A note on the newsboy model with a cutoff transaction size and Gauss holding and penalty cost functions

In recent papers, the inventory models were presented in which customers with an order larger than a prespecified cutoff transaction size are satisfied in an alternative way, against additional cost. They assumed the holding and penalty cost functions are linear functions. In this paper, the Gauss function can be applied such as the cost for mailing letters or packages in the post office. Therefore, we address a variant of the holding and penalty cost functions by considering the Gauss holding and penalty cost functions to fit in with the most practical situations. In addition, 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. Thus, we adopt and modify the algorithm of the Golden Section Search Technique to determine the optimal order-up-to level S and the cutoff transaction size q systematically and provide illustrative numerical example.