A Robust Cycle-Based Policy for Inventory Management with Fixed Ordering Costs

We consider a single-installation, single-product inventory management problem with positive fixed ordering costs. We allow the unfulfilled demand to be either backlogged or lost and the lead time to be either zero or positive, and assume that the stochastic demand is correlated and information about the demand distribution is limited. A simple implication of non-negligible fixed ordering costs is that any viable inventory control policy implicitly divides the planning horizon into a sequence of {\em inventory cycles}, where an order is only placed at the beginning of the cycles. Building on this observation, we propose a new policy that manages inventory by directly selecting the order quantity and the cycle length for each cycle using robust optimization. Our cycle-based policy offers a simple and unified approach to solving the inventory problem, and we show that the policy decisions can be computed extremely efficiently by solving a small number of linear programs for all model instances (i.e., backlogging versus lost sales, zero lead time versus positive lead time). To the best of our knowledge, our policy is the first robust policy that can accommodate lost sales, and also the first linear programming-based robust policy that can handle positive fixed ordering costs. Results of extensive numerical experiments show that our policy outperforms several strong benchmark policies