An exploration of models that minimize leadtime through batching of arrived orders

In the last decade interest in work-in-process inventory control has grown. Many papers deal with this topic by considering the manufacturing leadtime as the critical factor that determines the amount of work-in-process. Several authors studied the influence of a batching decision on the average manufacturing leadtime. To this end queueing models with batch arrivals and batch service times were analyzed. One of the underlying assumptions made in the analysis is that the arrival process of the batches can be approximated by a Poisson process for each choice of the batchsize. However, when the interarrival times of individual clients are negative exponentially distributed an Erlang distribution may be more appropriate as distribution of the interarrival time of the batches at the production unit. In this paper we consider the single item case. A very tractable analytical approximation for the average leadtime when batches arrive according to an Erlang distribution will be derived. Expressions for the optimal batchsize and the associated minimal leadtime are calculated and compared with experimental values obtained by simulation experiments. The approximation appears to be good. Finally, the huge differences in outcomes between Poisson and Erlang arrivals of the batches are highlighted.