Multi-Item Inventory System Policies Using Statistical Estimates: Sporadic Demands (Variance/Mean = 9).

摘要

Although the inventory research literature typically assumes that the distribution of demand is exactly known, the designer of an actual inventory control system must, in reality, specify the demand distribution by means of statistically estimated parameters. Two previous studies have considered the performance of multi-item inventory control systems when knowledge of the underlying demand distribution is incomplete. In the simulation study by MacCormick (1974), the distributions used to generate demands were either poisson or negative binomial (variance/mean = 3). Estey and Kaufman (1975) then explored the impact of higher variance of demand on system performance by employing a negative binomial distribution with variance-to-mean ratio of 9. This report considers the situation in which there is a considerable probability of zero demand in any given period. The distribution used to generate these 'sporadic' demand sequences is a compound negative binomial. That is, the demand in a given period is characterized by a probability q of certain zero demand and probability 1-q that the demand is drawn from a negative binomial distribution. In particular, the simulation study that forms the basis for this report uses q = 0.25 and a negative binomial distribution, fitted so that the overall variance-to-mean ratio of the compound negative binomial distribution is 9. The statistical phenomena are studied employing computer simulation methods and time-series analyses. The study treats a wide range of parameter settings (mean and variance of demand, lead time, penalty cost, reorder cost), enabling extensive sensitivity testing to parameter choices.