Improved solution process for inventory model with ramp-type demand under stock-dependent consumption rate

We use the smoothly connected property to simplify the solution process for inventory model with ramp-type demand under stock-dependent consumption rate. This article is a response to a complicated solution process of Wu et al. [“Retailer's optimal ordering policy for deteriorating items with ramp-type demand under stock-dependent consumption rate,” International Journal of Information and Management Sciences, 19, 245–262 (2008)]. They extended a minimum cost inventory model to a maximized profit problem and presented a detailed analysis for the solution procedure. However, their solution process may be too lengthy to involve many right but unnecessary results. In this article, we use the smooth connected property to dramatically simplify their solution structure. Our approach is also applied to minimum cost inventory models that were demonstrated by simplifying the paper of Deng et al. [“A note on the inventory models for deteriorating items with ramp type demand rate,” European Journal of Operational Research, 178, 112–120 (2007)]. Our findings will help ordinary readers to understand their important inventory models.