An Lp-based Approach to the Ring Loading Problem with Integer Demand Splitting

We consider the Ring Loading Problem with integer demand splitting (RLP). The problem is given with a ring network, in which a required traffic requirement between each selected node pair must be routed on it. Each traffic requirement can be routed in both directions of the ring network while splitting each traffic requirement in two directions only by integer is allowed. The problem is to find an optimal routing of each traffic requirement which minimizes the maximum of traffic loads imposed on each link on the network. By characterizing extreme points of the LP relaxation of an IP formulation, we analyze the strength of the LP relaxation. Then we present a strengthened LP which provides enough information to determine the optimal objective value of RLP. Finally, we give an LP-based polynomial-time algorithm for the problem which can handle more general cases where nontrivial upper and lower bounds are imposed on the amount of traffic routed in one direction for some node pairs.