  In a given production planning horizon, the demands may only be comfirmed in
part of the whole periods, and the others are uncertain. In this paper, we
consider a two-stage stochastic lot-sizing problem with chance-constrained
condition in the second stage. In the first stage, the demand is deterministic
in each period, while in the second stage, the demands are random variables
with finite distribution. We prove the optimality condition of the solutions
under modified Wagner-Whitin condition and further develop a new equivalent MIP
formulation which can depict the feasible region better. We also show that any
subproblem fixing the selection of occurred scenarios has a complete linear
description of its convex hull. A branch-and-bound algorithm is provided
utilizing the character of the given subproblems.
