Multi-Item, Multi-Period Production Planning with Uncertain Demand

We provide a formulation and solution algorithm for the finite-horizon capacitated production planning problem with random demand for multiple products. Using Lagrangian relaxation, we develop a subgradient optimization algorithm to solve this formulation. We also provide some computational results that indicate this approach works well for rolling-horizon planning compared with the rolling-horizon performance of the corresponding optimal finite-horizon solution. The advantage of our approach is that realistic problem instances can be solved quickly while optimal solutions to such instances are computationally intractable.