REFORMULATION AND EVALUATION OF CLASSIC MILP MODELS FOR JUST-IN-TIME PARALLEL MACHINE SCHEDULING

Production scheduling directly affects the operational efficiency of manufacturing environments. From a Just-in-Time perspective, minimizing early and tardy deliveries -- measured by the Total Weighted Earliness-Tardiness (TWET) objective -- represents the ideal optimization scenario. This paper proposes the reformulation and computational evaluation of four exact mathematical models for the unrelated parallel machine scheduling problem : positional, general precedence, immediate precedence, and time-indexed. The research fills a gap in the literature by systematically analyzing the structural complexity and computational performance of these distinct modeling paradigms. Implemented in the Julia programming language utilizing the JuMP package, the models are tested against adapted benchmark instances to evaluate execution times and solver efficiency. Ultimately, the objective is to determine the computational tractability of each approach according to problem size, providing a rigorous analytical guide for selecting the most appropriate mathematical architecture for real-world production processes.