Improved convergence rate for a recursive procedure in a production and storage problem

Abstract

We study a stochastic optimal impulse control problem which arises in a production and storage system involving identical items and stochastic demand. The problem is posed in the class of piecewise deterministic Markov process and it can be solved by two successive approximation methods. The first uses an uniformly contraction operator that has identical end costs at demand arrival time and at completion of an item time. The other method proposed in this work uses an extension of this operator with different end costs at these times. We show that the second method yields a recursive procedure with faster convergence rate.