A model for planning of production, inventory and combined routing of delivery and pick-up

This work studies the effectiveness of a new modeling approach that integrates decisions concerning production-inventory and transportation of both raw materials and finished products. We refer to this problem as the Production, Inventory, Distribution and Pick-up Routing Problem (PIDPRP). By permitting transportation of both finished products and raw materials in the same vehicle tour, we propose an alternative to the phenomena of empty truck movements. The problem is formulated as a mixed integer program with tours enumeration. A commercial solver is used to validate and solve a variety of small instances.The impact of some parameters of the problem on the solution time and on the properties of the solutions is analyzed. The integrated model is compared with three alternative decomposition approaches.