Instantaneous Control of Brownian Motion with a Positive Lead Time

Published Online:https://doi.org/10.1287/moor.2018.0951

References

  • [1] Bather JA (1966) A continuous time inventory model. J. Appl. Probab. 3(2):538–549.CrossrefGoogle Scholar
  • [2] Chen H, Yao DD (2001) Fundamentals of Queueing Networks, Applications of Mathematics, vol. 46 (Springer, New York).CrossrefGoogle Scholar
  • [3] Chen X, Pang Z, Pan L (2014) Coordinating inventory control and pricing strategies for perishable products. Oper. Res. 62(2):284–300.LinkGoogle Scholar
  • [4] Constantinides GM, Richard SF (1978) Existence of optimal simple policies for discounted-cost inventory and cash management in continuous time. Oper. Res. 26(4):620–636.LinkGoogle Scholar
  • [5] Dai JG, Yao D (2013) Brownian inventory models with convex holding cost, part 1: Average-optimal controls. Stochastic Systems 3(2):442–499.LinkGoogle Scholar
  • [6] Dai JG, Yao D (2013) Brownian inventory models with convex holding cost, part 2: Discount-optimal controls. Stochastic Systems 3(2):500–573.LinkGoogle Scholar
  • [7] Davis MHA (1993) Markov Models and Optimization (Chapman and Hall, London).CrossrefGoogle Scholar
  • [8] Dynkin EB (1956) Infinitesimal operators of Markov processes. Teor. Veroyatnost. Primenen. 1(1):38–60.Google Scholar
  • [9] Harrison JM, Reiman MI (1981) Reflected Brownian motion on an orthant. Ann. Probab. 9(2):302–308.CrossrefGoogle Scholar
  • [10] Harrison JM, Taksar MI (1978) Optimal control of Brownian motion storage system. Stochastic Processes Appl. 6(2):179–194.CrossrefGoogle Scholar
  • [11] Harrison JM, Taksar MI (1983) Instantaneous control of Brownian motion. Math. Oper. Res. 8(3):439–453.LinkGoogle Scholar
  • [12] Harrison JM, Sellke TM, Taylor AJ (1983) Impulse control of Brownian motion. Math. Oper. Res. 8(3):454–466.LinkGoogle Scholar
  • [13] Murota K (2005) Note on multimodularity and L-convexity. Math. Oper. Res. 30(3):658–661.LinkGoogle Scholar
  • [14] Øksendal B, Sulem A (2009) Applied Stochastic Control of Jump Diffusions, 3rd ed. (Springer, Berlin).Google Scholar
  • [15] Ormeci M, Dai JG, Vande Vate J (2008) Impulse control of Brownian motion: The constrained average cost case. Oper. Res. 56(3):618–629.LinkGoogle Scholar
  • [16] Pang Z, Chen FY, Feng Y (2012) Technical note—A note on the structure of joint inventory-pricing control with leadtimes. Oper. Res. 60(3):581–587.LinkGoogle Scholar
  • [17] Porteus E (2002) Foundations of Stochastic Inventory Theory (Stanford University Press, Stanford, CA).CrossrefGoogle Scholar
  • [18] Puterman ML (1994) Markov Decision Processes: Discrete Stochastic Dynamic Programming, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics (John Wiley & Sons Inc., New York).CrossrefGoogle Scholar
  • [19] Reiman MI (1984) Open queueing networks in heavy traffic. Math. Oper. Res. 9(3):441–458.LinkGoogle Scholar
  • [20] Skorokhod A (1961) Stochastic equations for diffusion processes in a bounded region 1. Teor. Veroyatnost. Primenen. 6:264–274.Google Scholar
  • [21] Skorokhod A (1962) Stochastic equations for diffusion processes in a bounded region 2. Teor. Veroyatnost. Primenen. 7:3–23.Google Scholar
  • [22] Taksar MI (1985) Average optimal singular control and a related stopping problem. Math. Oper. Res. 10(1):63–81.LinkGoogle Scholar
  • [23] Whitt W (2002) Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues, Springer Series in Operations Research (Springer, New York).CrossrefGoogle Scholar
  • [24] Zipkin P (2008) On the structure of lost-sales inventory models. Oper. Res. 56(4):937–944.LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.