The Sizes of Simulation Samples Required to Compute Certain Inventory Characteristics with Stated Precision and Confidence

This study presents calculations of sample sizes, measured in number of simulated time periods, required to estimate certain parameters of selected inventory models with specified precision and confidence. In particular, the inventory models used include the classical zero procurement lead-time case, plus selected non-zero procurement lead-time cases having 2-, 5-, and 10-period lead-times. The parameters estimated are the mean number of shortages and of overages per time period, an overage being the amount of stock on hand at the end of the period, with negative amounts (or shortages) equated to zero. The calculations presented include the number of time periods to be sampled to produce estimates of mean shortages and overages per time period within approximately 100 per cent of the true value, with 95-per-cent confidence. These calculations were done for the procurement lead-time models described above, using 100 different inventory policies with each model, as defined by selected stock-control levels and reorder points. The underlying demand distribution was assumed to be exponential. From this brief study of sample sizes on comparatively simple inventory models, we find that over the range of conditions examined, the sample sizes required to estimate shortages per period and overages per period tend not to be excessive; that is, sample sizes of less than 100 are usually required to obtain the level of precision specified (a sample estimate within approximately 100 per cent of the true value) at a 95-per-cent confidence level.