On the newsboy model with a cutoff transaction size and concave holding and penalty cost functions

In this paper, we extend the expected inventory cost of Dekker et al. [6] by considering the concave holding and penalty cost functions to fit in with the most practical situations. Customers with an order larger than a prespecified cutoff transaction size are still assumed to be satisfied in an alternative way. Moreover, when the maximum demand is large, much more time may be required to determine the optimal solution. In addition, we establish a faster and useable new algorithm for considering Gauss function to determine the optimal order-up-to level S and the cutoff transaction size q systematically based on the Fibonacci and the Golden Section Search Technique.