Robust Bilevel Resource Recovery Planning

In this study, we consider a resource recovery planning problem under a public–private partnership. The local authority's problem is to determine the waste sorting scheme, and also a cost‐sharing budget, to minimize her expected payout, subject to a requirement of economic feasibility of the private operator. Given the budget and sorting scheme, the private operator's problem is to site and operate resource recovery facilities, and his goal is to maximize his expected total profits. A salient feature of the problem is that the feedstock condition (composition and volume) is uncertain, but can be influenced by the sorting‐at‐source scheme implemented. This feature drives the interactions of the public and private partners. We develop a bilevel resource recovery planning model in the framework of distributionally robust optimization, where a decision‐dependent ambiguity set is defined to model the influence of sorting schemes on the feedstock uncertainty. We perform the model analysis on the cost‐share ratio, which suggests the importance of sorting investment in achieving the sustainable resource recovery. Computationally, we show that the solutions of the bilevel problem can be obtained by solving one instance of a mixed‐integer linear program that does not induce any additional integer variable. Our proposed optimization framework provides a useful decision‐analysis tool for effectively utilizing and balancing the instruments of sorting and facility installation investments for resource recovery planning under feedstock ambiguity. For instance, the computational experiments with partial real data in the Singapore context justify several important insights: (i) the suitable sorting scheme implementation serves as a cost‐effective instrument that could significantly enhance the utility of the cost sharing; (ii) the sorting dependency of feedstock condition is critical in affecting the private operator's recovery performance; and (iii) the robust planning is effective in hedging against ambiguously poor feedstock condition. These findings should deserve attentions of both public and private sectors in current waste management practice.