Date on Master's Thesis/Doctoral Dissertation


Document Type

Master's Thesis

Degree Name



Industrial Engineering

Committee Chair

Bai, Lihui

Author's Keywords

Fill rate; Monte Carlo simulation; Base stock policy; Periodic review


Business logistics; Monte Carlo method


Fill rate is one of the most important measurements for inventory systems in the supply chain management. The primary goal of this thesis is to give a comprehensive review of existing analytical expressions for the system fill rate, and provide numerical comparison for all relevant expressions in terms of their accuracy against (simulated) fill rate from the Monte Carlo simulation. We prove relationships between several expressions. Although majority of the expressions discussed herein are designed for standard periodic review system, we conduct numerical simulations for the general periodic review system. Under this general periodic review setting, numerical results indicate that all else being equal, replenishment lead time has larger effect on the system's fill rate than does the review interval. In addition, numerical comparison suggests that Johnson et al.'s approach, Zhang and Zhang's approach, Hadley and Whitin's approach dominate the traditional approach, exponential approximation and Silver's modified approach. The dominance is especially true for cases with high demand variability. For general periodic review system, our numerical results indicate that scaling is necessary for Silver's modified, Johnson et al.'s and Johnson et al.'s modified approaches.