Deciding how indivisible units of a scarce resource or tasks should be assigned to people is a common problem in our society. Applications range from assigning shifts to employees, students to schools or internship positions, patients to admission dates in hospitals, deciding which patients can receive an organ transplant, etc. In some cases, monetary transfers are allowed to compensate those that receive less than what they desire, or those that get more than what they deserve. More often, however, this is not considered desirable. In this research project, we aim to develop optimization methods that either mitigate the differences between the involved parties with respect to the allocation by assuming a long-term perspective (in a case the optimization/allocation is repeated), or incorporate an acceptable random (lotterly) mechanism (in case of a one-time optimization/allocation). In both cases, we study the trade-off between global efficiency, and individual fairness.