Optimal Control Applications in the Study of Production Management

Abstract

A mathematical model for an economic problem of production management is proposed. The continuous optimal control problem is solved, by using the Pontryagin Maximum Principle at the level of a new space, called Lie algebroid. The controllability of the economic system is studied by using Lie geometric methods and involves restrictions on the final stock quantities. Finally, a numerical application is given.

Lie Geometric Methods in the Study of Driftless Control Affine Systems with Holonomic Distribution and Economic Applications

“…In addition, ẋ3 = u 1 x 2 + u 2 x 1 ≥ 0, and using x 3 (0) = 0, we obtain x 3 (t) ≥ 0. Some different mathematical models can be found in the papers [10,[12][13][14][15]. It results that the system ( 17) is a driftless control affine system on R 3 + , written in the following form:…”

“…In addition, a new approach to maximizing the profit in a stockdependent demand inventory model is presented in [9]. Otherwise, there are a multitude of papers that study the optimization of production and storage costs with various restrictions (see form instance, [10][11][12][13][14][15]).…”

“…In addition, some facts and methods of control theory treated from the geometric point of view are presented in [29]. The geometry of Lie algebroids is used in the study of distributional systems (driftless control afine system) in the papers [12,14,[30][31][32][33][34][35][36].…”

Archives of Control Sciences

“…Agrachev and Sachkov [1] studied the control theory from the geometric viewpoint. Also, Lie geometric methods and framework of Lie algebroids have been used by Popescu [22][23][24] in order to solve some problems involving inventory and production.…”