Multi-Commodity Network Flow Model Applied to Waste Processing Cost Analysis for Producers

Abstract

Supply chain models and network flow models represent a frequent task, where transport of product(s) or service(s) between supplier(s) and consumer(s) is optimized. Several models applied to energy systems and supply chains including biofuels and/or renewables have been developed and recently published. In this paper, we deal with a network flow problem where waste is transported from producers (municipalities) through pre-processing facilities to its final treatment. The results obtained for minimum total treatment cost including transport provide us with optimal total waste flow along edges (roads, railways) in a selected region. However, the information about the waste flow through the network from a particular producer and related processing cost is often lost due to the merging and splitting streams in vertices. This limits the practical utilization of the results. This shortage can be solved by a secondary network flow problem where capacities of edges are given by results from total waste flow problem and waste from different producers is modelled by new variables. The needed constraints are introduced and new suitable criterion is specified. The model follows principle ideas of multi-commodity network flow modelling. It is implemented in GAMS and presented through a case study.