For the uncapacitated two-level production-in-series T period lot-sizing model, a dynamic program with running time O(T^2 log T) and a compact and tight extended formulation with O(T^3) variables and O(T^2) equality constraints are presented. Limited computational comparisons of various formulations of two level production/transportation problems with multiple clients are reported.
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De Melo, R. A., & Wolsey, L. (2010). Uncapacitated two-level lot-sizing. Operations Research Letters, 38(4), 241-245. https://doi.org/10.1016/j.orl 2010.04.001 (Original work published 2010)