Controlling chaos in a manufacturing system with two machines and two part-types based on the Hogg-Huberman strategy

This paper considers a resource allocation problem in a manufacturing system consisting of two machines and two types of parts. We introduce a discrete-time model of the system and examine stability and bifurcation phenomena. We show by computer simulation that chaotic behaviors are observed after successive occurrence of period-doubling bifurcations. It is also shown that the optimal state of the system is stabilized by a reward mechanism proposed by Hogg and Huberman (1991).