Assignment Problem: Workers assigned Tasks each Day in a Week. Priorize similar tasks across days

Question

Set of Workers W assigned to Tasks T. Workers can only work 1 task on a given day, and only 1 task can be worked by a worker on a given day. Cost to work a given task is equal for all workers and tasks.

However I would like to take into account different behaviors such as location or task type.

• On Day One:

  • Worker W1 assigned to Task T1 with type Y1 at Location L1
  • Worker W2 assigned to Task T2 with type Y2 at Location L1

• On Day Two:

  The assignment of W1 would be be incentivized to tasks with type Y1 and location L1. Similarly I would like the assignment of W1 to be incentivized to choose tasks with type Y2 and location L1.

I have a brute force approach that arbitrarily starts with one Worker-Task combination, assigns them, and recalculates the incentive weights, until every worker is assigned. This approach considers all days at the same time, but does not seem optimal.