We consider an integrated optimization problem including the production, inventory, and outbound transportation decisions where a central plant fulfills the demand for several final products at its customers. More specifically, we investigate cases where the production planning and routing period lengths are not the same, e.g., days vs. shifts. Thus, we consider the fact that two different discretizations of the planning horizon exist in the decision-making process. This practical feature is a major source of complication for supply chain planners. With respect to the production planning aspect, we consider both big-bucket and small-bucket lot-sizing models. We mathematically formulate the problem under different practical scenarios for the production and route planning period lengths. An exact solution method, as well as heuristic algorithms, are proposed to efficiently solve large problem instances with this feature. To assess the effectiveness of our approach, we generate many test instances and perform an extensive computational study.