A mathematical model to optimize decisions to impact multi-attribute rankings

We formulate the problem of how to climb in multi-attribute rankings with known weights using mathematical optimization. A model is derived based on familiar practices used in rankings in higher education where several attributes are combined using known weights to obtain a score. The method applies in any situation where multiple attributes are used to rank entities. We invoke several assumptions such as independence among attributes and that administrators can affect the values of some of the attributes and know the cost of doing so. Our results suggest that a strategy to advance in the rankings is to focus on modifying the value of fewer rather than more attributes. The model is generalized to allow for synergies and antagonisms among the attributes.