Analysis and algorithm for the stochastic control problem of a production/storage system

One of the simplest problems of optimal control of production rate in a production storage system is studied. A single type of item is produced to meet a random demand, and resources can be channeled either to production or to financial assets. Queuing or renewal theory approaches are not appropriate to deal with this problem, and it is best modeled by a piecewise deterministic Markov process as defined by M.H.A. Davis (1984). Optimal solutions are fully characterized by means of the Hamilton-Jacobi-Bellman equation, and an efficient algorithm is proposed for which a recursive procedure over the whole domain and an optimization test are performed in two distinct phases.< >