This work discusses what should be the desirable path and correct tools for the optimal re-design and operation of processes in the Industry 4.0 framework, as illustrated in a challenging case study corresponding to a complex network of evaporation plants in a viscose-fiber factory. The goal is to integrate optimal design, to improve the existing cooling systems, together with the optimal operation of the whole network, balancing the initial investment with the potentially achievable savings. A rigorous mathematical model for such optimization purpose has been built. The model explicitly considers different structural alternatives as a superstructure for the incorporation of new equipment into the network. The uncertainty associated to future operating conditions is also considered by using a two-stage stochastic formulation. Furthermore, the model is also the base from which a deterministic real-time optimization (RTO) builds upon to support the daily management of the future network operation. The RTO tool suggests the allocation of different products to evaporation plants, the distribution of the cooling water and the suitable number of heat pumps to switch on for optimal economic operation. Design and operation problems are formulated and solved via mixed-integer non-linear programming and the results have been tested with historical plant data.