We focus on fair division of chores (objects with non-positive utility), in a continuous period of time. That is, a group of agents should write their preferences every day (for a week for example), and we should divide the tasks between them. To solve this problem, we decided to treat each day as a category. Our goal is to find an algorithm that limits the number of tasks an agent can get from each category (i.e. each day), thus preventing an unbalanced division.
Terms / Assumptions:
- Indivisible Chores (non-positive utility for all agents)
- Additive valuations
- Capacity Constraints (a limit s_i on the number of chores an agent can get from category C_i)
- superior_value(|Ch|/n) ≤ kh
- Chores cannot be discarded