Supply streams

Manufacturing and Service Operations Management

Volumn 15, Issue 3, 2013, Pages 444-457

  Song, Jing Sheng ^a   Zipkin, Paul ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Diffusion; Inventory production; Multiechelon; Partial differential equations; Probability; Uncertainty

Indexed keywords

BASE STOCK POLICY; CLOSED-FORM EXPRESSION; FIRST-PASSAGE TIME; INVENTORY SYSTEMS; INVENTORY/PRODUCTION; MULTIECHELON; OPTIMAL COST FUNCTION; UNCERTAINTY;

DIFFUSION; OPTIMIZATION; PROBABILITY; SUPPLY CHAINS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 84881271511     PISSN: 15234614     EISSN: 15265498     Source Type: Journal    
DOI: 10.1287/msom.2013.0431     Document Type: Article

References (50)

1. Axsäter S, Lundell P (1984) In-process safety stocks. Proc. 23rd IEEE Conf. Decision and Control 23:839-842.
2. Bather J (1966) A continuous time inventory model. J. Appl. Probab. 3:538-549.
3. Berling P, Martínez-De-Albéniz V (2011a) A characterization of optimal base-stock levels for a continuous-stage serial supply chain. Working paper, IESE Business School, Barcelona, Spain.
4. Berling P, Martínez-De-Albéniz V (2011b) Optimal expediting decisions in a continuous-stage serial supply chain. Working paper, IESE Business School, Barcelona, Spain.
5. Broadie M, Yamamoto Y (2003) Application of the fast Gauss transform to option pricing. Management Sci. 49:1071-1088.
6. Cannon J (1984) The One-Dimensional Heat Equation (Cambridge University Press, Cambridge, UK).
7. Chaudhari G (2007) Cost-time profiling as a tool in value engineering. Value World 30:1-8.
8. Chen F, Zheng Y (1994) Lower bounds for multi-echelon stochastic inventory systems. Management Sci. 40:1426-1443.
9. Chen H, Yao D (2001) Fundamentals of Queueing Networks (Springer- Verlag, New York).
10. Cheng L, Chen X, Chadam J, Saunders D (2007) Analysis of an inverse first passage problem from risk management. SIAM J. Math. Anal. 38:845-873.
11. Clark A, Scarf H (1960) Optimal policies for a multi-echelon inventory problem. Management Sci. 6:475-490.
12. Crank J (1987) Free and Moving Boundary Problems (Oxford University Press, Oxford, UK).
13. Daniels H (1982) Sequential tests constructed from images. Ann. Statist. 10:394-400.
14. Daniels H (1996) Approximating the first crossing-time density for a curved boundary. Bernoulli 2:133-143.
15. DeCroix G, Song J, Zipkin P (2005) A series system with returns: Stationary analysis. Oper. Res. 53:350-362.
16. de Kok TG, Fransoo JC (2003) Planning supply chain operations: Definition and comparison of planning concepts. de Kok AG, Graves SC, eds. Supply Chain Management: Design, Coordination and Operation, Handbooks in Operations Research and Management Science, Vol. 11, Chap. 12 (Elsevier, Amsterdam).
17. Dogru MK, van Houtum G, de Kok AG (2008) Newsvendor equations for optimal reorder levels of multi-echelon inventory systems with fixed batch sizes. Oper. Res. Lett. 36: 551-556.
18. Dong L, Lee H (2003) Optimal policies and approximations for a serial multiechelon inventory system with time-correlated demand. Oper. Res. 51:969-980.
19. Durbin J (1988) A reconciliation of two different expressions for the first-passage density of Brownian motion to a curved boundary. J. Appl. Probab. 25:829-832.
20. Durbin J (1992) The first-passage density of the Brownian motion process to a curved boundary. J. Appl. Probab. 29: 291-304.
21. Federgruen A, Zipkin P (1984) Computational issues in an infinitehorizon, multiechelon inventory model. Oper. Res. 32:818-836.
