IPA Derivatives for Make-to-Stock Production-Inventory Systems with Backorders

详细信息    查看全文

• 作者：Yao Zhao (1)
  Benjamin Melamed (1)
  
• 关键词：Infinitesimal Perturbation Analysis ; IPA ; IPA derivatives ; IPA gradients ; Make ; to ; Stock ; Production ; inventory systems ; Stochastic fluid models ; SFM
• 刊名：Methodology and Computing in Applied Probability
• 出版年：2006
• 出版时间：June 2006
• 年：2006
• 卷：8
• 期：2
• 页码：191-222
• 全文大小：614KB
• 参考文献：1. J. Buzacott, S. Price, and J. Shanthikumar, 鈥淪ervice level in multi-stage MRP and base-stock controlled production systems,鈥?In G. Fandel, T. Gulledge, and A. Hones (eds.), / New Directions for Operations Research in Manufacturing, pp. 445鈥?63, Springer, Berlin, Germany, 1991.
  2. C. G. Cassandras, Y. Wardi, B. Melamed, G. Sun, and C. G. Panayiotou, 鈥淧erturbation analysis for on-line control and optimization of stochastic fluid models,鈥? / IEEE Transactions on Automatic Control vol. AC-47(8) pp. 1234鈥?248, 2002. CrossRef
  3. M. C. Fu, 鈥淥ptimization via simulation: A review,鈥? / Annals of Operations Research vol. 53 pp. 199鈥?47, 1994a. CrossRef
  4. M. C. Fu, 鈥淪ample path derivatives for $(s,S)$ inventory systems,鈥? / Operations Research vol. 42 pp. 351鈥?64, 1994b.
  5. P. Glasserman, / Gradient Estimation via Perturbation Analysis, Kluwer Academic Publishers, Boston, MA, 1991.
  6. P. Glasserman, and S. Tayur, 鈥淪ensitivity analysis for base-stock levels in multiechelon production-inventory systems,鈥? / Management Science vol. 41 pp. 263鈥?81, 1995.
  7. H. Heidelberger, X. R. Cao, M. Zazanis, and R. Suri, 鈥淐onvergence properties of infinitesimal analysis estimates,鈥? / Management Science vol. 34 pp. 1281鈥?302, 1988.
  8. Y. C. Ho, and X. R. Cao, / Perturbation Analysis of Discrete Event Simulation, Kluwer Academic Publishers, Boston, MA, 1991.
  9. U. Karmarkar, 鈥淟ot sizes, lead-times and in-process inventories,鈥? / Management Science vol. 33 pp. 409鈥?19, 1987.
  10. I. Paschalidis, Y. Liu, C. G. Cassandras, and C. Panayiotou, 鈥淚nventory Control for Supply Chains with Service Level Constraints: A Synergy between Large Deviations and Perturbation Analysis,鈥? / Annals of Operations Research vol. 126 pp. 231鈥?58, 2004. CrossRef
  11. R. Y. Rubinstein, and A. Shapiro, / Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method, John Wiley and Sons, New York, NY, 1993.
  12. M. H. Veatch, 鈥淯sing fluid solutions in dynamic scheduling,鈥?In S. B. Gershwin, Y. Dallery, C. T. Papadopoulos, and J. M. Smith (eds.), / Analysis and Modeling of Manufacturing Systems, pp. 399鈥?26, Kluwer, New York, 2002.
  13. Y. Wardi, and B. Melamed, 鈥淰ariational bounds and sensitivity analysis of continuous flow models,鈥? / Journal of Discrete Event Dynamic Systems vol. 11(3) pp. 249鈥?82, 2001. CrossRef
  14. Y. Wardi, B. Melamed, C. G. Cassandras, and C. G. Panayiotou, 鈥淥n-line IPA gradient estimators in stochastic continuous fluid models,鈥? / Journal of Optimization Theory and Applications vol. 115(2) pp. 369鈥?05, 2002. CrossRef
  15. L. M. Wein, 鈥淒ynamic scheduling of a multiclass Make-to-Stock queue,鈥? / Operations Research vol. 40 pp. 724鈥?35, 1992. CrossRef
  16. Y. Zhao, and B. Melamed, 鈥淢ake-to-Stock systems with backorders: IPA gradients,鈥?In Winter Simulation Conference (WSC 04), Washington D.C., December 5鈥?, pp. 559鈥?67, 2004.
  17. P. Zipkin, 鈥淢odels for design and control of stochastic, multi-item batch production systems,鈥? / Operations Research vol. 34 pp. 91鈥?04, 1986.
  
• 作者单位：Yao Zhao (1)
  Benjamin Melamed (1)
  
  1. Department of MSIS, Rutgers Business School 鈥?Newark and New Brunswick, Rutgers University, 94 Rockafeller Rd., Piscataway, NJ, 08854, USA
  

文摘

A single-stage Make-to-Stock (MTS) production-inventory system consists of a production facility coupled to an inventory facility, and is subject to a policy that aims to maintain a prescribed inventory level (called base stock) by modulating production capacity. This paper considers a class of single-stage, single-product MTS systems with backorders, driven by random demand and production capacity, and subject to a continuous-review base-stock policy. A model from this class is formulated as a stochastic fluid model (SFM), where all flows are described by stochastic rate processes with piecewise constant sample paths, subject to very mild regularity assumptions that merely preclude accumulation points of jumps with probability 1. Other than that, the MTS model in SFM setting is nonparametric in that it assumes no specific form for the underlying probability law, and as such is quite general. The paper proceeds to derive formulas for the (stochastic) IPA (Infinitesimal Perturbation Analysis) derivatives of the sample-path time averages of the inventory level and backorders level with respect to the base-stock level and a parameter of the production rate. These formulas are comprehensive in that they are exhibited for any initial condition of the system, and include right and left derivatives (when they do not coincide). The derivatives derived are then shown to be unbiased and their formulas are seen to be amenable to fast computation. The generality of the model and comprehensiveness of the IPA derivative formulas hold out the promise of gradient-based applications. More specifically, since the base-stock level and production rate are the key control parameters of MTS systems, the results provide the theoretical underpinnings for optimizing the design of MTS systems and for devising prospective on-line adaptive control algorithms that employ IPA derivatives. The paper concludes with a discussion of those issues.