Newton–Raphson method for the expected present value of total inventory costs

We derive a simple expression for the expected present value of the total inventory costs. Then we show that the objective function is positive and concave up, so the unique critical point is indeed the absolute minimum point. Moreover, we ascertain that the Newton–Raphson method is suitable to locate the optimal solution. From the numerical examples, we know that the Newton–Raphson method is superior to the bisection algorithm. Finally, we point out the problem for choosing the threshold value in the bisection algorithm.