Scheduling can be defined as the allocation of available resources over time while optimising a set of criteria like early completion time of task, holding inventory, etc. The complexity of the scheduling problem, already known to be high, increases if dynamic events and disruptions are considered. In addition, in production and logistics, designers of scheduling systems must consider sustainability-related expectations. This paper presents an energy-efficient scheduling and rescheduling method (named Green Rescheduling Method, GRM). GRM aims at the solving of the dynamic scheduling problem under the condition of a certain level of routing flexibility enabling the reassignment of tasks to new resources. The key performance indicators integrated into the proposed GRM are effectiveness and efficiency-oriented. Applications concern the domains of production and logistics. In order to assess the proposed approach, experimentations have been made and results illustrate the applicability of GRM to build efficient and effective scheduling and rescheduling both for flexible manufacturing systems and inventory distribution systems in a physical internet network. A mathematical formulation for flexible job shop problem with energy consumption is also proposed using mixed Integer programming to evaluate the performance of the predictive part of GRM.