Rolling horizon, multi-product production planning with chance constraints and forecast evolution for wafer fabs

In this paper, we study production planning models for semiconductor wafer fabrication facilities (wafer fabs) that consider both safety stocks at the finished goods inventory level and workload-dependent lead times. The evolution of demand forecasts over time follows the multiplicative Martingale Model of Forecast Evolution (MMFE) for multiple products and is incorporated into the planning models via shortfall-based chance constraints, permitting the simultaneous determination of production quantities and safety stocks. We study two variants of this formulation, one that considers forecast updates and one that does not. A planning model with workload-dependent lead times that does not consider safety stocks is used for comparison. The performance of the planning models is assessed in a rolling horizon environment using a simulation model of a scaled-down wafer fab. We find that the chance-constrained model with forecast updates outperforms the one without forecast updates with respect to expected service level and profit. Both chance-constrained models outperform the model without safety stocks. These results indicate that considering forecast evolution in production planning models can lead to improved performance by exploiting the advance demand information provided by the forecast updates.