Numerical Validation of Fill Rate Estimation Methods for Two- and Three-Demand Class Rationing Policies with One-for-One Replenishment and General Lead Time Distributions
Vicil, Oguzhan; Jackson, Peter
In this report, we conduct numerical simulations of two- and three-demand class inventory threshold rationing systems under one-for-one replenishment policies. The performance metrics of interest are the fill rates of the high priority demand classes (the gold fill rate in the two demand class system and the platinum and gold fill rates in the three-demand class system). Our main interest is in the sensitivity of these fill rates to the form of the replenishment lead time probability distribution and the resulting quality of approximation methods used to estimate these fill rates. We consider three approximation methods: what we call the single cycle approach attributed to Dekker et al and Deshpande et al, the embedded Markov chain approach of Fadigloglu and Bulut, and the continuous time Markov chain approach of Vicil and Jackson. We confirm the superiority of the embedded Markov chain approach for the case of constant lead times but we find that the fill rates are relatively insensitive to the form of the lead time distribution and both latter approaches, the embedded Markov chain approach and the continuous time Markov chain approach, perform well over wide ranges of lead time variability. For the three-demand class system, we demonstrate that it is possible to achieve highly differentiated fill rates by demand class and show that these fill rates can be estimated with high accuracy using the continuous time Markov chain approach, provided the fill rate of the lowest priority demand class (the silver fill rate) is not too low.
inventory management; allocation policies; continuous-time Markov processes; threshold policies; multiple demand classes