A demand independent inventory model

This paper is an extension of Deng et al. (2007) that was published in the European Journal of Operational Research. We have generalized their model from ramp type demand to arbitrary positive demand while theoretically discovering an important phenomenon: the optimal solution is actually independent of the demand as pointed out by Wou (2010), Hung (2011) and Lin (2011). We extend their inventory models in which the deteriorated rate is any non-negative function and backlog rate is inversely linearly related to the waiting time. Our findings will provide a new inventory system to help decision makers decide the optimal ordering quantity and replenishment policy.