Optimizing Bernoulli routing policies for balancing loads on call centers and minimizing transmission costs

We address the problem of assigning probabilities at discrete time instants for routing toll-free calls to a given set of call centers in order to minimize a weighted sum of transmission costs and load variability at the call centers during the next time interval. We model the problem as a tripartite graph and decompose the problem of finding the optimal probability assignment in the graph into an estimation problem and a convex quadratic program problem. Using a heuristic that uses gradient information around a given probability assignment we further address a practical variant in which the number of probability assignments that can be changed for each constrained instant