Active schedule is one of the most basic and popular concepts in production scheduling research. For identical parallel machine scheduling with jobs＇ dynamic arrivals, the tight performance bounds of active schedules under the measurement of four popular objectives are respectively given in this paper. Similar analysis method and conclusions can be generalized to static identical parallel machine and single machine scheduling problem.
By considering the flow control of urban sewer networks to minimize the electricity consumption of pumping stations, a decomposition-coordination strategy for energy savings based on network community division is developed in this paper. A mathematical model characterizing the steady-state flow of urban sewer networks is first constructed, consisting of a set of algebraic equations with the structure transportation capacities captured as constraints. Since the sewer networks have no apparent natural hierarchical structure in general, it is very difficult to identify the clustered groups. A fast network division approach through calculating the betweenness of each edge is successfully applied to identify the groups and a sewer network with arbitrary configuration could be then decomposed into subnetworks. By integrating the coupling constraints of the subnetworks, the original problem is separated into N optimization subproblems in accordance with the network decomposition. Each subproblem is solved locally and the solutions to the subproblems are coordinated to form an appropriate global solution. Finally, an application to a specified large-scale sewer network is also investigated to demonstrate the validity of the proposed algorithm.
