A Multiclass Hybrid Production Center in Heavy Traffic

This paper presents an analysis of a single-stage hybrid production system that makes multiple types of products, some of which are made to-order while others are made to-stock. The analysis begins with a formal heavy traffic limit theorem of the production system, which is modeled as a mixed queueing network. Taking insights from the limit theorem, the analysis continues with the development of an approximation procedure. Numerical experiments indicate that this procedure provides good estimates for performance measures such as fill rates and average inventory levels.

[1]  P. Moran,et al.  Reversibility and Stochastic Networks , 1980 .

[2]  李幼升,et al.  Ph , 1989 .

[3]  Hong Chen,et al.  Stochastic discrete flow networks : diffusion approximations and bottlenecks , 1991 .

[4]  A. Federgruen Chapter 3 Centralized planning models for multi-echelon inventory systems under uncertainty , 1993, Logistics of Production and Inventory.

[5]  Viên Nguyen,et al.  Fluid and Diffusion Approximations of a Two-Station Mixed Queueing Network , 1995, Math. Oper. Res..

[6]  Ward Whitt,et al.  Some Useful Functions for Functional Limit Theorems , 1980, Math. Oper. Res..

[7]  Peter L. Jackson,et al.  An Exact Analysis of a Production-Inventory Stretegy for Industrial Suppliers , 1993 .

[8]  Lode Li The role of inventory in delivery-time competition , 1992 .

[9]  Frank Kelly,et al.  Reversibility and Stochastic Networks , 1979 .

[10]  J. Michael Harrison,et al.  The QNET method for two-moment analysis of open queueing networks , 1990, Queueing Syst. Theory Appl..

[11]  John A. Buzacott,et al.  Stochastic models of manufacturing systems , 1993 .

[12]  J. Harrison,et al.  The QNET Method for Two-Moment Analysis of Closed Manufacturing Systems , 1993 .

[13]  J. Harrison,et al.  Reflected Brownian Motion on an Orthant , 1981 .

[14]  Graham K. Rand,et al.  Logistics of Production and Inventory , 1995 .

[15]  J. Harrison,et al.  Brownian motion and stochastic flow systems , 1986 .

[16]  D. Iglehart,et al.  Multiple channel queues in heavy traffic. I , 1970, Advances in Applied Probability.

[17]  Viên Nguyen,et al.  Sequential Bottleneck Decomposition: An Approximation Method for Generalized Jackson Networks , 1994, Oper. Res..

[18]  S. Nahmias,et al.  Mathematical Models of Retailer Inventory Systems: A Review , 1993 .

[19]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[20]  Madan L. Puri,et al.  The space D , 1990 .

[21]  T. Williams Special products and uncertainty in production/inventory systems☆ , 1984 .

[22]  Sven Axsäter,et al.  Chapter 4 Continuous review policies for multi-level inventory systems with stochastic demand , 1993, Logistics of Production and Inventory.

[23]  J. Michael Harrison,et al.  Brownian models of multiclass queueing networks: Current status and open problems , 1993, Queueing Syst. Theory Appl..

[24]  S. Nahmias Demand estimation in lost sales inventory systems , 1994 .

[25]  J. Michael Harrison,et al.  Brownian Models of Queueing Networks with Heterogeneous Customer Populations , 1988 .