Inventory Control with Multiple Setup Costs

We consider an infinite-horizon, periodic-review, single-item production/inventory system with random demand and back-ordering, where multiple set-ups are allowed in any period, and a separate fixed cost is associated for each set-up. Contrary to 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 for developing 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.