Bilevel Recycling Facility Location

This chapter presents an application of distributional robust facility location to a resource recovery planning problem under a public-private partnership. The problem intertwines two subproblems: one of interest to the local authority and another sought by a private operator. The former seeks a waste sorting scheme and a cost-sharing budget to minimize the expected financial benefit. The economic feasibility of the private operator must be ensured. Given the budget and sorting scheme, the private operator seeks to locate and operate resource recovery facilities. The goal is to maximize the expected total profit. A salient feature of the problem is that the feedstock condition (composition and volume) is uncertain. Moreover, it can be influenced by the sorting-at-source scheme implemented. This feature drives the interactions between public and private partners. A bilevel resource recovery planning model is devised under a distributionally robust optimization framework. A decision-dependent ambiguity set is defined to model the influence of sorting schemes on the feedstock uncertainty. The problem can be formulated and solved as a mixed-integer linear program. Numerical experiments are reported demonstrating that the optimization framework provides a helpful decision-analysis tool for resource recovery planning under feedstock ambiguity.