The Study Of Matching Theory,Approach And Application In Health Care Area

The matching theory has a great development since the matching problem with preference was presented by Gale and Shapley.Different models have been developed,from one-to-one two-side matching model,one-to-many two-side matching model,to three-side matching model.Meanwhile,these models have been applied to many areas.This thesis focuses on the both one-to-many two-side matching problem and three-side matching problem.These problems have a great application prospect for hospital operation,including the expert outpatient appointment,the surgery room scheduling,the hierarchical medical system,etc.Many aspects can be improved by exploring these matching problems,such as the utilization rate of medical resource,the relationship between patients and doctors,and the medical service.First,the thesis discusses the one-to-one two-side matching problem.Specifical-1y,the one-to-many two-side matching problem is transferred to one-to-one two-side matching problem;it is demonstrated that the one-to-many two-side matching problem is equivalent to one-to-one two-side matching problem.These discussions are the foun-dation for further exploring the one-to-many two-side matching problem.Next,this thesis studies the three-side matching model with two partners(repre-sented by 3D-1).The main set U has the relationship of partial order with main set V1 and V2 respectively,and the main set V1 and V2 are partners.K c V1 ×V2 represents the partner relationship between V1 and V2.This thesis proposed the concept of satisfied pair and stable matching in the three-side matching problem 3D-1.Then the thesis discussed the two situations,K = V1 x V2 and K(?)V1 x V2,the existence of stable matching was demonstrated and the corresponding algorithm was proposed as well.At last,the thesis considers the three-side matching model with partial order situ-ation.The two different concepts for satisfied pair and stable matching was identified.One is total advantage occupied,the other is partial advantage occupied.The existence of stable matching is demonstrated for the two situations,and the corresponding algorithm was proposed as well.