Stochastic modelling and analysis: a computational approach
Stochastic modelling and analysis: a computational approach
Mathematics of Operations Research
An optimal stochastic production planning problem with randomly fluctuating dem and
SIAM Journal on Control and Optimization
Infinite horizon optimal control: theory and applications
Infinite horizon optimal control: theory and applications
A queueing model to analyze the value of centralized inventory information
Operations Research
Stochastic Optimal Control: The Discrete-Time Case
Stochastic Optimal Control: The Discrete-Time Case
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A control problem of a production system involving identical items is presented here. The requests for the items arrive at random, and operational costs are due to unsold items or non-supplied demand. The production rate of an item can be modified during production, and eventually the production can be interrupted, to meet the corresponding demand. This forms a Markov decision process in which one has to choose the production rate to minimize the expected value of a discounted cost. We rely on the structure of the model to provide a characterization of the optimal control, including the general qualitative behavior of solutions. Under some conditions on the data, we show that the optimal policy possesses a simple form. The model and the analysis also apply to a capacity expansion problem, and an extension to the production problem involving two types of items is pursued.