Demand Management Based on Model Predictive Control Techniques

Davizón, Yasser A.; Soto, Rogelio; Rodríguez, José de J.; Rodríguez-Leal, Ernesto; Martínez-Olvera, César; Hinojosa, Carlos

doi:10.1155/2014/702642

Cited by 4 publications

(3 citation statements)

References 46 publications

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“…In general, a production system combines humans, machinery and equipment that are next to common material and information flow [23]. In a previous work [24], a PDE for production level subject to dynamic pricing and time, was presented, with the form:…”

Section: Infinite Dimensional Production Level Modelingmentioning

confidence: 99%

Mathematical Modeling for Infinite and Finite Dimensional Production-Inventory Systems Subject to Demand Fluctuation

Davizón,

Amillano-Cisneros,

Leyva Morales

et al. 2023

Preprint

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This research work aims to develop a mathematical modeling for production-inventory systems. Two mathematical models are present: An infinite dimensional, partial differential equation (PDE), production level modeling is present and a finite dimensional system for a coupled dynamic pricing, production rate and inventory level ordinary differential equations (ODE), integrating a proper Lyapunov stability analysis of the dynamical system and simulations.

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Section: Infinite Dimensional Production Level Modelingmentioning

confidence: 99%

Mathematical Modeling for Infinite and Finite Dimensional Production-Inventory Systems Subject to Demand Fluctuation

Davizón,

Amillano-Cisneros,

Leyva Morales

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In general, a production system combines humans, machinery, and equipment that are next to common material and information flow [31]. In [32], a PDE for the production level subject to dynamic pricing and time was presented with the form:…”

Section: Infinite Dimensional Product Level Modelingmentioning

confidence: 99%

Mathematical Modeling of Dynamic Supply Chains Subject to Demand Fluctuations

Davizon,

Amillano-Cisneros,

Leyva-Morales

et al. 2023

Eng. Technol. Appl. Sci. Res.

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This research work aims to develop the mathematical modeling for a class of dynamic supply chains. Demand fluctuation corresponds to product demand volatility, which increases or decreases over a given time frame. Industrial engineering practitioners should consider the function that applied mathematical modeling plays in providing approximations of solutions that may be used in simulations and technical implementations at the strategic, tactical, and operational levels of an organization. In order to achieve proper results, two mathematical models are presented in this paper: In addition to a finite-dimensional system of Ordinary Differential Equations (ODEs) for coupled dynamic pricing, production rate, and inventory level, which properly integrates Lyapunov stability analysis of the dynamical system and simulations, there is an infinite-dimensional Partial Differential Equation (PDE) production level modeling system available. Infinite and finite-dimensional systems incorporate a dynamic pricing approach in the mathematical modeling. The main research goal of this work is to explore the dynamic nature of supply chains applying PDE and ODE methods, with proper analytical analysis and simulations for both systems.

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“…Based on a previous work [51], and [52] which applies second-order differential equation analogizing production system with mechanical vibration systems, here the approach is to propose an energy based analogy to obtain the dynamic equation for APP in production-inventory systems. In order to develop a consistent energy based analogy for APP, the following energy based function for APP, where E APP is the total energy of the APP system which is proposed: …”

Section: Mathematical Modeling Of Appmentioning

confidence: 99%

Optimal Control Approaches to the Aggregate Production Planning Problem

Davizón¹,

Martínez-Olvera

Soto

et al. 2015

Sustainability

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Abstract:In the area of production planning and control, the aggregate production planning (APP) problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC) formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.

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Demand Management Based on Model Predictive Control Techniques

Cited by 4 publications

References 46 publications

Mathematical Modeling for Infinite and Finite Dimensional Production-Inventory Systems Subject to Demand Fluctuation

Mathematical Modeling for Infinite and Finite Dimensional Production-Inventory Systems Subject to Demand Fluctuation

Mathematical Modeling of Dynamic Supply Chains Subject to Demand Fluctuations

Optimal Control Approaches to the Aggregate Production Planning Problem

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