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Optimal Control Approaches to the Aggregate Production Planning Problem

Unidad Académica de Ingeniería Mecatrónica, Universidad Politécnica de Sinaloa, 82199 Mazatlán, Mexico
Industrial Engineering Department, Tecnológico de Monterrey, Campus Aguascalientes, 20328 Aguascalientes, Mexico
School of Sciences and Engineering, Tecnológico de Monterrey, Campus Monterrey, 64849 Monterrey, Mexico
Author to whom correspondence should be addressed.
Academic Editors: Tin-Chih Toly Chen and Marc A. Rosen
Sustainability 2015, 7(12), 16324-16339;
Received: 30 September 2015 / Revised: 19 November 2015 / Accepted: 2 December 2015 / Published: 10 December 2015
(This article belongs to the Special Issue Competitive and Sustainable Manufacturing in the Age of Globalization)
PDF [1255 KB, uploaded 10 December 2015]


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. View Full-Text
Keywords: aggregate production planning; capacity; inventory; optimal control; Hamiltonian-present value aggregate production planning; capacity; inventory; optimal control; Hamiltonian-present value

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Davizón, Y.A.; Martínez-Olvera, C.; Soto, R.; Hinojosa, C.; Espino-Román, P. Optimal Control Approaches to the Aggregate Production Planning Problem. Sustainability 2015, 7, 16324-16339.

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