In this work we propose an efficient dynamic programming approach for computing replenishment cycle policy parameters under non-stationary stochastic demand and service level constraints. The replenishment cycle policy is a popular inventory control policy typically employed for dampening planning instability. The approach proposed in this work achieves a significant computational efficiency and it can solve any relevant size instance in trivial time. Our method exploits the well known concept of state space relaxation. A filtering procedure and an augmenting procedure for the state space graph are proposed. Starting from a relaxed state space graph our method tries to remove provably suboptimal arcs and states (filtering) and then it tries to efficiently build up (augmenting) a reduced state space graph representing the original problem. Our experimental results show that the filtering procedure and the augmenting procedure often generate a small filtered state space graph, which can be easily processed using dynamic programming in order to produce a solution for the original problem.
- service-level constraints
- shortest-path problem
- lot-sizing problem
Rossi, R., Tarim, S. A., Hnich, B., & Prestwich, S. D. (2011). A State Space Augmentation Algorithm for the Replenishment Cycle Inventory Policy. International Journal of Production Economics, 133(1), 377-384. https://doi.org/10.1016/j.ijpe.2010.04.017