319–341.
   Web of Science ®Google Scholar
• Weiß, C. H. 2013. “Integer-valued Autoregressive Models for Counts Showing Underdispersion.” Journal of Applied Statistics 40 (9): 1931–1948.
   Web of Science ®Google Scholar
• Zhang, X. 2004a. “The Impact of Forecasting Methods on the Bullwhip Effect.” International Journal of Production Economics 88 (1): 15–27.
   Web of Science ®Google Scholar
• Zhang, X. 2004b. “Evolution of ARMA Demand in Supply Chains.” Manufacturing and Services Operations Management 6 (2): 195–198.
   Google Scholar