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Power Approximation for Computing (s, S) Policies Using Service Level

Author

Listed:
  • Helmut Schneider

    (Department of Quantitative Business Analysis, Louisiana State University, Baton Rouge, Louisiana 70803)

  • Jeffrey L. Ringuest

    (Operations and Strategic Management Department, Boston College, Chestnut Hill, Massachusetts 02167)

Abstract

The paper presents an analytic approximation for computing (s, S) policies for single items under periodic review with fixed ordering costs, linear holding costs and a service level requirement. The replenishment lead time is fixed and unfilled demand is backlogged. The approximation is similar to Ehrhardt's "Power Approximation." However, we do not assume the knowledge of shortage costs, which are difficult to estimate in practice. We define a \gamma -service level which measures the average backlog relative to the average demand. This quantity is easy to understand and frequently used in practice. The resulting power approximation policies are easy to compute and require only knowledge of the mean and variance of demand. Computational results show that the approximation gives a \gamma -service level which is within one percentage point of the required service level in most cases. Furthermore, the expected total costs of the approximation, taking into consideration a penalty cost for stockouts, are well within one percent of optimal.

Suggested Citation

  • Helmut Schneider & Jeffrey L. Ringuest, 1990. "Power Approximation for Computing (s, S) Policies Using Service Level," Management Science, INFORMS, vol. 36(7), pages 822-834, July.
    • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:7:p:822-834
    DOI: 10.1287/mnsc.36.7.822
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    Citations

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    Cited by:

    1. Noordhoek, Marije & Dullaert, Wout & Lai, David S.W. & de Leeuw, Sander, 2018. "A simulation–optimization approach for a service-constrained multi-echelon distribution network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 292-311.
    2. Strijbosch, L.W.G. & Moors, J.J.A., 1999. "Simple Expressions for Safety Factors in Inventory Control," Discussion Paper 1999-112, Tilburg University, Center for Economic Research.
    3. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
    4. E A Silver & H Naseraldin & D P Bischak, 2009. "Determining the reorder point and order-up-to-level in a periodic review system so as to achieve a desired fill rate and a desired average time between replenishments," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(9), pages 1244-1253, September.
    5. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "The Value of Information in an (R,s,Q) Inventory Model," Discussion Paper 1996-21, Tilburg University, Center for Economic Research.
    6. J J A Moors & L W G Strijbosch, 2002. "Exact fill rates for (R, s, S) inventory control with gamma distributed demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1268-1274, November.
    7. Alain Bensoussan & Qi Feng & Suresh P. Sethi, 2011. "Achieving a Long-Term Service Target with Periodic Demand Signals: A Newsvendor Framework," Manufacturing & Service Operations Management, INFORMS, vol. 13(1), pages 73-88, February.
    8. Kleijnen, J.P.C. & Wan, J., 2007. "Optimization of simulated systems : OptQuest and alternatives [also see “Simulation for the optimization of (s, S) inventory system with random lead times and a service level constraint by using Arena," Other publications TiSEM ffaee312-9f6a-4452-9ccc-9, Tilburg University, School of Economics and Management.
    9. Mario Guajardo & Mikael Rönnqvist & Ann Mari Halvorsen & Svein Inge Kallevik, 2015. "Inventory management of spare parts in an energy company," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(2), pages 331-341, February.
    10. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "On the (R,s,Q) Inventory Model when Demand is Modelled as a Compound Process," Other publications TiSEM 95c56aed-8108-4122-a689-5, Tilburg University, School of Economics and Management.
    11. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "On the (R,s,Q) Inventory Model when Demand is Modelled as a Compound Process," Discussion Paper 1996-11, Tilburg University, Center for Economic Research.
    12. Hu, Jason & Watson, Edward & Schneider, Helmut, 2005. "Approximate solutions for multi-location inventory systems with transshipments," International Journal of Production Economics, Elsevier, vol. 97(1), pages 31-43, July.
    13. Anne E. Lordahl & James H. Bookbinder, 1994. "Order‐statistic calculation, costs, and service in an (s, Q) inventory system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 81-97, February.
    14. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "The Value of Information in an (R,s,Q) Inventory Model," Other publications TiSEM 4b589d1f-2822-4c0f-9dea-6, Tilburg University, School of Economics and Management.
    15. van Donselaar, Karel H. & Broekmeulen, Rob A.C.M., 2012. "Approximations for the relative outdating of perishable products by combining stochastic modeling, simulation and regression modeling," International Journal of Production Economics, Elsevier, vol. 140(2), pages 660-669.
    16. Janssen, F.B.S.L.P., 1998. "Inventory management systems : Control and information issues," Other publications TiSEM 710d54d2-5447-4e2f-bb60-0, Tilburg University, School of Economics and Management.
    17. Janssen, Fred & Heuts, Ruud & de Kok, Ton, 1998. "On the (R, s, Q) inventory model when demand is modelled as a compound Bernoulli process," European Journal of Operational Research, Elsevier, vol. 104(3), pages 423-436, February.
    18. Saif, Ahmed & Elhedhli, Samir, 2016. "Cold supply chain design with environmental considerations: A simulation-optimization approach," European Journal of Operational Research, Elsevier, vol. 251(1), pages 274-287.
    19. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    20. Tamer Boyacı & Guillermo Gallego, 2002. "Managing waiting times of backordered demands in single‐stage (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 557-573, September.
    21. Zied Babai, M. & Syntetos, Aris A. & Teunter, Ruud, 2010. "On the empirical performance of (T, s, S) heuristics," European Journal of Operational Research, Elsevier, vol. 202(2), pages 466-472, April.
    22. B S Maddah & M Y Jaber & N E Abboud, 2004. "Periodic review (s, S) inventory model with permissible delay in payments," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 147-159, February.
    23. Chen, Frank Y. & Krass, Dmitry, 2001. "Inventory models with minimal service level constraints," European Journal of Operational Research, Elsevier, vol. 134(1), pages 120-140, October.
    24. van Donselaar, Karel H. & Broekmeulen, Rob A.C.M., 2013. "Determination of safety stocks in a lost sales inventory system with periodic review, positive lead-time, lot-sizing and a target fill rate," International Journal of Production Economics, Elsevier, vol. 143(2), pages 440-448.
    25. Dettenbach, Marcus & Thonemann, Ulrich W., 2015. "The value of real time yield information in multi-stage inventory systems – Exact and heuristic approaches," European Journal of Operational Research, Elsevier, vol. 240(1), pages 72-83.

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