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In this paper, we develop an inventory model for non-instantaneous   deteriorating items under the consideration of the facts: deterioration rate   can be controlled by using the preservation technology (PT) during   deteriorating period, and holding cost and demand rate both are linear   function of time, which was treated as constant in most of the deteriorating   inventory models. So in this paper, we developed a deterministic inventory   model for non-instantaneous deteriorating items in which both demand rate and   holding cost are a linear function of time, deterioration rate is constant,   backlogging rate is variable and depend on the length of the next   replenishment, shortages are allowed and partially backlogged. The model is   solved analytically by minimizing the total cost of the inventory system. The   model can be applied to optimizing the total inventory cost of   non-instantaneous deteriorating items inventory for the business enterprises,   where the preservation technology is used to control the deterioration rate,   and demand & holding cost both are a linear function of time

Controllable deterioration rate for time-dependent demand and time-varying holding cost