Inventory control with partial batch ordering

In an in¯nite-horizon, periodic-review, single-item production/inventory system with random demand and back-ordering, we study the feature of batch ordering, where a separate ¯xed cost is associated for each batch ordered. Contrary to majority of the literature on this topic, we do not restrict the order quantities to be integer multiples of the batch size and instead allow the possibility of partial batches, in which case the ¯xed cost for ordering the batch is still fully charged. We build a model that particu- larly takes the batch ordering cost structure into account. We introduce an alternative cost accounting scheme to analyze the problem, and we discuss several properties of the optimal solution. Based on the analysis of a single-period problem and a multi-period lower-bound problem, we study two heuristic policies for the original partial batch or- dering problem, both of which perform very well computationally for a wide range of problem parameters. Finally, we compare the performance of the optimal policy to the performance of the best full-batch-size ordering policy to quantify the value of partial ordering °exibility.