Stochastic Inventory Management

Abstract: This bachelor thesis is about a stochastic inventory theory and how changes in different parameters affect the cost system. The inventory is based on a stochastic version of an economic quantity order (EOQ) model with planned shortages. For the deterministic EOQ-model with planned shortages there is a convenient formula for optimal order quantity $Q$ minimizing the cost per time unit. For the stochastic version an ($R$,$Q$)-policy is applied where $R$ is a reorder point such that if the inventory level is below $R$ and order is sent and the ordered products arrive after a lead time $L$. Since a formula for the stochastic inventory is not known, optimal choice of $Q$ is numerically obtained by simulations and compared with the optimal $Q$ for the deterministic EOQ with planned shortages. The demand is for simplicity described by a Poisson process. Since having a stochastic inventory model the basic mathematical EOQ formula is inadequate and is replaced with an approximate EOQ formula with planned shortages. By the simulations the accuracy of the EOQ model with planned shortages approximation is investigated and optimal values for some of the  parameters are obtained.