Route-cost-assignment with joint user and operator behavior as a many-to-one stable matching assignment game

Rasulkhani, Saeid; Chow, Joseph Y.J.

doi:10.1016/j.trb.2019.04.008

We consider the online facility assignment problem, with a set of facilities F of equal capacity l in metric space and customers arriving one by one in an online manner. We must assign customer ci to facility fj before the next customer ci+1 arrives. The cost of this assignment is the distance between ci and fj. The total number of customers is at most |F|l and each customer must be assigned to a facility. The objective is to minimize the sum of all assignment costs. We first consider the case where facilities are placed on a line so that the distance between adjacent facilities is the same and customers appear anywhere on the line. We describe a greedy algorithm with competitive ratio 4|F| and another one with competitive ratio |F|. Finally, we consider a variant in which the facilities are placed on the vertices of a graph and two algorithms in that setting.

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