Integrated planning and scheduling under production uncertainties: Bi-level model formulation and hybrid solution method

We propose a novel method for integrating planning and scheduling problems under production uncertainties. The integrated problem is formulated into a bi-level program. The planning problem is solved in the upper level, while the scheduling problems in the planning periods are solved under uncertainties in the lower level. The planning and scheduling problems are linked via service level constraints. To solve the integrated problem, a hybrid method is developed, which iterates between a mixed-integer linear programming solver for the planning problem and an agent-based reactive scheduling method. If the service level constraints are not met, a cutting plane constraint is generated by the agent-based scheduling method and appended to the planning problem which is solved to determine new production quantities. The hybrid method returns an optimality gap for validating the solution quality. The proposed method is demonstrated by two complicated problems which are solved efficiently with small gaps less than 1%.