A tight bound for 3-partitioning

Let t be a list of n items with nonnegative weights assigned to them. We want to assign these items to m bins (n = 3m) with the object of minimizing the maximum weight of the bins such that no bin contains more than three items. As approximation algorithm for this NP-complete problem we use a modified version of the famous LPT-algorithm for multiprocessor scheduling. The main subject is to prove a worst-case bound of 4/3–1/3 m.