A linear description for the economic lot-sizing problem consisting of exponentially many linear inequalities was given by Barany, Van Roy and Wolsey in 1984. Using this formulation we present a dual algorithm for the economic lot-sizing problem, which is of the same complexity as the Wagner and Whitin dynamic programming algorithm. Besides its use in sensitivity analysis the dual algorithm also provides an alternative proof of the fact that the linear description is complete.
van Hoesel, C. P. M., Wagelmans, A. P. M., & Kolen, A. W. J. (1991). A dual algorithm for the economic lot-sizing problem. European Journal of Operational Research, 52(3), 315-325. https://doi.org/10.1016/0377-2217(91)90166-S