《2016 A Macro-Level Scheduling Method Using Lagrangian Relaxation》.pdf

70 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 17, NO. 1, FEBRUARY 2001 A Macro-Level Scheduling Method Using Lagrangian Relaxation Yuanhui Zhang, Peter B. Luh, Fellow, IEEE, Katsumi Narimatsu, Tetsuro Moriya, Tsuyoshi Shimada, and Lei Fang Abstract—In this paper, a macro-level scheduling method is Total number of resource types; developed to provide high-level planning support for factories with A set of resources required simultaneously for the pro- multiple coordinating cells. The key challenges are large problem cessing operation ; sizes, complicated product process plans, stringent cell coordi- nation requirements, and possible resource overload. To model Index of product from 1 to ; the problem with manageable complexity, detailed operations of Total number of products; a product within a cell are aggregated as a single operation whose The set of successor operations of operation ; processing time is related to the amount of resources allocated. Number of operations in product ; “Overload variables” are introduced and penalized in the objec- Index of time unit from 1 to ; tive function. The goal is to properly allocate resources, efficiently Total number of time units within the time horizon; handle complicated process plans, and coordinate cells to ensure on-time delivery, low working-in-process inventory, and small Capacity of resource at time unit ;