Approximating the EOQ with partial backordering at an exponential or rational rate by a constant or linearly changing rate

A significant extension of the classic EOQ model is the assumption that realized demand decreases if customers are forced to backorder. To capture the way this decrease depends on the waiting time, different functional forms have been proposed, ranging from the simple (e.g., constant or linear forms) to the complex (e.g., exponential or rational forms.) This paper explores the question of whether the computationally more tractable simple forms can give high quality approximations to the complex ones. We calculated average and worst case performance on a representative suite of test problems, each characterized by a “backorder resistance” parameter. We show that for low values of this parameter, results from the approximating functions are virtually as good as those from the correct ones, and for high values of the parameter, very good results can be achieved by using an iterative technique.