Minimization of maximum absolute deviation in integers

A resource allocation problem of the integer minimization of maximum absolute deviation of monotone functions is under investigation. The optimal solution is shown to belong to one of the four possible classes. The optimality conditions of two kinds (“local” and “global” ones) are derived along with an algorithm, which utilizes the solutions of simple min-max and max-min integer allocation problems.The Apportionment problem is considered as an application.