The myopic Order-Up-To policy with a proportional feedback controller

The myopic Order-Up-To policy with a proportional feedback controller

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Article ID: iaor20072702
Country: United Kingdom
Volume: 45
Issue: 2
Start Page Number: 351
End Page Number: 368
Publication Date: Jan 2007
Journal: International Journal of Production Research
Authors: ,
Keywords: control
Abstract:

We develop a discrete control theory model of a myopic Order-Up-To (OUT) policy reacting to a stochastic demand pattern with Auto Regressive and Moving Average (ARMA) components. We show that the bullwhip effect arises with such a policy despite the fact that it is optimal when the ordering cost is linear. We then derive a set of z-transform transfer functions of a modified OUT policy that allows us to avoid the bullwhip problem by incorporating a proportional controller into the inventory position feedback loop. With this technique, the order variation can always be reduced to the same level as the demand variation. However, bullwhip-effect avoidance always comes at the cost of holding extra inventory. When the ordering cost is piece-wise linear and increasing, we compare the total cost per period under the two types of control policies: with and without bullwhip-effect reduction. Numerical examples reveal that the cost saving can be substantial if the order variance is reduced by using the proportional controller.

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