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Setting Base Stock Levels Using Product-Form Queueing Networks

Author

Listed:
  • Rodrigo Rubio

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Lawrence M. Wein

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

A manufacturing facility produces multiple products in a make-to-stock manner, and unsatisfied demand is backordered. A simple production control policy is analyzed: When the amount of work-in-process inventory plus finished goods inventory for a particular product falls below a base stock level, then release another unit of that product onto the shop floor. Assuming that the work-in-process inventory has a steady state distribution and that there are different costs incurred for carrying in-process, completed and backordered units, we show that the cost minimizing base stock level for each product is a critical fractile of the steady state distribution of the product's total work-in-process inventory. By exploiting the relationship between the make-to-stock system and an open queueing network, we identify specific formulas for the base stock levels under standard product-form assumptions. For the lost sales case, a similar relation to a closed queueing network can be used to characterize the optimal control parameters.

Suggested Citation

  • Rodrigo Rubio & Lawrence M. Wein, 1996. "Setting Base Stock Levels Using Product-Form Queueing Networks," Management Science, INFORMS, vol. 42(2), pages 259-268, February.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:2:p:259-268
    DOI: 10.1287/mnsc.42.2.259
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    Citations

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    Cited by:

    1. Nha-Nghi Cruz & Hans Daduna, 2019. "Optimal capacity allocation in a production–inventory system with base stock," Annals of Operations Research, Springer, vol. 277(2), pages 329-344, June.
    2. Bayindir, Z. Pelin & Erkip, Nesim & Gullu, Refik, 2003. "A model to evaluate inventory costs in a remanufacturing environment," International Journal of Production Economics, Elsevier, vol. 81(1), pages 597-607, January.
    3. René Caldentey & Lawrence M. Wein, 2006. "Revenue Management of a Make-to-Stock Queue," Operations Research, INFORMS, vol. 54(5), pages 859-875, October.
    4. Liberopoulos, George & Koukoumialos, Stelios, 2005. "Tradeoffs between base stock levels, numbers of kanbans, and planned supply lead times in production/inventory systems with advance demand information," International Journal of Production Economics, Elsevier, vol. 96(2), pages 213-232, May.
    5. Toktay, Latife Beril, 1970- & Wein, Lawrence A. & Zenios, Stefanos A., 1997. "Inventory management of remanufacturable products," Working papers WP 3965-97., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    6. Toktay, Latife Beril, 1970- & Wein, Lawrence M., 1999. "Analysis of a forecasting-production-inventory system with stationary demand," Working papers WP 4070-99., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. L. Beril Toktay & Lawrence M. Wein, 2001. "Analysis of a Forecasting-Production-Inventory System with Stationary Demand," Management Science, INFORMS, vol. 47(9), pages 1268-1281, September.
    8. René Caldentey & Lawrence M. Wein, 2003. "Analysis of a Decentralized Production-Inventory System," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 1-17, November.
    9. Saif Benjaafar & William L. Cooper & Joon-Seok Kim, 2005. "On the Benefits of Pooling in Production-Inventory Systems," Management Science, INFORMS, vol. 51(4), pages 548-565, April.
    10. Ganesh Janakiraman & Mahesh Nagarajan & Senthil Veeraraghavan, 2018. "Simple Policies for Managing Flexible Capacity," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 333-346, May.
    11. Apurva Jain & Kamran Moinzadeh, 2005. "A Supply Chain Model with Reverse Information Exchange," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 360-378, November.
    12. Apurva Jain, 2006. "Priority and dynamic scheduling in a make‐to‐stock queue with hyperexponential demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(5), pages 363-382, August.
    13. Ananth V. Iyer & Apurva Jain, 2004. "Modeling the Impact of Merging Capacity in Production-Inventory Systems," Management Science, INFORMS, vol. 50(8), pages 1082-1094, August.
    14. L. Beril Toktay & Lawrence M. Wein & Stefanos A. Zenios, 2000. "Inventory Management of Remanufacturable Products," Management Science, INFORMS, vol. 46(11), pages 1412-1426, November.
    15. Caldentey, René. & Wein, Lawrence M., 1999. "Analysis of decentralized production-inventory system," Working papers WP 4099-99., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    16. Sanajian, Nima & BalcIog[small tilde]lu, BarIs, 2009. "The impact of production time variability on make-to-stock queue performance," European Journal of Operational Research, Elsevier, vol. 194(3), pages 847-855, May.

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