•A novel mathematical formulation for the multi-product Production-Routing Problem (PRP) with Delivery Time Windows is proposed.•A decomposition approach is used to reduce the problem size and divide the problem into several tractable subproblems.•An improvement matheuristic based on a fix-and-optimize scheme is proposed to explore the solution space of large PRPs.•The algorithm is tested on literature instances and validated with real-world instances provided by a European meat store chain. Even though the joint optimization of sequential activities in supply chains is known to yield significant cost savings, the literature concerning optimization approaches that handle the real-life features of industrial problems is scant. The problem addressed in this work is inspired by industrial contexts where vendor-managed inventory policies are applied. In particular, our study is motivated by a meat producer whose supply chain comprises a single meat processing centre with several production lines and a fleet of vehicles that is used to deliver different products to meat stores spread across the country. A considerable set of characteristics, such as product family setups, perishable products, and delivery time windows, needs to be considered in order to obtain feasible integrated plans. However, the dimensions of the problem make it impossible to be solved exactly by current solution methods. We propose a novel three-phase methodology to tackle a large Production-Routing Problem (PRP) combining realistic features for the first time. In the first phase, we attempt to reduce the size of the original problem by simplifying some dimensions such as the number of products, locations and possible routes. In the second phase, an initial PRP solution is constructed through a problem decomposition comprising several inventory-routing problems and one lot-sizing problem. In the third phase, the initial solution is improved by different mixed-integer programming models which focus on small parts of the original problem and search for improvements in the production, inventory management and transportation costs. Our solution approach is tested both on simpler instances available in the literature and on real-world instances containing additional details, specifically developed for a European company’s case study. By considering an integrated approach, we achieve global cost savings of 21.73% compared to the company’s solution.