Decision horizons for the capacitated lot size model with inventory bounds and stockouts

In this paper the authors consider the lot size model for the production and storage of a single commodity with limitations on production capacity and storage capacity. There is also the possibility of not meeting demand, i.e. stockouts in the form of lost sales, at a penalty. The stockout option means that horizons can exist and permits the use of horizons to develop a forward algorithm for solving the problem. The forward algorithm is shown to be asymptotically linear in computational requirements, in contrast to the case for the classical lot size model which has exponential computing requirements. Besides the forward algorithm, a number of necessary conditions are derived which reduce the computational burden of solving the model.