An impulse control problem of a production model with interruptions to follow stochastic demand

The paper deals with the stochastic optimal intervention problem which arises in a production and storage system involving identical items. The requests for items arrive at random and the production of an item can be interrupted during production to meet the corresponding demand. The operational costs considered are due the stock/backlog, running costs and set up costs associated to interruptions and re-initializations. The process presents distinct behaviour on each of two disjoint identical subsets of the state space, and the state process can only be transferred from one subset to the other by interventions associated with interruptions/re-initializations. A characterization is given in terms of piecewise deterministic Markov process, which explores the aforementioned structure, and a method of solution with assured convergence, that does not require any special initialization, is provided. Additionally, under some conditions on the data, it is shown that the optimal policy is to produce the item completely in a certain region of the state space of low stock level