Estimation of Inventory Re-Order Levels Using the Bootstrap Statistical Procedure

It can be difficult to set the reorder point in an inventory system because often one does not have much knowledge of the lead-time demand (LTD)distribution. A frequent practice is to assume a “standard” distribution, such as the Normal. The reorder point is then taken as the p-th fractile of that standard distribution, where (1 −p) is the specified probability of stockout during a replenishment cycle. When the desired service level p is high and the “true” LTD distribution is skewed, previous research has shown that the reorder point and inventory costs are strongly affected by the shape of the assumed LTD distribution. Ideally, no assumptions about this distribution should be necessary. One such “distribution-free” approach is the bootstrap procedure. Beginning with a single sample W = {x1x2,…,xn} of lead-time demand, the bootstrap repeatedly samples with replacement from W, A family of bootstrap samples of size n is thereby created, each sample furnishing an estimate Xp∗ of the p-th fractile of the LTD...

[1]  Graham K. Rand,et al.  Decision Systems for Inventory Management and Production Planning , 1979 .

[2]  Hon-Shiang Lau,et al.  The Use of Versatile Distribution Families in Some Stochastic Inventory Calculations , 1980 .

[3]  Edward A. Silver,et al.  Operations Research in Inventory Management: A Review and Critique , 1981, Oper. Res..

[4]  J. Mentzer,et al.  THE EFFECT OF THE ASSUMPTION OF NORMALITY ON INVENTORY CONTROL CUSTOMER SERVICE , 1985 .

[5]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[6]  Eliezer Naddor,et al.  Note---Sensitivity to Distributions in Inventory Systems , 1978 .

[7]  R. J. Mumford.  The Numerical Generation of Lead Time Demand Distributions for Inventory Models , 1977 .

[8]  Pandu R. Tadikamalla,et al.  A comparison of several approximations to the lead time demand distribution , 1984 .

[9]  D. W. Magson.  Stock Control When the Lead Time Cannot be Considered Constant , 1979 .

[10]  B. Efron.  The jackknife, the bootstrap, and other resampling plans , 1987 .

[11]  Robert Tibshirani,et al.  Bootstrap confidence intervals and bootstrap approximations , 1987 .

[12]  Hon-Shiang Lau,et al.  The Sensitivity of Inventory Decisions to the Shape of Lead Time-Demand Distribution , 1982 .

[13]  P. Diaconis,et al.  Computer-Intensive Methods in Statistics , 1983 .

[14]  P. G. Carlson,et al.  AN ALTERNATE MODEL FOR LEAD‐TIME DEMAND: CONTINUOUS‐REVIEW INVENTORY SYSTEMS , 1982 .

[15]  Shie-Shien Yang.  A Smooth Nonparametric Estimator of a Quantile Function , 1985 .

[16]  W. D. Kaigh.  Quantile interval estimation , 1983 .

[17]  Uttarayan Bagchi,et al.  MODELING DEMAND DURING LEAD TIME , 1984 .

[18]  Leonard Fortuin.  Erratum: Five Popular Probability Density Functions: A Comparison in the Field of Stock-Control Models , 1981 .

[19]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[20]  John F. Kottas,et al.  A Realistic Approach for Modeling Stochastic Lead Time Distributions , 1979 .

[21]  Fred R. McFadden.  ON LEAD TIME DEMAND DISTRIBUTIONS , 1972 .

[22]  K. Baken,et al.  An inventory model: What is the influence of the shape of the lead time demand distribution? , 1986, Z. Oper. Research.