This paper addresses the Integrated Production Routing Problem (IPRP), which requires the joint coordination of lot-sizing and vehicle routing decisions over a finite planning horizon. The problem accounts for several real-world features, including multiple products with different items, weights and sizes, sequence-dependent setup times and costs, limited production capacity, and safety stock requirements. For distribution operations, a heterogeneous fleet must serve customers with multiple time windows and strict deadlines, with routes possibly spanning several periods. The objective is to determine an integrated production and routing plan that minimizes setup changeover, inventory holding, and transportation costs. For this purpose, a Skewed Hybrid Variable Neighborhood Search (SHVNS) algorithm is proposed, relying on neighborhood structures specifically designed to modify routing decisions, while production planning is obtained from a mixed-integer programming model. Extensive computational experiments on benchmark instances demonstrate the effectiveness of the method in solving large-scale instances.