Bullwhip reduction for ARMA demand: The proportional order-up-to policy versus the full-state-feedback policy |
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Authors: | Gerard Gaalman [Author Vitae] |
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Affiliation: | Faculty of Management and Organization, Production Systems Design Department, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands |
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Abstract: | A ‘proportional’ order-up-to policy reacting to ARMA demand is analyzed using stochastic optimal control theory. This policy is compared with a full-state-feedback order-up-to policy. Necessary conditions for an optimum of a weighted sum of the inventory and the ordering variances for both policies are formulated. Based on this a relatively simple expression for the ‘full-state’ policy is derived. The comparison between the two policies demonstrates that the ‘intuitively’ designed proportional policy does not fulfill the objective of controlling both the inventory and ordering variance for all parameter values of the demand model as well as the full-state-feedback policy. The full-state-feedback policy outperforms the proportional policy in several aspects. |
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Keywords: | Bullwhip Order-up-to policy ARMA demand State space representation Stochastic optimal control |
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