Fairness is crucial in transportation systems to ensure that all drivers are treated equally and have the same opportunities. Fair payment policies, equal access to work opportunities, and fair scheduling are some of the policies delivery companies implement to ensure fairness between drivers. In this paper, we study a fair scheduling mixed-integer programming problem where we consider a bi-objective function that aims to maximize profit and improve fairness between drivers by minimizing the maximum deviation from the average driving time. To solve this problem, we employ the weighted comprehensive criterion method and propose an iterative population-based heuristic. The results show that the relative gap between the heuristic and exact approach is acceptable. We also report the fairness price which is the relative difference between total profit with and without incorporating fairness. We find out that improving fairness between drivers does not always lead to a significant reduction in total profit. When the reduction in total profit is important, we recommend formulating the scheduling problem differently where instead of minimizing the maximum deviation from the average driving time, drivers are rewarded when their driving times are longer than the average. We explore incorporating the cost of rewarding these drivers in the objective function.