Relief goods distribution with conditional earmarking donation

Supplies reserved by the government are the main source of relief goods in disaster. Donations are also an important part of relief goods. The relief goods distribution problem with the considering of donation is studied. Donations from the humanitarian organization include the earmarking donation and non-earmarking donation. The conditional earmarking means that only a part of donations are earmarked to the demand area. The rest donations are arranged by the emergency management agency. Both the two organization want to maximize its utility. Therefore, competition exists between the two organizations. A utility model is proposed based on the marginal utility. The marginal utility is used to measure the added utility when the demand area receives the relief goods. Then, the Lagrange multiplier method is incorporated to solve the proposed model. At last, a numerical experiment is provided. The conditional earmarking donation strategy and the full earmarking donation strategy are discussed. Results show that the conditional earmarking donation strategy is preferred by the humanitarian organization. The full earmarking donation strategy is preferred by the emergency management agency. The proposed problem is helpful to promote the utility of the relief goods distribution.