Application of agglomerative hierarchical clustering to optimize matching problems in ridesharing for maximize total distance savings

Ridesharing is transportation mode which brings together its participant whose similar itineraries and time schedule. The problem is how to compute matching requests with the large number of participants in short optimization time. For m driver n rider at the same time period, there is mxn driver-rider combination (possible match / pm) which will be considered whether time feasibility constraint is satisfied or not, if it satisfied then the pair is feasible match (fm). This paper purposed Agglomerative Hierarchical Clustering (AHC) to be applied for determining pm. By applying AHC, the pair which is not feasible based on their location is eliminated. AHC is clustering which merge two closest cluster, recursively, until all objects merge into one cluster. After we get fm set, we will check is there any pair whose distance saving less than zero? If it is, then it will be eliminated. To decide pairs that will do ridesharing trip (optimum match) we use Hungarian Algorithm. As the result, we obtain same number of optimum matched with and without applying AHC. At the process, by applying AHC, we can reduce the number of pm, so that total calculation of the driver-rider match that will be optimized is less.