Inventory control with partial batch ordering

Abstract

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