Effects of Arrival Uncertainty on Solver Performance in Dynamic Stacking Problems

In this paper, we present a dynamic stacking problem with uncertainty. We developed a simulation environment, an optimizer for solving it, and performance measures to determine the success of the optimizer. The problem requires handling incoming blocks, stacking them efficiently, and meeting deadlines for delivery, while not knowing exactly when blocks will arrive or when they will be ready for delivery. The optimizer models the problem as a dynamic Block Relocation Problem and solves it using a branch&bound based heuristic. The simulation and optimizer run concurrently and the distribution of random variables is not disclosed to the solver and must, therefore, be estimated. We study the influence of uncertainty on the solver and show that the degree of uncertainty has a significant impact on the performance of the overall system. We also experiment with different measures to estimate uncertain arrival times and show that the choice of measure is important for achieving good performance.