Optimal Control Approaches to the Aggregate Production Planning Problem

Sustainability

Yasser A. Davizón³  César Martínez-Olvera²  Rogelio Soto¹  Carlos Hinojosa¹  Piero Espino-Román³  Tin-Chih Toly Chen⁴ 

[1] School of Sciences and Engineering, Tecnológico de Monterrey, Campus Monterrey, 64849 Monterrey, Mexico;Industrial Engineering Department, Tecnológico de Monterrey, Campus Aguascalientes, 20328 Aguascalientes, Mexico;Unidad Académica de Ingeniería Mecatrónica, Universidad Politécnica de Sinaloa, 82199 Mazatlán, Mexico;;Unidad Académica de Ingeniería Mecatrónica, Universidad Politécnica de Sinaloa, 82199 Mazatlán, Mexico

关键词: aggregate production planning;    capacity;    inventory;    optimal control;    Hamiltonian-present value;   

DOI  :  10.3390/su71215819

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.