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

Chen, Y. F. and Disney, Stephen Michael ORCID: https://orcid.org/0000-0003-2505-9271 2007. The myopic Order-Up-To policy with a proportional feedback controller. International Journal of Production Research 45 (2) , pp. 351-368. 10.1080/00207540600579532

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Business (Including Economics) Research Institutes & Centres > Centre for Advanced Manufacturing Systems At Cardiff (CAMSAC)
Subjects:	H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management
Uncontrolled Keywords:	Bullwhip effect; Inventory; Order-Up-To policy; Control theory
Publisher:	Taylor & Francis
ISSN:	0020-7543
Date of First Compliant Deposit:	30 March 2016
Last Modified:	28 Nov 2024 13:15
URI:	https://orca.cardiff.ac.uk/id/eprint/42382

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