In this paper, we consider an integrated production and outbound distribution scheduling problem with a single production site, and its extension to multiple plants. A set of orders must be satisfied such that the required pieces from a single product must be first processed on a single machine in a plant, then must be delivered to the customers before their lifespan expire using a single vehicle. The goal is to minimize the makespan of the solution, which is the return time of the vehicle after its last trip. We propose an elementary variable neighborhood search to solve the problem, using two new local search operators. Our computational results show that this simple procedure outperforms the existing, sometimes complex approaches on the widely used benchmark dataset. We also review the existing computational results, and demonstrate that in some cases the comparisons in the literature are invalid due to the use of different rounding of the data. By re-evaluating the accessible solutions we provide a fair comparison for each rounding method. We also consider the extension of the problem to multiple plants, and adapt our solution approach for this extension. Our experiments show that our method is competitive in terms of solution quality with the existing solution approach for the problem.