Mathematical Optimization Models for Automated Calibration and Performance Consistency in Industrial Engineering Systems

Abstract

Industrial engineering systems depend on measuring instruments, sensors and actuators whose behavior drifts over time. Drift degrades the accuracy of process data, erodes product conformity and undermines the consistency of system performance. Calibration restores accuracy, but it consumes labor, equipment time and production capacity, and it is still commonly managed through fixed intervals and manual curve fitting. Using a three-phase methodology that combines an integrative synthesis of 96 sources published to date, conceptual model development and a computational experiment, this paper formulates calibration as an integrated mathematical optimization problem with two coupled layers. The first layer estimates calibration functions automatically through robust M-estimation, which limits the influence of outlying reference readings without manual screening. The second layer schedules calibration events across a population of instruments through a mixed-integer linear program (MILP) that minimizes calibration and downtime cost subject to drift tolerance, crew capacity and performance consistency constraints. Chance-constrained and robust counterparts are derived to handle uncertain drift rates, and a weighted multi-objective form exposes the trade-off between cost and measurement capability. A numerical study on a simulated plant with twelve instruments over a 52-week horizon shows that robust estimation reduced the root mean square curve error by 42 percent relative to ordinary least squares, and that the optimized schedule eliminated all tolerance violations while lowering total cost by 34 percent against a fixed 13-week policy and by 57 percent against a conservative fixed 8-week policy. The paper sets out theoretical, managerial and policy implications, states its limitations and proposes directions for future research. The framework offers a transparent and computationally tractable basis for automated calibration management in modern production environments.