Numerical schemes and genetic algorithms for the optimal control of a continuous model of supply chains

Abstract In this paper, we consider supply chains modelled by partial and ordinary differential equations, for densities of parts on suppliers and queues among consecutive arcs, respectively. The considered numerical schemes, whose properties are discussed, foresee the upwind method for goods densities, described by conservation laws, and a Differential Quadrature based explicit formula for queues evolutions. An optimization scheme is also discussed, by considering a cost functional that, according to a pre-defined outflow, weights the queues through variations of processing velocities of suppliers. We get the minimization of the cost functional via a genetic algorithm, which uses mechanisms of selection, crossover and mutation for the processing velocities. An example application is discussed in light of the numerical approaches and the optimization procedure.