In recent years, the inventory model for deteriorating items gets the focus of many researchers. Deteriorating items having more importance due to high margin which also results in high loss associated with them. In real life, deterioration is a natural phenomenon that can be defined as a process of becoming impaired or inferior in quality from being used for its original purpose. It is quite essential for the consideration of the deterioration rate in the analysis of items like fruits, vegetables, perfumes, pharmaceutical, radioactive substances etc.. With a view to address this research problem and provide pragmatic solutions on offer, several inventory models have been developed in the past.
In this paper, we have developed an inventory model with time-dependent deterioration rate, shortage allowed with partial backlogging presuming trapezoidal type demand function with infinite replenishment. Three phases of the trapezoidal demand function has been adopted with three different price and time-dependent demand functions. During the shortage, the number of customer decrease as waiting time increases. The graphical analysis approach used to show the concavity of profit function with respect to decision variables. Trapezoidal type demand function consists of three stages, in the first stage demand increases then it reached saturation in the second stage in last demand rate decreases. This demand pattern is commonly observed in fruits, vegetables, seafoods items etc.