22. Fleming W, Soner M (1993) Controlled Markov Processes and Viscosity Solutions (Springer-Verlag, New York).
23. Fooks J (1993) Profiles for Performance (Addison-Wesley, Reading, MA).
24. Gallego G, Özer Ö (2005) A new algorithm and a new heuristic for serial supply systems. Oper. Res. Lett. 33:349-362.
25. Gallego G, Zipkin P (1999) Stock positioning and performance estimation for serial production-transportation systems. Manufacturing Service Oper. Management 1:77-88.
26. Greengard L, Strain J (1991) The fast Gauss transform. SIAM J. Sci. Statist. Comput. 12:79-94.
27. Harrison J (1985) Brownian Motion and Stochastic Flow Systems (Wiley, New York).
28. Jaimungal S, Kreinin A, Valov A (2009) Integral equations and the first passage time of Brownian motion. Working paper, University of Toronto, Toronto, ON.
29. Kumar S, Muthuraman M (2004) A numerical method for solving singular stochastic control problems. Oper. Res. 52:563-582.
30. Kushner H, Dupuis P (1992) Numerical Methods for Stochastic Control Problems in Continuous Time (Springer-Verlag, New York).
31. Lerche H (1986) Boundary Crossing of Brownian Motion (Springer, Heidelberg).
32. Lo V, Roberts G, Daniels H (2002) Inverse method of images. Bernoulli 8:53-80.
33. Narasimhan T (2010) The discrete and the continuous: Which comes first? Current Sci. 98:1003-1005.
34. Novikov A, Frishling V, Kordzakhia N (1999) Approximations of boundary crossing probabilities for a Brownian motion. J. Appl. Probab. 36:1019-1030.
35. Peskir G (2002a) Limit at zero of the Brownian first-passage density. Probab. Theory Related Fields 124:100-111.
36. Peskir G (2002b) On integral equations arising in the first-passage problem for Brownian motion. J. Integral Equations Appl. 14: 397-423.
37. Plambeck E, Ward A (2006) Optimal control of a high-volume assemble-to-order system. Math. Oper. Res. 31:453-477.
38. Plambeck E, Ward A (2008) Optimal control of a high-volume assemble-to-order system with leadtime quotation and expediting. Queueing Systems 60:1-69.
39. Redner S (2001) A Guide to First-Passage Processes (Cambridge University Press, Cambridge, UK).
40. Reiman M, Rubio R, Wein L (1999) Heavy traffic analysis of the dynamic stochastic inventory-routing problem. Transportation Sci. 33:361-380.
41. Sato S (1977) Evaluation of the first-passage time probability to a square root boundary for the Wiener process. J. Appl. Probab. 14:850-856.
42. Schraner E, Hausman W (1997) Optimal production operations sequencing. IIE Trans. 29:651-660.
43. Shang K, Song J (2003) Newsvendor bounds and heuristic for optimal policies in serial supply chains. Management Sci. 49:618-638.
44. Sobel M (2004) Fill rates of single-stage and multistage supply systems. Manufacturing Service Oper. Management 6:41-52.
45. Song J, Zipkin P (2011) An approximation for the inverse firstpassage time problem. Ann. Appl. Probab. 43:264-275.
46. van Houtum G, Zijm W (1991) Computational procedures for stochastic multi-echelon production systems. Internat. J. Production Econom. 23:223-237.
47. Wang L, Pötzelberger K (1997) Boundary crossing probability for Brownian motion and general boundary. J. Appl. Probab. 34: 54-65.
48. Zipkin P (2000) Foundations of Inventory Management (McGraw-Hill, Boston).
49. Zipkin P (2013) On the method of images and the asymptotic behavior of first-passage times. Ann. Oper. Res. Forthcoming.
50. Zucca C, Sacerdote L (2009) On the inverse first-passage-time problem for a Wiener process. Ann. Appl. Probab. 19:1319-1346.