The cutoff transaction size and Gauss cost functions to the information value applying to the newsboy model

In this paper, two models are considered which differ in terms of information completeness. The first model involves the retailer having incomplete information regarding the state of customers demand. The second model involves the retailer having full information on the state of customers demand. Step function (here called Gauss function) can be applied such as the cost for mailing letters or packages in the post office and for shipping goods in containers. Therefore, the holding and penalty costs are represented by the Gauss functions to fit in with these practical situations. In addition, we assume that customers with an order larger than a prespecified quantity (here called cutoff transaction size) are still assumed to be satisfied in an alternative way, against additional cost. 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.