Optimum ordering policies with random lead times

This paper studies an optimum ordering policy for a single unit system with general life times and two kinds of orders (regular and emergency) with generally distributed lead times. The costs considered include salvage and observation costs along with shortage and reordering costs and an expression for cost effectiveness defined as (s-availability)/(s-expected cost rate), which balances the system effectiveness and the cost is derived. Two theorems regarding the existence of a finite and unique reordering time for regular orders maximizing the cost effectiveness are proved. For purpose of illustration numerical results are also obtained. © 1981.