Storage instances beyond the decomposition assumptions

Develop a solution method for district-heating-network scheduling instances with thermal storages that do not satisfy the assumptions required for optimality of the proposed time-decomposition approach.

Background

The paper proves optimality of its decomposition approach only under structural and cost assumptions, including parallel storage and heating arcs, unique connections, unrestricted corresponding heat supply, equal pump efficiencies, and equal pump costs. The authors explicitly identify instances with storages that violate these assumptions as an unresolved challenge; outside the assumptions, the decomposition may be infeasible or may produce only a suboptimal heuristic solution.