Improving humanitarian supply chain operations through multi-agency collaborations using cooperative game theory

Abstract

Humanitarian supply chains support agency goals regarding disaster response, recovery, and development operations. However, increased efficiency and effectiveness of humanitarian operations are essential as disaster occurrences multiply (CRED, n.d.). Although collaboration between agencies involved in humanitarian response, recovery, and development can help improve operations, identifying the collaborative arrangements that optimize societal goals and remain attractive to autonomous agencies is challenging. Two aspects must be addressed: coalition formation, or which agencies should collaborate with one another, and cost allocation, or how to share the costs and benefits of collaboration among partners in a way that is acceptable to them. This research advances knowledge of coalition formation and cost allocation in a non-subadditive context, which encompasses settings in which large collaborative groups are not guaranteed to be optimal from the societal perspective. Few prior studies have considered this, and doing so is necessary to accurately model systems where collaboration can achieve cost savings among some partners and lead to increased costs among others. Humanitarian operations are one example, because scale economies can be achieved by collaborating, but large partnerships require additional costs to manage. This thesis presents new game theory and optimization models, solution methodologies, problem characterization, and computational analysis to address collaboration in non-subadditive settings. First, the author presents a literature review of cooperation among supply chain entities, focusing on studies that utilize cooperative game theory. Findings from the review reveal that cooperative game theory has primarily been studied on systems with subadditive cost functions. Next, the author introduces an optimization model focused on coalition formation to determine which humanitarian agencies should collaborate to minimize total societal cost. The problem is shown to be NP-complete, and a computational study is presented to compare the results from the optimization model with two proposed heuristics. Finally, the author examines cost allocations by proving analytical properties of the associated problems and introducing computational approaches to find stable and near-stable allocations. Notably, this thesis provides the first-known application of relaxation concepts to the non-subadditive game setting, which are generalized from the ε-core in subadditive games. Taken together, the coalition formation and cost allocation methods described in this research offer a foundation for improved collaboration in humanitarian supply chains and others characterized by non-subadditive costs.