Morell–Skutella-type conjecture for unsplittable transshipments

Let $G=(V,A)$ be the transshipment network, let $b$ specify the vertex balances, and let $x$ be a feasible $b$-transshipment. Write $d_{\max}$ for the maximum demand, and let $A$ be the set of arcs. An unsplittable $b$-transshipment routes each demand along a single path while satisfying the balance requirements.

Morell–Skutella-type conjecture. Given a $b$-transshipment $x$, one can efficiently compute an unsplittable $b$-transshipment $y$ such that

$$x_a-d_{\max}\leq y_a\leq x_a+d_{\max}\qquad\text{for all }a\in A.$$

This extends a conjecture for single-source unsplittable flows by Morell and Skutella to transshipments. The statement asks for simultaneous additive upper and lower arc-flow guarantees; the source describes it as an open question, even in the special single-source case, and conjectures both existence and efficient computability.