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The Power Approximation for Computing (s, S) Inventory Policies

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  • Richard Ehrhardt

    (University of North Carolina at Chapel Hill)

Abstract

In this paper we present a new analytic approximation for computing (s, S) policies for single items under periodic review with a set-up cost, linear holding and shortage costs, fixed replenishment lead time, and backlogging of unfilled demand. The approximation formulae are derived by using existing results of asymptotic renewal theory to characterize the behavior of the optimal policy numbers as functions of the model parameters. These functions are then used to construct regressions with coefficients that are calibrated by using a grid of 288 known optimal policies as data. The resulting Power Approximation policies (formulae) are easy to compute and. require for demand information only the mean and variance of demand over lead time. Extensive computational results show that the approximations yield expected total costs that typically are well within one percent of optimal. The approximation's robustness is exemplified by analyzing its performance when statistical estimates are used in place of the actual mean and variance of demand.

Suggested Citation

  • Richard Ehrhardt, 1979. "The Power Approximation for Computing (s, S) Inventory Policies," Management Science, INFORMS, vol. 25(8), pages 777-786, August.
  • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:8:p:777-786
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    File URL: http://dx.doi.org/10.1287/mnsc.25.8.777
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    Cited by:

    1. Nenes, George & Panagiotidou, Sofia & Tagaras, George, 2010. "Inventory management of multiple items with irregular demand: A case study," European Journal of Operational Research, Elsevier, vol. 205(2), pages 313-324, September.
    2. Andrew S. Caplin & Daniel F. Spulber, 1987. "Menu Costs and the Neutrality of Money," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 703-725.
    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. Bijvank, Marco & Bhulai, Sandjai & Tim Huh, Woonghee, 2015. "Parametric replenishment policies for inventory systems with lost sales and fixed order cost," European Journal of Operational Research, Elsevier, vol. 241(2), pages 381-390.
    5. 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.
    6. Vargas, Vicente & Metters, Richard, 2011. "A master production scheduling procedure for stochastic demand and rolling planning horizons," International Journal of Production Economics, Elsevier, vol. 132(2), pages 296-302, August.
    7. 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.
    8. Altay, Nezih & Litteral, Lewis A. & Rudisill, Frank, 2012. "Effects of correlation on intermittent demand forecasting and stock control," International Journal of Production Economics, Elsevier, vol. 135(1), pages 275-283.
    9. Diks, E. B. & de Kok, A. G. & Lagodimos, A. G., 1996. "Multi-echelon systems: A service measure perspective," European Journal of Operational Research, Elsevier, vol. 95(2), pages 241-263, December.
    10. Teunter, R.H. & Syntetos, A.A. & Babai, M.Z., 2010. "Determining order-up-to levels under periodic review for compound binomial (intermittent) demand," European Journal of Operational Research, Elsevier, vol. 203(3), pages 619-624, June.
    11. Kelle, Peter & Milne, Alistair, 1999. "The effect of (s, S) ordering policy on the supply chain," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 113-122, March.
    12. 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.
    13. Tarim, S. Armagan & Smith, Barbara M., 2008. "Constraint programming for computing non-stationary (R, S) inventory policies," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1004-1021, September.
    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. Pujawan, I Nyoman & Silver, Edward A., 2008. "Augmenting the lot sizing order quantity when demand is probabilistic," European Journal of Operational Research, Elsevier, vol. 188(3), pages 705-722, August.
    16. repec:pal:jorsoc:v:55:y:2004:i:2:d:10.1057_palgrave.jors.2601675 is not listed on IDEAS
    17. Chew, Ek Peng & Tang, Loon Ching, 1995. "Warehouse-retailer system with stochastic demands -- Non-identical retailer case," European Journal of Operational Research, Elsevier, vol. 82(1), pages 98-110, April.
    18. Rego, José Roberto do & Mesquita, Marco Aurélio de, 2015. "Demand forecasting and inventory control: A simulation study on automotive spare parts," International Journal of Production Economics, Elsevier, vol. 161(C), pages 1-16.
    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. Roman Kapuscinski & Sridhar Tayur, 1999. "Variance vs. Standard Deviation: Variability Reduction Through Operations Reversal," Management Science, INFORMS, vol. 45(5), pages 765-767, May.
    21. Baker, H. & Ehrhardt, R., 1995. "A dynamic inventory model with random replenishment quantities," Omega, Elsevier, vol. 23(1), pages 109-116, February.
    22. repec:pal:jorsoc:v:55:y:2004:i:9:d:10.1057_palgrave.jors.2601758 is not listed on IDEAS
    23. Lagodimos, A.G. & Christou, I.T. & Skouri, K., 2012. "Computing globally optimal (s,S,T) inventory policies," Omega, Elsevier, vol. 40(5), pages 660-671.

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    Keywords

    inventory/production: approximations;

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