A deterministic lot-size inventory model with shortages and a linear trend in demand

A single-item order-level lot-size-type inventory model is developed for items with a deterministic time-dependent demand. Shortages are allowed during the fixed finite planning horizon whose initial and final inventory levels are zero. A general inventory model is developed first and then an exact solution for the particular case of the linearly increasing demand rate is derived. An operating schedule for calculating the optimal solution is suggested. A numerical example is also given.