A Continuous Review Model for an Inventory System with Two Supply Modes

In this paper we develop an approximate model of an inventory control system in which there exist two options for resupply, with one having a shorter lead time. Because the optimal policy appears to be extremely complex, we consider a reasonable extension of the standard (Q, R) policy to allow for two different lot sizes Q₁ and Q₂, and two different reorder levels, R₁ and R₂. Expressions for the expected on hand inventory and the expected backorders are developed and a procedure for determining the policy parameters is given. The model is validated by simulation, and calculations are included which compare the average annual cost with and without emergency ordering.