Optimal order-limit policies for an (r, Q) inventory system

The reorder-point-reorder-quantity policies referred to as (r,Q) policies are widely used in industry and extensively studiedin the inventory literature. It should be noted, however, thatshortages often occur in practice even when the optimal reorderpoint and reorder quantity are achieved. In this paper, we presenta mathematical model to control a shortage period by an emergencyorder. The problem is the determination of the best timing todeliver items after a shortage occurs. By applying the conceptof repair-limit replacement policy in the context of maintenancetheory, the optimal order time limits based on three kinds ofcost criteria are derived in the framework of a simple (r, Q)inventory system. Finally, some examples of the inventory controlmodel with a stochastic lead time are given to explain the optimalorder-limit policies.     

Optimizing monitoring time in a continuous-review cyclic inventory system

This paper discusses a mathematical model for controlling amonitoring time by a sensing device in a continuous-review cyclicinventory system. The level of the inventory is monitored bythe sensor for a continuous period, whether the stock runs outor not. First, we consider the case where the lifetime of commoditiesis finite. It is shown that, under certain conditions, thereexists a finite and unique optimal monitoring time minimizingthe long-run average cost. Secondly, we discuss the case wherethe lifetime is infinite, with an appropriately modified restockingpolicy, and obtain an equation for the optimal monitoring timeunder milder conditions. Finally, some numerical examples arepresented, and sensitivity analyses for the optimal policiesare carried out.