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Online Facility AssignmentWe 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 c(i) to facility f(j) before the next customer c(i+1) arrives. The cost of this assignment is the distance between ci and fj. The total number of customers is at most vertical bar F vertical bar 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 vertical bar F vertical bar and another one with competitive ratio vertical bar F vertical bar. Finally, we consider a variant in which the facilities are placed on the vertices of a graph and two algorithms in that setting.