Weibull-based benchmarks for bin packing

Bin packing is a ubiquitous problem that arises in many practical applications. The motivation for the work presented here comes from the domain of data centre optimisation. In this paper we present a parameterisable benchmark generator for bin packing instances based on the well-known Weibull distribution. Using the shape and scale parameters of this distribution we can generate benchmarks that contain a variety of item size distributions. We show that real-world bin packing benchmarks can be modelled extremely well using our approach. We also study both systematic and heuristic bin packing methods under a variety of Weibull settings. We observe that for all bin capacities, the number of bins required in an optimal solution increases as the Weibull shape parameter increases. However, for each bin capacity, there is a range of Weibull shape settings, corresponding to different item size distributions, for which bin packing is hard for a CP-based method.