An application of robust control technique to manufacturing systems with uncertain processing time

Boukas, El‐Kébir; Shi, Peng; Agarwal, Ramesh K.

doi:10.1002/oca.677

Cited by 25 publications

(20 citation statements)

References 24 publications

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“…Rodrigues and Boukas [11] design a piecewise affine control law for a production system with deteriorating on-hand inventory and zero lead-time. In [12], a robust controller for the continuous system with uncertain processing time and delay in control is designed by minimizing an H ∞ -norm. However, the implementation of the strategy proposed in [12] requires numerical procedures for obtaining the control law parameters which limits its tractability at the analytical level.…”

Section: Introductionmentioning

confidence: 99%

Dead-beat and reaching-law-based sliding-mode control of perishable inventory systems

Ignaciuk¹,

Bartoszewicz²

2011

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. In this paper we consider the problem of efficient control of inventory systems with perishable goods. In the analyzed setting the deteriorating stock at a distribution center used to fulfill unknown, time-varying demand is replenished with delay from a supply source. The challenging issue is to achieve the high service level with minimum costs when the replenishment orders are procured with lead-time delay spanning multiple review periods. On the contrary to the typical heuristic approaches, we apply formal methodology based on discrete-time sliding-mode (SM) control. The proposed SM controller with the sliding plane selected for a dead-beat scheme ensures that the maximum service level is obtained in the system with arbitrary delay and any bounded demand pattern. In order to account for the supplier capacity limitations in the systems with input constraints, we also develop an alternative control strategy based on reaching law. Both controllers achieve a given service level with smaller holding costs and reduced order-to-demand variance ratio as compared to the classical order-up-to policy.

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Section: Introductionmentioning

confidence: 99%

Dead-beat and reaching-law-based sliding-mode control of perishable inventory systems

Ignaciuk¹,

Bartoszewicz²

2011

Bulletin of the Polish Academy of Sciences: Technical Sciences

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“…Therefore, using the principle of the mathematical induction, it may be concluded that inequalities (16) are satisfied for arbitrary k ≥ 0. This conclusion ends the proof.…”

Section: Sp-based Controllermentioning

confidence: 99%

“…The difficulty in developing suitable control schemes for decaying inventories [8][9][10], in particular in the systems with long delays and rapidly varying demand, typically enforces the use of heuristics, for example, [11]. Very few successful design examples using formal control-theoretic methodology either disregard demand uncertainty in establishing the analytical solution [12], neglect the effects of delay [13][14][15] or recur to the numerical procedures to obtain the controller parameters [16].…”

Section: Introductionmentioning

confidence: 99%

Discrete inventory control in systems with perishable goods – a time‐delay system perspective

Ignaciuk

2014

IET Control Theory & Applications

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This study considers the problem of providing efficient control of periodic-review production-inventory systems with perishable goods. The stock storage and replenishment is modelled as a first-order process with delay subject to external perturbations. The study investigates formally the classical delay compensation mechanisms used in inventory control and shows deficiencies of inventory position and Smith predictor-based concepts in the context of systems with deteriorating stock. Then, a new dead-time compensation mechanism is developed and non-linear control law synthesised. The proposed control scheme is proved robust with respect to arbitrary demand and delay variations.

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“…It should be noted that both the delay in quality control and the real demand rate cannot be characterized by a known probability distribution. Therefore, some assumptions used in the literature, such as discretization of the demand distribution into given values (Hu et al, 2004) or giving some specific form to the demand fluctuation (Boukas et al, 2000), cannot be used here. Moreover, the solution of the inventory control problem with uncertain processing delay given by Boukas et al (2000), which needs difficult calculations to solve some linear matrix inequalities, is not easily implementable to our case.…”

Section: Optimization Problem Formulationmentioning

confidence: 99%

Joint optimal lot sizing and production control policy in an unreliable and imperfect manufacturing system

Bouslah

Gharbi

Pellerin

2013

International Journal of Production Economics

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This paper deals with the problem of the joint determination of the optimal lot sizing and optimal production control policy for an unreliable and imperfect manufacturing system, where the quality control of lots produced is performed using an acceptance sampling plan. The proportion of defective items, the time between failures and the time to repair are generally distributed. The incurred total cost includes manufacturing cost, transportation cost, inspection costs, rejection cost of defective items, replacement cost for returned defective items from customers, and holding and backlog costs. The associated cost minimization problem is formulated with a stochastic dynamic programming model where the lot sizing and production rate are considered as decision variables. Given the difficulties in solving such a highly stochastic model analytically or numerically, we adopted a modified hedging point policy (HPP) to control the production rate, as well as an economic lot sizing policy for batch processing control; we also relied on a simulation-based experimental approach to determine a close approximation of the optimal control parameters. It is shown that production should be accelerated at the maximum production rate, not only when building the safety stock, as in the classical HPP, but also after rejecting a lot, in order to recuperate the loss in inventory and to maintain the on-hand safety stock. Numerical experiments and thorough sensitivity analyses are provided to illustrate the effectiveness of the proposed control policy and the robustness of the resolution approach. Some interesting behaviours regarding the impact of different parameters on the optimal decision variables are observed and discussed.

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An application of robust control technique to manufacturing systems with uncertain processing time

Cited by 25 publications

References 24 publications

Dead-beat and reaching-law-based sliding-mode control of perishable inventory systems

Dead-beat and reaching-law-based sliding-mode control of perishable inventory systems

Discrete inventory control in systems with perishable goods – a time‐delay system perspective

Joint optimal lot sizing and production control policy in an unreliable and imperfect manufacturing system

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