A disturbance rejection approach in the control of production-distribution systems with uncertain demand

A class of production-distribution planning problems with non-stochastic uncertain demands is modeled as a dynamic game between two players controlling flows on a network with node and arc capacity constraints. Simple conditions are derived that have to be checked to determine which player wins the game. These conditions are then used to design a minimum cost network with the property that its feasible control strategies allow to meet the demand without violating the capacity constraints. The approach proposed in this paper offers a new framework to deal with production-distribution networks with uncertain demand, based on previous results concerning pursuit-evasion dynamic games. Although this approach (often referred to as set-theoretic control) is in general extremely heavy from a computational point of view, for special classes of systems, such as production-distribution networks, set-theoretic control offers an efficient and reliable way to solve the problem