A Note on Minimax Mixture of Distributions Free Procedure for Inventory Model with Variable Lead Time

In recent papers, Moon and Choi (1998) and Hariga and Ben-Daya (1999)considered a continuous review inventory model with a mixture of backordersand lost sales in which the lead time, the order quantity, and the reorder pointare decision variables was studied. Moreover, they also develop a minimaxdistribution free procedure for the problem. While the demands of differentcustomers are not identical in the lead time, then we can't only use a singledistribution (such as Moon & Choi (1998) and Hariga & Ben-Daya (1999))to describe the demand of the lead time. Hence, we correct and extend the modelof Moon and Choi (1998) and Hariga and Ben-Daya (1999) by considering thelead time demand with the mixture of distributions. In addition, we also applythe minimax mixture of distributions free approach to the model by simultaneouslyoptimizing the order quantity, the reorder point, and the lead time to devise a practical procedure which can be used without specific information on demand distribution.     

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, we also assume that 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.