Mixed integer formulations for a coupled lot-scheduling and vehicle routing problem in furniture settings

We propose and analyze two mathematical programming models for a production, inventory, distribution and routing problem considering real and relevant features from the furniture industry, such as production sequence-dependent setup times, heterogeneous fleet of vehicles, routes extending over one or more periods of the production planning horizon, multiple time windows and customers' deadlines, among others. These features are rarely jointly considered in the related literature, but commonly found in real-world applications. The models properly represent the problem in this industrial sector and can be used as a tool to support production and distribution planning in small companies. A large set of random and realistic instances is used to contrast the performance of the models in terms of both solution quality and computational effort. It is shown how much integrating production and distribution decisions in a single framework helps to reduce the total cost of the system, in comparison with a sequential approach that follows a common practice in this industry. This cost reduction comes at a higher computational effort, though.