Optimal Job Selection and Scheduling in Hybrid Manufacturing Systems using Linear Programming and Sensitivity Analysis

Abstract

This study introduces an interpretable linear model for worker selection and scheduling in hybrid manufacturing that considers profitability, resource usage, and energy simultaneously in the same objective while respecting capacity, sequencing, and time bucket coupling constraints. By assigning tunable weights to selection rewards, use penalties, lateness penalties, and energy costs, the approach supports policy tunability and, through an explicit objective decomposition, reveals marginal effect of each component on the final plan. Empirical application to operational data indicates that such an equilibrium trade-off between value, completion, and delay control is possible, with temporal load staying in effective capacity; behavioral indicators within actual records also suggest a substantial relationship between delays, energy intensity, and machine availability variations. From a management viewpoint, the model offers an reproduceable low-cost decision basis well suited for sensitivity analysis, scenario planning in terms of capacity and energy policy alternatives, and periodic fine tuning to day-to-day fluctuations. Explainability allows integration with learning or metaheuristic elements where higher predictive power and scalability are needed while allowing transparent attributions from parameters to outcomes. Such established limitations as weight calibration dependency and unavoidable process dynamics approximations; yet, the model's expansibility provides for a realistic pathway towards incremental real-world data-driven refinement and establishes groundwork for future extensions, including coupling with learned estimators and more refined logistical constraints.