A macro-level scheduling method using Lagrangian relaxation

In this paper, a macro-level scheduling method is developed to provide high-level planning support for factories with multiple coordinating cells. To model the 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 resources allocated. "Overload variables" are introduced and penalized in the objective function. The goal is to properly allocate resources, efficiently handle complicated process plans, and coordinate cells to ensure on-time delivery, low working-in-process inventory, and small resource overload. The formulation obtained is "separable" and can be effectively decomposed by using Lagrangian relaxation. A combined backward and forward dynamic programming (BFDP) method is developed to solve a product sub-problem after a novel transformation of its process plan. The BFDP is further simplified and solved approximately.