Hierarchical Controls in Stochastic Manufacturing Systems with Convex Costs
Journal of Optimizztion Theory and Applications, Vol. 80, No. 2, pp. 299-317, FEBRUARY 1994
19 Pages Posted: 21 Jun 2009 Last revised: 25 Jul 2017
Date Written: February 1994
This paper presents an extension of earlier research on heirarchical control of stochastic manufacturing systems with linear production costs. A new method is introduced to construct asymptotically optimal open-loop and feedback controls for manufacturing systems in which the rates of machine breakdown and repair are much larger than the rate of fluctuation in demand and rate of discounting of cost. This new approach allows us to carry out an asymptotic analysis on manufacturing systems with convex inventory/backlog and production costs as well as obtain error bound estimates for constructed open loop controls. Under appropriate conditions, an asymptotically optimal Lipschitz feedback control law is obtained.
Keywords: Stochastic manufacturing systems, convex production planning, hierarchical control, dynamic programming, viscosity solutions, convergence rates, error bounds
JEL Classification: M11, C61
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