Dynamic economic lot size models with period-pair-dependent backorders and inventory costs

Inventory and backorder cost functions in the classical Wagner–Whitin economic lot size (ELS) models are typically period-pair-independent (pp-independent) in the sense that inventoried units carried (or backorders in existence) in a given period are treated the same regardless of the periods in which they are produced (placed) or the periods in which they are used (filled). We consider versions of the problem where inventory and backorder costs are pp-dependent, as well as versions where backorder costs, but not inventory costs, are pp-dependent. Recognizing that the problems considered are NP-hard, we provide cases where the cost structure allows polynomial solvability via dynamic programming.