A Rolling Horizon Approach to Solve the Simultaneous Lot Sizing and Scheduling Problem

This paper proposes a method for production planning and control at the operational level, addressing the simultaneous lot-sizing and scheduling problem. It introduces a mixed-integer programming (MIP) formulation and a three-phase solution method for the multi-level generalized lot-sizing and scheduling problem in a multi-machine, multi-level, and multi-period setting. The model accounts for sequence-dependent setups, setup carry-over, and production capacity constraints, while not allowing backlogs. Although the proposed solution method is not yet scalable for solving large real-world instances involving the weekly demand for thousands of finished products, the algorithm demonstrates significant improvements over commercial solvers and remains practical for optimizing production planning in smaller instances, such as the bottleneck section of a production system.