This research concerns a deterministic multi-item lot-sizing problem with capacity constraints, demand time windows, backlogging and speculative cost. The extreme points of the uncapacitated lot size polytope are analyzed, and an equivalent mixed-integer programming formulation is developed by applying modified Dantzig-Wolfe decomposition to the original problem. The lower bound is obtained by column generation processing. Furthermore, a heuristic branch and bound algorithm is developed to find near optimal solution. Numerical experiments generated randomly are tested and compared. The result shows that the gaps between the lower and upper bounds are very small. Moreover,