vehicle routing problem that considers soft time windows and fuel costs

Hi @yuyu. The AIMMS example Capacitated Vehicle Routing Problem with Time Windows can solve instances with 50 customers in 2 minutes. Your model only contains 11 customers. It might be an idea to start using the model formulation of this AIMMS example and modify that to your needs. Changing the hard time window constraints from the AIMMS example into soft constraints should be easy. I think that adding the fuel costs is also possible but I am not completely sure. Your model uses variable and parameter names that are not very descriptive and there are no comments to explain the meaning of the variables and parameters.

Do you want to use soft or hard time window constraints? The penalty value b (150) is small compared to the cost of using an extra vehicle (1000), so if the program has to choose between an extra vehicle or violating a time window constraint then it will pick the latter.