Inventory lot-sizing with supplier selection
Computers and Operations Research
A Two-Echelon Inventory Optimization Model with Demand Time Window Considerations
Journal of Global Optimization
An efficient dynamic programming algorithm for a special case of the capacitated lot-sizing problem
Computers and Operations Research
Dynamic Lot Sizing with Batch Ordering and Truckload Discounts
Operations Research
Some new properties for capacitated lot-sizing problem with bounded inventory and stockouts
Math'04 Proceedings of the 5th WSEAS International Conference on Applied Mathematics
On the Interaction Between Demand Substitution and Production Changeovers
Manufacturing & Service Operations Management
Capacitated Lot size problems with fuzzy capacity
Mathematical and Computer Modelling: An International Journal
A polynomial algorithm for a lot-sizing problem with backlogging, outsourcing and limited inventory
Computers and Industrial Engineering
A Lagrangean heuristic for a two-echelon storage capacitated lot-sizing problem
Journal of Intelligent Manufacturing
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We consider the Capacitated Economic Lot Size Problem with piecewise linear production costs and general holding costs, which is an NP-hard problem but solvable in pseudo-polynomial time. A straightforward dynamic programming approach to this problem results in an O(n2cd) algorithm, where n is the number of periods, and d and c are the average demand and the average production capacity over the n periods, respectively. However, we present a dynamic programming procedure with complexity O(n2qd), where q is the average number of pieces required to represent the production cost functions. In particular, this means that problems in which the production functions consist of a fixed set-up cost plus a linear variable cost are solved in O(n2d) time. Hence, the running time of our algorithm is only linearly dependent on the magnitude of the data. This result also holds if extensions such as backlogging and startup costs are considered. Moreover, computational experiments indicate that the algorithm is capable of solving quite large problem instances within a reasonable amount of time. For example, the average time needed to solve test instances with 96 periods, 8 pieces in every production cost function, and average demand of 100 units is approximately 40 seconds on a SUN SPARC 5 workstation.