Optimal Control Approaches to the Aggregate Production Planning Problem

Yasser A. Davizón, César Martínez-Olvera, Rogelio Soto, Carlos Hinojosa and Piero Espino-Román
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Yasser A. Davizón: Unidad Académica de Ingeniería Mecatrónica, Universidad Politécnica de Sinaloa, 82199 Mazatlán, Mexico
César Martínez-Olvera: Industrial Engineering Department, Tecnológico de Monterrey, Campus Aguascalientes, 20328 Aguascalientes, Mexico
Rogelio Soto: School of Sciences and Engineering, Tecnológico de Monterrey, Campus Monterrey, 64849 Monterrey, Mexico
Carlos Hinojosa: School of Sciences and Engineering, Tecnológico de Monterrey, Campus Monterrey, 64849 Monterrey, Mexico
Piero Espino-Román: Unidad Académica de Ingeniería Mecatrónica, Universidad Politécnica de Sinaloa, 82199 Mazatlán, Mexico

Sustainability, 2015, vol. 7, issue 12, 1-16

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.

Keywords: aggregate production planning; capacity; inventory; optimal control; Hamiltonian-present value (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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