A control policy of an inventory system with compound Poisson demand

This papers deals with the problem of controlling the replenishment rates of a single item lost sales inventory system with compound Poisson demands and two types of reorders with varying order quantities. The replenishment rate for each of these orders can be chosen from a given set. The problem is to determine a decision rule that specifies the rates of these reorders as a function of the state of the system so as to minimize the long-run total expected cost rate. The optimal policy is computed using the linear programming algorithm and the results are illustrated numerically.