A deterministic model for planning production quantities in a multi-plant, multi-warehouse environment with extensible capacities

We have developed a deterministic model for planning production and transportation quantities in multi-plant and multi-warehouse environment with extensible capacities. The model determines a production mix that maximizes total profit over a finite planning horizon. When production cannot meet demand due to lack of adequate resources, the models allows shortfalls to be met through subcontracting or the use of inventory. However, it does not allow subcontracting when adequate resources are available. When solved, the model produces the quantity of each product to be: (1) produced at each plant, (2) transported from each plant to each warehouse, (3) subcontracted at each warehouse, and (4) kept in inventory at each warehouse. Furthermore, it identifies the warehouses that need extensions at any period and the corresponding amounts of extensions needed. We also develop a procedure for reducing the size of the zero–one MILP problem that can be obtained during any application of the model. Numerical examples given to illustrate the model and to compare the full and the reduced versions of the model show that the model works well and that both the full and the reduced version produce exactly the same results. Finally, we discuss the assumptions underlining the model and highlight the approaches that can be taken to eliminate or, at least, prevent errors that are associated with violations of the assumptions.