@article{Chen2007,
author = {Y.F. Chen and S.M. Disney},
title = {The myopic Order-Up-To policy with a proportional feedback controller},
journal = {International Journal of Production Research},
volume = {45},
number = {2},
pages = {351-368},
year  = {2007},
publisher = {Taylor & Francis},
doi = {10.1080/00207540600579532},
URL = {https://doi.org/10.1080/00207540600579532},
eprint = {https://doi.org/10.1080/00207540600579532},
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. }
}