Cost-effective ordering policies for inventory systems with emergency order

Most of the studies on inventory control reported in earlier contributions deal with the optimization problems minimizing an expected cost criterion such as the long-run average cost. However, when the plant engineers design the inventory systems in practical situations, they must take account of reliability into the inventory system as well as economical aspect, where reliability can be defined as the probability that the stock is not depleted until a pre-specified time. In this paper, we discuss the inventory control policies that provide a balance between economical and reliability requirements. By applying the cost effectiveness criterion, which simultaneously includes the effects of system availability and expected cost, as optimality one, we derive the optimal inventory replenishment policies of two kinds of inventory models. Finally, with a set of numerical examples, we show that the optimal inventory policies of the models under consideration make the stationary availability increase.