In short, Heroku needs to hire someone with some operations research experience. This is a mathematical modelling problem, not really a code problem. Break out

In short, Heroku needs to hire someone with some operations research experience. This is a mathematical modelling problem, not really a code problem. Break out Mathematica, Matlab or R and model the damn problem. Then go research the solutions already available (Hint: look at many grocery stores, queuing problems).