Responsiveness is one of the significant performance measures in today's market based on which organisations can measure their success in seizing markets opportunities within Fractal Supply Chain. This paper aims to present this fractal supply network and also proposes a new mathematical model through which replenishment; transportation, production and handling time can be optimised at different stages of the fractal supply network. Both the proposed Fractal Supply Network and the mathematical model are implemented and validated using Supply Chain GURU Software. Application of the proposed mathematical model has led to a reduction in the total replenishment time and enables practitioners to systematically decide upon the optimum replenishment time at different stage of the network.