Optimal Lot-Sizing for Dynamic Assembly Systems

The simple case of a dynamic assembly system with no initial stocks is investigated as a test case for some new ideas on lot-sizing for Materials Requirements Planning. The model relies on the facility location formulation of Wagner’s and Whitin’s inventory problem. An iterative procedure is proposed that derives close upper and lower bounds through cost modifications based on Benders Decomposition and level-by-level optimization. The bounding procedure is integrated into a branch and bound scheme that outperforms by at least an order of magnitude its probably best competitor, the algorithm due to Afentakis et al (1984). The bounding procedure behaves excellently well as a heuristic and relates interestingly to the well-known lot-sizing methods of Graves (1981) and Blackburn and Milien (1982).