A hierarchical planning approach for a production–distribution system

A production–distribution model involving production and transportation decisions in a central factory and its warehouse is developed. The model is based on the operating system of a multi-national company producing detergents in a central factory from which products are distributed to geographically distant warehouses. The overall system costs are optimized considering factory and warehouse inventory costs and transportation costs. Constraints include production capacity, inventory balance and fleet size integrity. Here, a hierarchical approach is adopted in order to make use of medium range aggregate information, as well as to satisfy weekly fluctuating demand with an optimal fleet size. Thus, a model which involves an aggregation of products, demand, capacity, and time periods is solved. In the next planning phase, the aggregate decisions are disaggregated into refined decisions in terms of time periods, product families, inventory and distribution quantities related to warehouses. Consistency between the aggregate and disaggregation models is obtained by imposing additional constraints on the disaggregation model. Infeasibilities in the disaggregated solution are resolved through an interactive constraint relaxation scheme which is activated in response to infeasible solutions pertaining to different causes. Here, we investigate the robustness of the hierarchical model in terms of infeasibilities occurring due to the highly fluctuating nature of demand in the refined time periods and also due to the aggregation process itself.