Efficient optimization of the Dual-Index policy using Markov Chain approximations

We consider the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster ‘emergency’ supply source. Unsatisfied demand is backordered and ordering decisions are made periodically. The optimal control policy for this type of system is known to be complex. For this reason we study a type of base-stock policy known as the Dual-Index policy as control mechanism for this inventory system. Under this policy ordering decisions are based on a regular and an emergency inventory position and their order-up-to-levels. In each period first an order is placed with the emergency supplier so that the emergency inventory position (onhand stock + outstanding orders arriving within the emergency lead time backorders) meets its order-up-to-level. Next a regular order is placed to raise the regular inventory position (on-hand stock + all outstanding orders backorders) to its order-up-to-level. Previous work on this type of policy assumes deterministic lead times and uses simulation to find the optimal order up to levels. We extend the policy to accommodate stochastic regular lead times and provide an approximate evaluation method so that optimization can be done without simulation. A numerical study shows that this approach yields excellent results for deterministic lead times and good results for stochastic lead-times. We also give managerial insights into the use of the model with deterministic lead-time, when in fact lead times are stochastic.