Optimization of Total Energy Consumption in Flexible Manufacturing Systems Using Weighted P-Timed Petri Nets and Dynamic Programming

Schedule optimization is crucial to reduce energy consumption of flexible manufacturing systems (FMSs) with shared resources and route flexibility. Based on the weighted p-timed Petri Net (WTPN) models of FMS, this paper considers a scheduling problem which minimizes both productive and idle energy consumption subjected to general production constraints. The considered problem is proven to be a nonconvex mixed integer nonlinear program (MINLP). A new reachability graph (RG)-based discrete dynamic programming (DP) approach is proposed for generating near energy-optimal schedules within adequate computational time. The nonconvex MINLP is sampled, and the reduced RG is constructed such that only reachable paths are retained for computation of the energy-optimal path. Each scheduling subproblem is linearized, and each optimal substructure is computed to store in a routing table. It is proven that the sampling-induced error is bounded, and this upper bound can be reduced by increasing the sampling frequency. Experiment results on an industrial stamping system show the effectiveness of our proposed scheduling method in terms of computational complexity and deviation from optimality.