Linear programming allows optimisation of value creation network management. In practice, the size of these problems requires the use of a computer to perform the necessary calculations, and the simplex algorithm, among other things, allows this task to be performed. However, these solutions are built on approximate models and the human is generally disingenuous about solutions from “black boxes”. Shared initiative systems allow synergy between, on the one hand, the intuition and experience of a human decision-maker and, on the other hand, the computing power of the computer. Previous work within FORAC has enabled this approach to be applied to tactical planning of value creation networks’ operations. The approach would allow for better accepted solutions. However, it has a limited user interface and forces the solutions obtained to a sub-space of all the strictly optimal solutions. As part of this memory, the human-machine interface design principles are applied to design a graphical interface more suited to the typical user of the system. An interface based on the Logilab data presentation model, incorporating the interactivities offered by Hamel et al. is presented. Secondly, in order to allow the human decision-maker’s experience and intuition to compensate for the approximations made during the modelling of the value creation network in the form of a linear problem, tolerance as to the optimal solutions is introduced for the interactive search for alternative solutions. There will be a new algorithm for indexing the solutions to be combined and a new convex combination to allow for this flexibility. In order to increase the coverage of the solution space accessible to the human decision-maker, an interactive solution search algorithm based on the simplex-based solution is introduced. This algorithm has similar stability to the Hamel et al. method, but its performance in computing times is too low to offer real-time interactivity on real industrial cases with the computers currently available. A second approach for full indexation of solution space is proposed in order to reduce calculation times. The new algorithms ‘Linear Redundancyless Recursive Research’ (LRRR) for mapping and indexing of the solution space and N-Dimension Navigation Direction (NDND) for interactive exploration are presented. These algorithms are fair and fast, but have a cost of memory beyond the capacity of contemporary computers. Finally, other exploration routes are presented, including the exploitation of the indoor point and Karmarkar algorithm methods and a geometric approach outline.