# Approximate bin-packing?

Let $$X_1,…X_n$$ denote some bins, and $$w_1,…w_m$$ some positive real numbers, where $$m \in \mathbb{N}$$, and the order matters, so e.g. we can’t switch the position of $$w_n$$ and $$w_1$$. The goal is to partition $$w_1,…w_m$$ into the bins, such that each bin contains "roughly" an equal sum of $$w_i’s$$, e.g. the sums for $$X_1,…X_n$$ could approximately equal $$100$$, so $$X_1$$ could have a sum of 104, $$X_2$$ could have a sum of 97,… etc. Let’s say this "equal sum" is $$Z$$.

Letting $$Y_i$$ be the sum for each $$i^{th}$$ bin, is there a way to choose Z such that the error is minimized, error being defined as $$\sum_i |Y_i-Z|$$, where $$1 \leq i \leq n$$?