The economic lot size of the integrated vendor–buyer inventory system derived without derivatives

In previous modellings of the vendor–buyer system, the buyer's economic order quantity and the vendor's optimal number of deliveries are derived by setting the first derivatives to zero and solving the simultaneous equations. The Hessian matrix of second derivatives is used to prove the convexity of the objective function. This procedure can be difficult for students who lack the background of differential calculus. This study develops algebraically the optimal policy of the integrated vendor–buyer inventory system without using differential calculus. A significant cost reduction is also achieved when Goyal's model is modified.