Efficient distribution is crucial in many industries today, especially in retail, where customer demand grows rapidly. The rise of online shopping and automation has led to a shift towards using Central Distribution Centers (CDCs). Retailers are part of this trend, which requires them to rethink how they handle their distribution. This study focuses on two main challenges: first, changing the distribution system to adapt to new CDCs, and second, dealing with the computational complexities when optimizing the distribution on a large scale. The aim is to design a large distribution system for the allocation of stores and the routing of vehicles. In this research, we introduce new elements to the mathematical model, which are mostly focused on the routing of vehicles. We also improve the computation by implementing a start solution, adjusting the parameters of the Gurobi optimization tool and including a callback function which bounds the run time. This model will determine the routing decisions for demand from several DCs to the stores and find the optimal vehicle routes. Through a case study at a company in the Netherlands, this paper provides insights into the changing world of distribution systems. It offers practical solutions for businesses trying to make their distribution processes better. The analysis revealed that consolidating demand at CDCs can lead to significant cost improvements while altering transport costs between CDCs and RDCs and adjusting order volumes can influence delivery strategies. Despite the absence of direct relationships between routing decisions, distances, and volumes, a logistic regression model provides guidance.