An optimal supply policy for time depending demand and deterioration with partial exponential backlogging.

We extend the inventory lot-size model in this paper to allow for products to deteriorate at variable rates, and demand is characterized by any log concave function of time that fulfils relatively mild criteria. Partial backlogging is possible with this model. The backlogging rate is a time-dependent, exponentially declining function provided by a parameter. We show that not only does the optimal replacement schedule exist, but that it is also unique. We also show that the inventory system's overall cost is a convex function of the number of replenishments. As a result, identifying a local minimum simplifies the search for the best number of replenishments. Finally, a numerical example is given to demonstrate the findings. [ABSTRACT FROM AUTHOR]