An Approximate Dynamic-Programming Approach to the Joint Replenishment Problem

The main contribution of this paper is to propose a new dynamic-programming approach that epsilon-approximates the joint replenishment problem, with stationary demands and holding costs, in its discrete-time finite-horizon setting. Our first and foremost objective is to show that the computation time of classical dynamic-programming algorithms can be improved on by orders of magnitude when one is willing to lose an epsilon-factor in optimality. Based on synthesizing ideas such as commodity aggregation, approximate dynamic programming, and a few guessing tricks, we show that one can attain any required degree of accuracy in near-polynomial time.