The criterion for the optimal solution of an inventory system with a negative exponential crashing cost

In a recent paper, Ben-Daya and Raouf presented a continuous review inventory model in which they considered both lead time and order quantity as decision variables where the total crashing cost is denoted by a negative exponential function of the lead time. However, the solution procedure of Ben-Daya and Raouf has some drawbacks sometimes. The Newton–Raphson method with an appropriate starting point is used to improve that of Ben-Daya and Raouf. Numerical examples illustrate how the Newton–Raphson method works.