A two-factor stochastic production model with two time scales

• Published in: Automatica (Oxford) Vol. 37; no. 10; pp. 1505 - 1513
• Main Authors: Filar, J.A., Haurie, A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2001
• Subjects: Controlled diffusions; Manufacturing systems; Production systems; Singular perturbation; Stochastic control; Two time scales; Production systems; Controlled diffusions; Stochastic control; Two time scales; Singular perturbation; Manufacturing systems
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/S0005-1098(01)00123-6

A two-factor production model where one factor is characterized by a continuous state variable and corresponds to the fast mode via a controlled diffusion process, whereas the second factor is characterized by a discrete variable and corresponds to the slow mode via a controlled jump process. This paper deals with an hybrid stochastic control problem with singular perturbation. The problem is related to the general class of production and manufacturing flow control models. We propose in this paper a two-factor production model where one factor is characterized by a continuous state variable and corresponds to the fast mode of the system in the form of a controlled diffusion process, whereas the second production factor is characterized by a discrete variable and corresponds to the slow mode of the system in the form of a controlled jump process. We define the limit-control problem approximating the solution of the two-time-scale control problem when the time scale ratio tends to 0. We show convergence in a class of control feedbacks that can be approximated numerically. We implement a numerical technique, using approximating Markov chains and we observe the claimed convergence for the numerical solutions.