A macro-level scheduling method using Lagrangian relaxation

A macro-level scheduling method is developed to provide high-level planning support for factories with multiple coordinating cells. The key challenges are the large problem size, complicated product process plans, stringent cell coordination requirements and possible resource overload in view of the overtime and reserve resources. To model the scheduling problem with manageable complexity, detailed operations of a product within a cell are aggregated as a single operation whose processing time is related to the amount of resource allocated. “Overload variables” are introduced in the resource capacity constraints, and penalties are imposed for having overload. The goal is to properly allocate resources, efficiently handle complicated process plans, and well coordinate cells to ensure on-time delivery, low working-in-process inventory, and small resource overload. The formulation obtained is “separable” and can be efficiently solved by Lagrangian relaxation