An Order-Level-Scheduling-Period System with Lost Sales

An order-level-scheduling-period system with lost sales is considered. The zero leadtime case is analyzed first and a method for computing the total average cost is presented. The nonzero leadtime case is then treated for a scheduling period of one time unit. The average cost for this case depends on the distribution of the inventory available on hand. This random variable, on-hand inventory, is denoted by Q and its distribution is given by g(Q). Methodologies are presented for finding this distribution for any leadtime L. A comparison of the Markov chain approach and the direct solution approach for finding g(Q) is also given.