Linear quadratic Gaussian problem with constraints applied to aggregated production planning

Filho, Oscar Salviano Silva

doi:10.1109/acc.2001.945914

Cited by 8 publications

(6 citation statements)

References 6 publications

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“…The generalized HMMS problem with imperfect information of inventory system follows the formulation defined in [10]. It is characterized by the optimal inventory, production and workforce policy that must be provided by the solution of the following state space problem: …”

Section: A the Classical Hmms Problem In A Space-state Patternmentioning

confidence: 99%

“…Based on above, Silva Filho [10] showed that it is possible to extend the unconstrained HMMS model in order to include explicit constraints on inventory and production variables, which are perfectly observed over the time periods. It is worth making clear that the constrained HMMS model is a generalization of the classical HMMS model.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the idea is to show that it is possible to deal with the constrained state-space HMMS model (see [10]) under hypothesis of imperfect observation of the inventory levels. Thus, the stochastic problem discussed here can be described as a constrained Linear Quadratic Gaussian problem under imperfect information of states of the system.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Production Planning Problem under Unobserved Inventory System

Filho

2007

2007 American Control Conference

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In this paper, an aggregate inventory, production, and workforce planning problem is formulated as a constrained stochastic linear quadratic problem under hypothesis of imperfect information of the inventory system. This stochastic problem generalizes the classical unconstrained production planning model developed by Holt, Modigliani, Muth and Simon, and known as HMMS model. Using the Kalman filter device, the conditional mean and covariance of the inventory variable can be estimated, and, as an immediate result, the certainty equivalence principle can be applied to transform the stochastic problem in an equivalent deterministic problem, which is easier to be solved then the original one. It proceeds then that, such an equivalent problem can be solved through a sub-optimal heuristics, known as Open-Loop Updating (OLU) procedure. At last, from a simple example, it is shown that the optimal OLU policy allows the manager to get insights about the use of the aggregate resources of the company.

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Section: A the Classical Hmms Problem In A Space-state Patternmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic Production Planning Problem under Unobserved Inventory System

Filho

2007

2007 American Control Conference

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“…Besides, it allows that the solution of the problem can be revised periodically. For production application, this means that the aggregated plan must be constantly revised; as a consequence, managerial insights about the dynamic of production environment can be improved, see Silva Filho (2001) and Silva Filho and Ventura (1999).…”

Section: Introductionmentioning

confidence: 99%

A Constrained Stochastic Production Planning Problem With Imperfect Information of Inventory

Filho

2005

IFAC Proceedings Volumes

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Abstract:In this paper, an aggregate production planning problem is formulated as a chance-constrained stochastic control problem under imperfect information of states (i.e., the inventory levels). Using the Kalman filter device, the mean and covariance of state variables are estimated. Then the certainty equivalence principle is applied, resulting in a deterministic problem that is equivalent to the original formulation. In order to provide a sequential optimal solution to the equivalent problem, the Naive Feedback Controller (NFC) approach is used. It provides a revised sub-optimal production policy to the stochastic problem. An example illustrates the applicability of this approach. Copyright@2005 IFAC

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“…The certainty equivalent principle is the approach used among this transformation: thanks to the linearity of the model and assuming that the demand's variation can be described by a Gaussian Process, we set the variables equal to their means ( [27,28]). We remind that the inventory variable I k is strongly affected by the demand, which made it a stochastic variable.…”

Section: Deterministic Transformationmentioning

confidence: 99%

Jointly Production and Correlated Maintenance Optimization for Parallel Leased Machines

2017

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This paper deals with a preventive maintenance strategy optimization correlated to production for a manufacturing system made by several parallel machines under lease contract. In order to minimize the total cost of production and maintenance by reducing the production system interruptions due to maintenance activities, a correlated group preventive maintenance policy is developed using the gravity center approach (GCA). The aim of this study is to determine an economical production plan and an optimal group preventive maintenance interval T n at which all machines are maintained simultaneously. An analytical correlation between failure rate of machines and production level is considered and the impact of the preventive maintenance policy on the production plan is studied. Finally, the proposed maintenance policy GPM is compared with an individual simple strategy approach IPM in order to illustrate its efficiency.

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Linear quadratic Gaussian problem with constraints applied to aggregated production planning

Cited by 8 publications

References 6 publications

Stochastic Production Planning Problem under Unobserved Inventory System

Stochastic Production Planning Problem under Unobserved Inventory System

A Constrained Stochastic Production Planning Problem With Imperfect Information of Inventory

Jointly Production and Correlated Maintenance Optimization for Parallel Leased Machines

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