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Hierarchical control of production with stochastic demand in manufacturing systems


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Ouaret, Samir, Kenné, Jean-Pierre and Gharbi, Ali. 2011. « Hierarchical control of production with stochastic demand in manufacturing systems ». Advanced Modeling and Optimization, vol. 13, nº 3. pp. 419-443.

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This paper addresses a stochastic optimal control problem for a reliable single-product manufacturing system with a finite capacity. The demand by customers is stochastic in a finite planning horizon, and is described by a known continuous function. A two-level hierarchical control model is developed. In the first level, a stochastic linear-quadratic optimal control problem is formulated to determine the target values of the state and control variables, with the variables being the desired inventory level and desired production rate, respectively. The goal of the second level is to maintain the inventory as close as possible to its desired level as well as to maintain the production rate as close as possible to its desired rate with fluctuating demand. This problem is represented as a recursive optimization control problem (predictive control) with one state variable (the inventory level) and one control variable (the production rate). The purpose of this study is to establish the optimal production control strategies satisfying a stochastic demand that minimizes the total average quadratic cost and the sum of the mean square deviations of inventory and production for the first and second levels, respectively. The solution is obtained by applying the stochastic optimal control principle based on Pontryagin’s maximum principle using the Euler-Maruyama scheme. A numerical example and sensitivity analyses are presented to illustrate the usefulness of the proposed approach.

Item Type: Peer reviewed article published in a journal
Kenné, Jean-Pierre
Gharbi, Ali
Affiliation: Génie mécanique, Génie de la production automatisée
Date Deposited: 16 Feb 2016 17:07
Last Modified: 11 Mar 2016 16:58

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