Novel MIP Formulation and Rule-Based Heuristics for the Simultaneous Lot Sizing and Scheduling Problem

This paper addresses production planning and control (PPC) at the operational level, focusing on the Simultaneous Lot-Sizing and Scheduling problem (SLSS). We introduce a new mixed-integer programming (MIP) formulation for the Multi-Level General Lot-Sizing and Scheduling Problem with Multiple Machines (MLGLSP_MM). The model incorporates sequence-dependent setups, setup carry-over, and production capacity constraints, while disallowing backlogs. To solve it, we propose two problem-specific heuristics, one rule-based and one greedy. These methods are evaluated on large-scale instances derived from a real-world case study in the agricultural tire industry. The results demonstrate significant improvements over commercial solvers in both solution quality and computation time, thereby confirming the effectiveness of the proposed approach and representing a substantial step toward the practical implementation of automation and optimization techniques in real-world industrial settings.