Linear programming with stochastic processes as parameters as applied to production planning

In formulating stochastic programming with recourse models, the parameters of the linear programs are usually assumed to be random variables with known distributions. In this paper, the requirement vector parameter is assumed to be a stochastic process {ξi(t),t∈T,i=1,...,m∈. The properties of the deterministic equivalents for the cases of the discrete and continuous index set T are derived. The results of the paper are applied to a multi-item production planning model with continuous (periodic) review of the stock on hand of various items.