In this work, we consider a Multi-Activity Tour Scheduling problem which often arises in human resources management.
Equity is one of the most important criteria for evaluating solutions of this problem. It aims at seeking the most balanced solution in the terms of employee's working time. In other words, a planning is called equal if the difference of working time of its resources is minimal. Most of research in the literature focuses on minimizing the difference between the lowest and the highest resource's gap. This formulation cannot ensure the equity of the employees whose working time is between the lowest and the highest, so, this paper proposes a new mathematical formulation to optimize the equity of plannings. Instead of shrinking the gap between those who works the most and the least, the proposed formulation minimizes the absolute gap between employee's real working time and their mean working time. The experimental results show that the proposed formulation outperformes the benchamrk
formulation and offer more balanced solutions.