Hierarchical production controls in a stochastic two-machineflowshop with a finite internal buffer
Sethi, S.P.; Qing Zhang; Xun Yu Zhou
Robotics and Automation, IEEE Transactions on
Volume 13, Issue 1, Feb 1997 Page(s):1 - 13
Digital Object Identifier 10.1109/70.554343
Summary:This paper presents an asymptotic analysis of hierarchical
production planning in a manufacturing system with two tandem machines
that are subject to breakdown and repair. The system produces a single
product, whose rate of demand over time is given to be constant. The
problem is formulated as a continuous-time dynamic programming problem
in which the objective is to minimize the cost of production,
inventories, and backlogs. The size of the buffer between the two
machines is assumed to be finite. As the rates of change in machines'
states approach infinity, the analysis results in a limiting problem in
which the stochastic machine capacity is replaced by the average
capacity. The value function for the original problem is shown to
converge to the value function of the limiting problem. Both open-loop
and feedback controls for the original problem are constructed from
near-optimal controls of the limiting problem in a way which guarantees
their asymptotic optimality as the rates of changes in machines' states
become large in comparison to the discount rate. The convergence rate of
the value function for the original problem to that of the limiting
problem together with the error estimate for the constructed asymptotic
optimal controls are obtained. In addition, the constructed feedback
control is compared to the Kanban control policy for the stochastic
two-machine flowshop
View citation and abstract |
Cart
