Bin packing problem with scenarios

Scheduling over scenarios is one of the latest approaches in modelling scheduling problems including uncertainty. However, to the best of our knowledge, scenarios have never been applied to the bin packing problem, so here we introduce the bin packing problem with scenarios. In this model, we have a list of items with sizes between 0 and 1, and each item is assigned to one or more scenarios. In reality, the items of only one scenario will occur, but this chosen scenario is unknown at the time of packing, so the algorithms have to examine all scenarios. This means that the items have to be packed into bins such that for any scenario, the total size of the items in this scenario is at most 1 in each bin. The objective of the standard bin packing problem is to minimize the number of bins. Here, we introduce some extensions of the objective function to the scenario based model, and we present our competitive analysis of some online bin packing algorithms adapted to scenarios.