Economic Lot-Sizing Problem with Bounded Inventory and Lost-Sales

In this paper we consider an economic lot-sizing problem with bounded inventory and lost-sales. Different structural properties are characterized based on the system parameters such as production and inventory costs, selling prices, and storage capacities. Using these properties and the results on the lot-sizing problems with bounded inventory, we present improved and new algorithms for the problem. Specifically, we provide algorithms for the general lot-sizing problem with bounded inventory and lost-sales, the lot-sizing problem with nonincreasing selling prices and the problem with only lost-sales

Improved Algorithms for a Lot-Sizing Problem with Inventory Bounds and Backlogging

This paper considers a dynamic lot-sizing problem with storage capacity limitation in which backlogging is allowed. For general concave production and inventory costs, we present an O(T2) dynamic programming algorithm where T is the length of the planning horizon. Furthermore, for fixed-charge and nonspeculative costs, we provide O(Tlog T) and O(T) algorithms, respectively. This paper therefore concludes that the time complexity to solve the bounded inventory lot-sizing problem with backlogging is the same as the complexity to solve the uncapacitated lot-sizing problem for the commonly used cost structure

Note on "An efficient approach for solving the lot-sizing problem with time-varying storage capacities"

In a recent paper Gutiérrez et al. (2008) show that the lot-sizing problem with inventory bounds can be solved in O(T log T) time. In this note we show that their algorithm does not lead to an optimal solution in general