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: | Disney S.M., Chen Y.F. |
Keywords: | control |
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.