An inventory stacking decision assigns positions to items which are stacked vertically, such as containers in container terminals and steel plates in steel plants. The performance of stacking decisions is greatly affected by the arrival and departure information on items. We study an inventory stacking problem with partial information based on industrial observation in a steel plant. On the inbound side, we investigate three levels of information on future arriving items and their effect on performance. On the outbound side, we study the impact of the retrieval sequence, which is often random. We develop models incorporating different availabilities of information and determine stacking strategies. The study shows that the stacking strategy and stacking performance depend highly on information quality and space utilisation. Especially, when the space utilisation is high, low-quality information deteriorates the performance and such information should be ignored. This contradicts the general belief that more information should bring better performance. The study further proposes a time window allocation approach to reduce the uncertainty in retrieval, and it is effective in improving stacking performance.