An ordering policy with allowable shortage and permissible delay in payments

It is common business practice to purchase inventory on an open account. Purchased inventory can be considered to be financed in whole or in part with permissible delay in payments. This paper develops a model to determine an optimal ordering policy under conditions of allowable shortage and permissible delay in payment and shows that the total annual variable cost function possesses some kinds of convexities. With those convexities, a theorem is presented to determine the optimal order quantity. Numerical examples are given to illustrate the theorem.