Optimal Control of a Mean-Reverting Inventory

Abel Cadenillas (), Peter Lakner () and Michael Pinedo ()
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Abel Cadenillas: Department of Finance and Management Science, and Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Peter Lakner: Department of Information, Operations, and Management Sciences, Stern School of Business, New York University, New York, New York 10012
Michael Pinedo: Department of Information, Operations, and Management Sciences, Stern School of Business, New York University, New York, New York 10012

Operations Research, 2010, vol. 58, issue 6, 1697-1710

Abstract: Motivated by empirical observations, we assume that the inventory level of a company follows a mean-reverting process. The objective of the management is to keep this inventory level as close as possible to a given target; there is a running cost associated with the difference between the actual inventory level and the target. If inventory deviates too much from the target, management may perform an intervention in the form of either a purchase or a sale of an amount of the goods. There are fixed and proportional costs associated with each intervention. The objective of this paper is to find the optimal inventory levels at which interventions should be performed as well as the magnitudes of the interventions to minimize the total cost. We solve this problem by applying the theory of stochastic impulse control. Our analysis yields the optimal policy, which at times exhibits a behavior that is not intuitive.

Keywords: inventory/production; uncertainty; stochastic; probability; stochastic model applications (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (19)

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