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Production and process management: An optimal control approach

This paper deals with a mathematical model in terms of ordinary differential equations (ODEs) that describe control of production and process arising in industrial engineering. The optimal control technique in the form of maximum principle, used to control the quality products in the operation processes, is applied to analyze the model. | Yugoslav Journal of Operations Research 26 (2016), Number 3, 331-342 DOI: 10.2298/YJOR141015008B PRODUCTION AND PROCESS MANAGEMENT: AN OPTIMAL CONTROL APPROACH Md. Haider Ali BISWAS Mathematics Discipline, Science Engineering and Technology School Khulna University, Bangladesh mhabiswas@yahoo.com Ahad ALI A. Leon Linton Department of Mechanical Engineering Lawrence Technological University Southfield, MI 48075, USA. aali@ltu.edu Received: October 2014 / Accepted: March 2016 Abstract: Optimal control and efficient management of industrial products are the key for sustainable development in industrial and process engineering. It is well-known that proper maintenance of process performance, ensuring the quality products after a long time operation of the system, is desirable in any industry. Nonlinear dynamical systems may play crucial role to appropriately design the model and obtain optimal control strategy in production and process management. This paper deals with a mathematical model in terms of ordinary differential equations (ODEs) that describe control of production and process arising in industrial engineering. The optimal control technique in the form of maximum principle, used to control the quality products in the operation processes, is applied to analyze the model. It is shown that the introduction of state constraint can be advantageous for obtaining good products during the longer operation process. We investigate the model numerically, using some known nonlinear optimal control solvers, and we present the simulation results to illustrate the significance of introducing state constraint onto the dynamics of the model. Keywords: Optimal Control, State Constraint, Production and Process, Industrial Engineering, Numerical Application. MSC: 49K15, 92D30. 332 H.A.Biswas, A.Ali / Production and Process 1. INTRODUCTION Optimal control theory has a long history in the literature for diverse applications in engineering science. There may have been some .