Two-stage Stochastic Lot-sizing Problem with Chance-constrained Condition in the Second Stage

Abstract

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.