Scheduling of a class of partial routing FMS in uncertain environments with beam search

In this paper, incremental computation of schedules for complex discrete event systems in an uncertain environment is studied. Uncertainties are assumed to occur due to uncontrollable events. A particular class of flexible manufacturing systems (FMSs) with partial precedence constraints is proposed where some operations are performed with total precedence constraints and others with full routing flexibility (namely partial routing FMSs). Interruptions may occur due to unavailability of resources and interruption of operations. Such interruptions may deviate the trajectory from the planed schedule. For the modeling of the partial routing FMS, a systematic multi-level formalism based on the hierarchical structuration of the operations is introduced. Then, the risk of deviation is integrated and a new cost function is defined accordingly. Finally, a modified beam search algorithm referred to as generation double filtered beam search algorithm that accelerates the convergence of the method is proposed. The new algorithm is based on a new filtering mechanism that uses the cost function to selectively explore the state space of Petri net model in order to find a control sequence from an initial state to a reference one with a trade-off between performance and robustness. Examples are used to illustrate the efficiency of the proposed scheduling approach.