So assume we have a MILP (e.g. inventory or capacity planning) and the objective is to minimize total costs (inventory costs, set-up costs, backorder costs, production costs etc.). The production of a product $x_{tp}$ must meet demand $D_{tp}$. Most models and papers I reviewed in this area only consider the variable costs of a product (e.g. material) in the objective function, but do not incorporate the fixed costs per unit (as they assume that they are fixed).
So normally, unit costs of a product $UC_p$ would consist of a variable term ($VC$) and a fixed term, with the fixed portion being proportionalized based on the whole output Level $\sum\limits_{p \in P}x_{tp}$ (simplified).
$$UC_p =\frac{FC}{\sum\limits_{p \in P}x_{tp}} + VC$$
The problem now is that, if i want to calculate the total costs, this term leads to non-linearity of my MILP, as i would need to multiply it with the production quantity $x_{tp}$.
The reason I am looking for such a formulation is that I want to incorporate the idea of economies of scale into the model, e.g. the more I produce of a specific product the lower are my unit costs. It is basically an alternative formulation to an utilization constraint that sets a lower bound on the output quantity. Still, i wanted to try if there is a way to formulate it completely from a cost perspective.