Optimal Planning for Two-Stage Stochastic Industrial Systems

Many applied problems are related to resource distribution in stochastic systems [1–4]. The stochastic approach lets us pose optimal planning and control problems for a wide class of industrial systems characterized by taking into account the randomized character of changes in the characteristics of industrial processes and resources transformed by the system. In this work, we give a general setting of the general planning problem for two-stage stochastic industrial systems, construct a mathematical model, and pose in this model optimization planning problems with respect to the criteria of maximizing revenue, minimizing costs, maximizing profits, and maximizing unit revenue. Constraints in these problems include conditions on manufacturing planned products and lower bounds on the probability of their manufacturing. We propose a solution scheme for these problems that sequentially solves a number of special linear (fractional linear) programming problems. We show examples of two-stage industrial systems that can be formalized in our mathematical model. As examples, we consider planning systems for processing gas condensate into oil products, manufacturing printed circuits, and open hearth process of steel production.