I want to solve a VRP with a column generation algorithm. The objective of the problem is makespan minimization. In more detail, I want to minimize the arrival time of the last vehicle in the depot. I want to know how I should write the path-based model?
In path-based models that I have ever seen for VRP, the objective was total cost minimization and all of the variables in the model were binary that corresponds to each route. I think in my problem, I should consider a continuous non-negative variable that represents the latest arrival time of vehicles to depot. I want to know if adding this variable is correct and how will it change the column generation algorithm?