Computing Near-Optimal Policies in Generalized Joint Replenishment

We provide a practical methodology for solving the generalized joint replenishment (GJR) problem, based on a mathematical programming approach to approximate dynamic programming. We show how to automatically generate a value function approximation basis built upon piecewise-linear ridge functions, by developing and exploiting a theoretical connection with the problem of finding optimal cyclic schedules. We provide a variant of the algorithm that is effective in practice, and exploit the special structure of the GJR problem to provide a coherent, implementable framework.