The optimal cycle time for the economic production quantity inventory model under permissible delay in payments

Goyal (IAOR 32445) discusses the economic order quantity under conditions of permissible delay in payments. An implicit assumption of Goyal is that the items are obtained from an outside supplier. The entire lot size is delivered at the same time. If we wish to adopt all results obtained by Goyal, then we are effectively assuming that the replenishment rate is infinite. The main purpose of this paper is to extend Goyal to the case that the units are replenished at a finite rate. When replenishment rate approaches infinite, Goyal will be a special case of this paper.