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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
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    File URL: http://dx.doi.org/10.1287/mnsc.36.7.822
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. repec:pal:jorsoc:v:60:y:2009:i:9:d:10.1057_palgrave.jors.2602655 is not listed on IDEAS
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. repec:pal:jorsoc:v:53:y:2002:i:11:d:10.1057_palgrave.jors.2601441 is not listed on IDEAS
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. repec:pal:jorsoc:v:55:y:2004:i:2:d:10.1057_palgrave.jors.2601675 is not listed on IDEAS
    17. 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.
    18. 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.
    19. 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.
    20. 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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