Online job shop rescheduling with reaction-diffusion equation on a graph

The job-shop scheduling problem (JSSP) is one of the most difficult NP-hard combinatorial optimization problems. It is extremely difficult to solve the complex job shop scheduling problems because of the disturbances of manufacturing environment. This paper proposes a new method based on the reaction-diffusion equation on a graph [Yuasa, H and Ito, M (1998)] to solve JSSP with disturbances. This method considers the operations of JSSP as the autonomous decentralized system elements. According to the definition of the local potential functions between two operations (two operations on the same machine or the same job), the original schedule can be revised to accommodate with the disturbances of manufacturing, such as machine breakdown, processing time variation, in a short time. The present method is tested for benchmark problems with disturbances.