The Sensitivity of Inventory Decisions to the Shape of Lead Time-Demand Distribution

Abstract This paper studies the effects of the shape of the lead-time-demand (ltd) distribution on some basic inventory decisions. We found that the shape of the ltd distribution significantly affects the reorder point, stock-out risk, and expected lost sales of an inventory item. In the continuous-review(Q, R) model, the shape of the ltd distribution significantly affects the shortage cost component of the cost function; however, in most inventory systems, the shortage cost component accounts for a very small proportion of the system's total cost. Therefore the shape of the ltd distribution has little effect on the optimum (Q, R) solutions. We then discuss the implications of these findings.

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

[2]  Chandrasekhar Das,et al.  Approximate Solution to the Q, r Inventory Model for Gamma Lead Time Demand , 1976 .

[3]  K. Pearson.  Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material , 1895 .

[4]  Stuart Jay Deutsch,et al.  A Versatile Four Parameter Family of Probability Distributions Suitable for Simulation , 1977 .

[5]  Pandu R. Tadikamalla.  The lognormal approximation to the lead time demand in inventory control , 1979 .

[6]  L. Zurich,et al.  Operations Research in Production Planning, Scheduling, and Inventory Control , 1974 .

[7]  Patrick Rivett,et al.  Principles of Operations Research , 1972 .

[8]  J. M. Norman,et al.  A Table for Determining the Probability of a Stock out and Potential Lost Sales for a Gamma Distributed Demand , 1976 .

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

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

[11]  E. S. Pearson.  Biometrika tables for statisticians , 1967 .

[12]  N. L. Johnson,et al.  Table of percentage points of Pearson curves, for given √β1 and β2, expressed in standard measure , 1963 .

[13]  L. R. Shenton,et al.  Approximate percentage points for Pearson distributions , 1979 .

[14]  Inventory control with gamma demand and gamma lead times , 1975 .

[15]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[16]  N. L. Johnson,et al.  Systems of Frequency Curves , 1969 .

[17]  Chandrasekhar Das.  Some Aids for Lot-Size Inventory Control under Normal Lead Time Demand , 1975 .

[18]  Pandu R. Tadikamalla.  Applications of the Weibull Distribution in Inventory Control , 1978 .

[19]  Bruce W. Schmeiser,et al.  Methods for modelling and generating probabilistic components in digital computer simulation when the standard distributions are not adequate: A survey , 1977, WSC '77.

[20]  L. R. Shenton,et al.  Further approximate pearson percentage points and Cornish-Fisher , 1979 .