A simple heuristic for computing non-stationary inventory policies based on function approximation

We consider a finite-horizon periodic-review inventory system with fixed replenishment costs that faces non-stationary demands. The structure of the optimal control policy for this system has long been known. However, finding optimal policy parameters requires solving a large-scale stochastic dynamic program. To circumvent this, we devise a recursion-free approximation for the cost function of the problem. This translates into an efficient and effective heuristic to compute policy parameters that significantly outperforms earlier heuristics. Our approach is easy-to-understand and easy-to-use as it follows by elementary methods of shortest paths and convex minimization.