A Minimum-Risk Dynamic Assignment Mechanism Along with Approximations, Extensions, and Application to Refugee Matching

In the classic linear assignment problem, items must be assigned to agents in a manner that minimizes the sum of the costs for each item-agent assignment, where the costs of all possible item-agent pairings are observed in advance. This is a well-known and well-characterized problem, and algorithms exist to attain the solution. In contrast, less attention has been given to the dynamic version of this problem where each item must be assigned to an agent sequentially upon arrival without knowledge of the future items to arrive. Motivated by an application in the globally pressing domain of international asylum and refugee resettlement, specifically that of matching refugees and asylum seekers to geographic localities within a host country, this study proposes an assignment mechanism that combines linear assignment programming solutions with stochastic programming methods to minimize the expected loss when assignments must be made in this dynamic sequential fashion, and offers an algorithm for implementing the mechanism. The study also presents an approximate version of the mechanism and accompanying algorithm that is more computationally efficient, a prediction-based alternative approximation that combines stochastic programming with machine learning to achieve even greater efficiency, as well as heuristic mechanisms. In addition, the study provides an extension to dynamic batch assignment, where items arrive and must be assigned sequentially in groups. Real-world refugee resettlement data in the United States are used to illustrate the methods and show how they could be practically implemented in order to optimize refugees' and asylum seekers' employment prospects (or other integration outcomes) in their host countries.