An analytical solution procedure for a batch production system under a linearly increasing time-varying demand

In many manufacturing systems, the quantity of raw materials needed for production is dependent on the production size. Therefore, it is preferable to unify the optimization of both elements under a single model. Recently, Omar and Smith applied a dynamic programming approach to determine an optimal batch size for the aforementioned model where demand for the product is deterministic and linearly varying with time over a finite planning horizon. However, the said dynamic programming approach is noted to be computational intensive and therefore may not be a desirable optimal solution procedure if a more efficient alternative is present. In this paper, we will explore an analytical solution procedure.