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

Hon‐Shiang Lau · Ahmed S. Zaki

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Supply Chain and Inventory Management Management and Optimization Techniques Logistics and Transportation Systems

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.

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References

1983Production and inventory management 1970Principles of Operations Research.1975Operations Research in Production Planning, Scheduling and Inventory Control.1971Principles of operations research 1980The Use of Versatile Distribution Families in Some Stochastic Inventory Calculations 1978Note—Sensitivity to Distributions in Inventory Systems 1976Approximate Solution to the (Q, r) Inventory Model for Gamma Lead Time Demand 1978Applications of the Weibull Distribution in Inventory Control

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2008Using the inventory-theoretic framework to determine cost-minimizing supply strategies in a stochastic setting 2003Nonrobustness of the normal approximation of lead‐time demand in a (Q, R) system 2007A SIMULATION OPTIMIZATION SOLUTION TO THE INVENTORY CONTINUOUS REVIEW PROBLEM WITH LOT SIZE DEPENDENT LEAD TIME 1987The effects of skewness and kurtosis of processing times in unpaced lines 1994A robust forecasting technique for inventory and leadtime management

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