Probabilistic Inventory Models

Abstract

This chapter attempts to capture variability of demand and lead times in inventory planning and incorporates the twin uncertainties in “just-in-case” inventory models to make these models more realistic. It is mathematically shown that these variabilities can be absorbed by having buffer stock or safety stock in addition to the average cycle stock. Lead time demand distribution approach is used to determine optimal buffer stock level for a desired “service level” using ABC-VED matrix. The higher the demand and/or lead time variability, the higher the buffer stock required for a stated service level desired. It has also been suggested to avoid the “99 percent” syndrome in insisting on 99 % service level for each item. Exchange curve analysis has also been briefly described to check if allocation of buffer stock across the entire organization is rational or otherwise. A generalized approach has been suggested using Laplace distribution for low turnover inventory and normal distribution for fast-moving items. For A class items (Q, R), policy is proposed with average demand rate taken as constant to determine EOQ. A periodic review inventory model under probabilistic demand for B class items is proposed by prescribing maximum stock level in (S _P, T). If (s, S) policy is chosen for Super A class item, then simulation models can be used for optimizing s, S, and T.