Optimal Control Approaches to the Aggregate Production Planning Problem

Abstract

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.

Competitive and Sustainable Manufacturing in the Age of Globalization

“…However, the existing models, either static or dynamic, have several shortcomings. To overcome these, Davizón et al [32] formulated a mathematical model to achieve optimal control. The mathematical model integrates a second-order dynamical system with a first-order system by considering the production rate, inventory level, capacity, and costs of the work force.…”

A multi-criteria decision analysis to include environmental, social, and cultural issues in the sustainable aggregate production plans

“…We observe that optimization and mathematical models deserve further discussion in terms of sustainability considerations since they are practically implementable for real-world problems (Davizón et al, 2015). The modification of traditional models by considering the requirements of sustainability is argued to be very important (Türkay, 2008;Benjaafar et al, 2013).…”

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

“…In [25] a dynamic production-inventory system is presented via optimal control theory. For mathematical modeling purposes an extension, of this previous work is present here, considering dynamic pricing and time delayed effects.…”