Privacy in Resource Allocation Problems

Collaborative decision-making processes help parties optimize their operations, remain competitive in their markets, and improve their performances with environmental issues. However, those parties also want to keep their data private to meet their obligations regarding various regulations and not to disclose their strategic information to the competitors. In this thesis, we study collaborative capacity allocation among multiple parties and present that (near) optimal allocations can be realized while considering the parties' privacy concerns.

We first attempt to solve the multi-party resource sharing problem by constructing a single model that is available to all parties. We propose an equivalent data-private model that meets the parties' data privacy requirements while ensuring optimal solutions for each party. We show that when the proposed model is solved, each party can only get its own optimal decisions and cannot observe others' solutions. We support our findings with a simulation study.

The third and fourth chapters of this thesis focus on the problem from a different perspective in which we use a reformulation that can be used to distribute the problem among the involved parties. This decomposition lets us eliminate almost all the information-sharing requirements. In Chapter 3, together with the reformulated model, we benefit from a secure multi-party computation protocol that allows parties to disguise their shared information while attaining optimal allocation decisions. We conduct a simulation study on a planning problem and show our proposed algorithm in practice.

We use the decomposition approach in Chapter 4 with a different privacy notion. We employ differential privacy as our privacy definition and design a differentially private algorithm for solving the multi-party resource sharing problem. Differential privacy brings in formal data privacy guarantees at the cost of deviating slightly from optimality. We provide bounds on this deviation and discuss the consequences of these theoretical results. We show the proposed algorithm on a planning problem and present insights about its efficiency.