Stochastic dual dynamic programming approach for cash-flow inventory problems with overdraft

We examine a multi-product cash-flow inventory problem that accounts for lead times and uncertain demand. Our analysis includes a specific type of financing—overdrafts—where retailers facing cash constraints can leverage overdrafts to manage unexpected cash shortfalls. To address this issue, we propose a stochastic programming model and solve it using stochastic dual dynamic programming (SDDP). Additional auxiliary variables are introduced in the sub-problems to facilitate the construction of cuts in the presence of lead times. To enhance computational efficiency, we provide two techniques: removing the duplicate added constraints in the model and exploiting dual value similarities of the constraints across sub-problems. Numerical experiments demonstrate that SDDP can solve the problem with small optimality gaps compared to the values obtained from stochastic dynamic programming, and the proposed acceleration strategies significantly reduce computation time with minor impact on solution quality.