A bi-level programming approach to joint network design and pricing problem in the municipal solid waste management system: A case study

The fast growth of urbanization and population has held to the increase of waste in cities and caused significant problems in urban management systems. In this study, the design of municipal solid waste management network as well as determination of outsourcing policies is studied from the viewpoint of an organization (e.g. municipality) which collects different types of wastes from all over the city and pays a certain amount of money in exchange. In case of outsourcing, auction will be held and the companies who their business is recycling and composting can participate in by bidding. This process results in the selection of a company or an insourcing alternative. The problem is modelled as a bi-level programming model, which in the first level, municipality decides as the leader on outsourcing, and if outsourcing is agreed upon, a company is selected. In the second level, bidders compete as followers in the auction for receiving more waste from the municipality and offer prices. An exact novel solution method is applied to convert the proposed bi-level programming model into a single-level one that can be solved by commercial solvers. To validate the proposed solution method the relevant results are compared with those obtained by Karush-Kuhn-Tucker (KKT) approach by using data extracted from a real case study. Numerical results show that the proposed method is able to decrease the complexity of the concerned problem and considerable saving in computational time.