Mixed mathematical programming models for integrated production scheduling and resource management in smart manufacturing systems
Keywords:
Mixed integer programming, production scheduling, resource management, smart manufacturing, benders decomposition, multi-objective optimization, linearization.Abstract
Smart manufacturing plants are increasingly forced not to just schedule their production but rather to optimize schedules and dynamic physical resources, such as machines, automated guided vehicles, energy budgets, and labor, at the same time since separated optimization consistently produces longer makespan and higher energy costs. In this paper an integrated multi-objective Mixed Integer Linear Programming model is proposed that simultaneously assigns operations to machines, determines the sequence-specific setup timing, and allocates resources with respect to the constraints on peak-power and connectivity in order to minimize the total makespan, total tardiness, and energy costs. For this purpose, bilinearity of resource consumption terms and nonlinear energy functions are linearized by utilizing McCormick envelopes and piecewise-linear approximation transforming the original Mixed Integer Nonlinear Programming problem to a solvable linear task. Then, Benders decomposition is applied separating the main scheduling problem from the resource allocation subtask and state-of-the-art matheuristic combining variable neighborhood search and linear programming seeded initialization is devised for solving large-scale problems which are impossible to solve exactly. The numerical experiments conducted on the basis of small, medium, and large-scale industrial problems (with the number of jobs from 10 to 120) have shown that the integrated model produces 18.6%, 27.4%, and 21.9% lower makespan, total tardiness, and energy cost than the traditional just-scheduling-and allocating processes. Benders decomposition algorithm allows to keep the optimality gap smaller than 3.1% and decrease calculation time up to 93.5% in comparison to direct solving large-scale industrial problems and sensitivity analysis confirms advantages of the integrated model for various degrees of resource constrains. These results confirm that jointly optimizing scheduling and resource management within a unified mixed programming formulation yields substantial, quantifiable operational gains for smart manufacturing systems while remaining computationally tractable at industrial scale.
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