Abstract
Order-selection problems are usually modeled through 0-1 programming methods to find an optimal package of orders from among a large number of candidates. However, in many real world order-selection problems, the decision to accepto or reject an arriving order should be made promptly upon its arrival without waiting for the arrival of other orders over a long-term time horizon. It is known that the rate of retum method in single-dimensional problems and the effective gradient method in multi-dimensional problems can be used to solve these types of real world problems. These methods determine acceptance or rejection of an order of comparing its rate of return or effective gradient with a given specified criterion. Here, the problem is how to establish the criterion. This paper presents a simple and easy method for establishing an acceptance/rejection criterion using back-log inventory in long-term order-selection problems. The method is applicable to such complex problems in which the distribution of profitability of arriving candidate orders changes over a specified time horizon.
