In this study, we consider an order promising problem at parallel machine shops where orders arrive dynamically. We develop methods for the problem, which instantly quote the due-dates of arrived orders. In this study, we first propose methods which can estimate flow times of orders, in which the current and future inventory status as well as the specific scheduling scheme used in the shop are taken into account, and then the due-dates are set by the order promising methods using the estimation results. The quoted due-dates of orders are compared with the actual completion times of those which are obtained from the simulation runs. The series of computational experiments show that the superior performance of the proposed methods in terms of the accuracy of due-date quotation.