This paper presents a multi-period, multi-product mixed-integer linear programming (MILP) model for production planning in a multi-factory environment with limited capacities, where customer demands must be satisfied over the planning horizon. In the proposed model, outsourcing strategies are also incorporated as an alternative means of meeting demand.
Another important aspect considered in the model is the presence of various types of potential failures in the production line. Some defective items can be repaired and sold as new products, some imperfect products are sellable at a reduced price, while others are classified as scrap. Moreover, machine processing times and setup times are assumed to be uncertain. By employing a stochastic optimization approach, a linear model is developed that provides feasible and robust solutions against data fluctuations within a specified uncertainty set.
The objective function aims to maximize the total profit of the manufacturing system, defined as the difference between total revenue from product sales and the overall system costs, including production, setup, inventory holding, shortage, scrap, and inter-factory transportation costs, while satisfying production capacity constraints, inventory balance, and material flow constraints across multiple factories.
To evaluate the performance of the proposed model, a numerical example is first designed, and the results are compared with those obtained from deterministic and stochastic approaches. Subsequently, a sensitivity analysis with respect to key parameters is conducted, demonstrating that the proposed model exhibits stable behavior under parameter variations. Finally, Monte Carlo simulation is employed for validation purposes, confirming the superior performance of the stochastic model compared to deterministic and conventional stochastic models, particularly under conditions of severe parameter uncertainty.