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State space investigation of the bullwhip problem with ARMA(1,1) demand processes

Gaalman, Gerard and Disney, Stephen Michael 2006. State space investigation of the bullwhip problem with ARMA(1,1) demand processes. International Journal of Production Economics 104 (2) , pp. 327-339. 10.1016/j.ijpe.2006.05.001

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Using state space techniques we study a “myopic” order-up-to policy. The policy is myopic because it is optimal at minimising local inventory holding and shortage costs. In particular we study the bullwhip effect produced by the replenishment policy reacting to a stochastic ARMA(1,1) demand processes. We reveal that bullwhip is fundamentally caused by the co-variance between the inventory level and the demand forecast. We go on to highlight the impact of a simple control engineering inspired bullwhip reduction technique, a proportional controller in the inventory feedback loop. Although it can be shown this approach is always able to remove bullwhip, we expose that it is not possible to arbitrarily “tune” the proportional controller, without knowing in advance the likely structure of the demand process. We conclude with an investigation of trade-offs and optimisations in the order and inventory variance (and their sum) produced by our policy.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Business (Including Economics)
Centre for Advanced Manufacturing Systems At Cardiff (CAMSAC)
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management
H Social Sciences > HF Commerce
Uncontrolled Keywords: Order-up-to policy; Bullwhip effect; ARMA(1,1) demand process; State space representation
Publisher: Elsevier
ISSN: 0925-5273
Last Modified: 03 Mar 2020 02:32

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