The deterministic EOQ and EPQ with partial backordering at a rate that is linearly dependent on the time to delivery

Our original models for the EOQ and EPQ with partial backordering assumed that the backordering rate, β, is a constant. In this paper we extend those models to allow β to increase linearly as the time until delivery decreases. We show how those previous models can be adapted to find the optimal decision variable values for this new assumption and develop, for each model type, a condition that the initial value of β must meet for partial backordering to be optimal.