Integration optimization of factory production planning and joint replenishment in the supply chain considering uncertain lead time

This study introduces a mixed integer linear programming (MILP) optimization model for factory production planning and joint replenishment in a supply chain with dynamic demand variations, aiming to minimize transportation, inventory, and replenishment costs. The approach transforms the problem into a stochastic optimization model by combining the Monte Carlo Simulation (MCS) algorithm with the Sample Average Approximation (SAA) method, addressing the uncertainty of replenishment lead times at the distribution centers. Using the MCS and the Gurobi solver, the model is applied to real-world data from X Beverage Supply Company, demonstrating its effectiveness. Finally, the detailed production plans for each factory and refined replenishment strategies for distribution centers are obtained from the proposed optimization model. Additionally, a comparative analysis of scenarios with and without uncertain replenishment lead times is conducted, and out-of-sample experiments are performed to further validate the effectiveness and practicability of the proposed model and solution.