Stacking under uncertainty: We know how to predict, but how should we act?

We consider the problem of stacking containers in a given set of stacks of fixed maximum capacity when the pick-up times are stochastic with unknown probability distributions. The goal is to minimize the expected number of times a container is picked up while it is not at the top of its stack. We formulate several algorithms under varying assumptions about the available knowledge about the pick-up-time distributions. We distinguish four qualitatively different settings: 1) we know nothing about the actual distributions, 2) we have point estimates of the means, 3) we have point estimates of means and variances, or 4) we have historical samples of actual pick-up times. For each assumption we propose one or more algorithms. We test the algorithms empirically in many different scenarios, considering both sequential and concurrent arrivals. Additionally, we consider the computational complexity and ease of use of each algorithm.