Multiple Integer Optimization with weighted / priority approaches



I am looking to model a multi-objective optimization problem where I have some hard constraints and soft constraints. I think of this as a goal-programming (multiple objectives - Constraint programming) like problem but I want to explore both MIP / CP approaches for multi-objective programming. For either of these approaches - does anybody have any solved examples? What libraries are available in the open source community (any language), and how do you suggest modeling this scenario? A simple example could be - Let’s say I am trying to route orders to fulfillment centers and my variables are time and shipping costs. I want my optimizer to accept weights and priorities for these 2 variables. I will also we supplying hard constraints in terms of allocation since my fulfillment centers have fixed capacities to allocate resources / day in terms of fulfilling those orders. It is assumed that all of the inventory is available in all the fulfillment centers.