A Lagrangian Relaxation Approach for Production Planning With Demand Uncertainty

A production planning problem with stochastic final demands is considered in this paper. The problem is to determine over a given time horizon the production quantity of each intermediate/final product at each facility of finite capacity so that a system-wide total cost is minimized while meeting given service level requirements for the final products. After reformulating the stochastic problem as a multi-item, multi-stage capacitated lot-sizing problem with a nonlinear cost function using deterministic equivalence, it is solved by using a Lagrangian relaxation approach enhanced with a local search based on a modified simplex algorithm. Numerical experiments show that the approach can find high quality near-optimal solutions for randomly generated problems of realistic sizes in a computation time much shorter than that of an exact algorithm