Towards optimal effort distribution in process design under uncertainty, with application to education

In most application areas, we need to take care of several (reasonably independent) participants: we want to make sure that all the economic regions prosper, that all the geographic regions have healthy environment, that all the students learn all the needed knowledge and skills. The amount of resources is usually limited, so we face the problem of optimally distributing these resources between different objects. To solve the resulting optimisation problem, we need to know for each participant i the utility resulting from investing effort e in the participant. In practice, we only know this value with (interval) uncertainty. So, for each distribution of efforts, instead of a single value of the group utility, we only have an interval of possible values. To compare such intervals, we use Hurwicz optimism pessimism criterion well justified in decision making. In this paper, we propose a solution to the resulting optimisation problems.