Approximate solutions for a stochastic lot-sizing problem with partial customer-order information

We address a stochastic single item production system in a make-to-stock environment with partial knowledge on future demand resulting from customers ordering in advance of their actual needs. The problem consists of determining the optimal size of a production lot to replenish inventory, so that delivery promises are met on time at the expense of minimal average costs. For this problem an optimal policy is formulated. However, since the optimal policy is likely to be too complex in most practical situations, we present approximate strategies for obtaining production lot sizes. The well-known (R, S) inventory policy is compared to two rules where production decisions take into account the available information on future customer requirements and the probabilistic characterisation of orders yet to be placed. It is shown that the (8, S) inventory policy is a special case of one of the rules. An extensive numerical study reveals that the newly developed strategies outperform the classical ones.