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 demand must be satisfied over the entire planning horizon. To provide additional flexibility, the model also incorporates outsourcing strategies as an alternative means of meeting demand. Another key aspect of the model is the consideration 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 the remainder are classified as scrap. In addition, machine processing times and setup times are assumed to be uncertain. By adopting a stochastic optimization approach, we develop a linear model that yields feasible and robust solutions against data fluctuations within a specified uncertainty set.
The objective function maximizes the total profit of the manufacturing system, defined as the difference between total revenue from product sales and overall system costs—including production, setup, inventory holding, shortage, scrap, and inter‑factory transportation costs. This is achieved while satisfying production capacity constraints, inventory balance, and material flow constraints across multiple factories.
To evaluate the performance of the proposed model, we first design a numerical example and compare its results with those obtained from deterministic and alternative stochastic approaches. Subsequently, a sensitivity analysis with respect to key parameters is conducted, which demonstrates 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 both deterministic and conventional stochastic models, especially under conditions of severe parameter uncertainty.