Optimizing monitoring time in a continuous-review cyclic inventory system

This paper discusses a mathematical model for controlling a monitoring time by a sensing device in a continuous-review cyclic inventory system. The level of the inventory is monitored by the sensor for a continuous period, whether the stock runs out or not. First, we consider the case where the lifetime of commodities is finite. It is shown that, under certain conditions, there exists a finite and unique optimal monitoring time minimizing the long-run average cost. Secondly, we discuss the case where the lifetime is infinite, with an appropriately modified restocking policy, and obtain an equation for the optimal monitoring time under milder conditions. Finally, some numerical examples are presented, and sensitivity analyses for the optimal policies are carried out.