Composite lot sizing with quantity and freight discounts

The EOQ model is aggregated into an extended composite model by including shipping costs, inspection costs, in-transit holding costs, backorder costs, finite replenishment, quality rejects, quantity discounts, and freight rate discounts in its formulation. The embellished model can be disaggregated into numerous different deterministic hybrid models by using simplified decomposition rules that apply to a variety of specific operational conditions. Optimum lot sizing formulations are derived for all non-discount situations as well as discount situations without stockouts. For these situations, efficient algorithms are used to obtain optimum lot sizes. For incremental discount situations with stockouts, efficient algorithms along with numerical analysis are required to converge upon optimum lot sizes. The simple EOQ is shown to be a special disaggregated case of its composite parent. A foundation is provided for a decision support system to deal with the variegated mix of operational conditions.