Inventory control with multiple setup costs

We consider an infinite-horizon, periodic-review, single-item production/inventory system with random demand and backordering, where multiple setups are allowed in any period and a separate fixed cost is associated for each setup. Contrary to the majority of the literature on this topic, we do not restrict the order quantities to be integer multiples of the exogenously given batch size and instead allow the possibility of partial batches, in which case the fixed cost for ordering the batch is still fully charged. We build a model that particularly takes the batch-ordering cost structure into account. We introduce an alternative cost-accounting scheme to analyze the problem, which we use to develop a computationally efficient optimal solution method and several properties of the optimal solution. In addition, we propose two heuristic policies, both of which perform extremely well computationally.