Mixed integer linear programming and building retrofits

When a building is subject for refurbishment it is important to add only such measures that will reduce the Life Cycle Cost (LCC), for the building. Even better is to add measures that will, not only reduce the cost, but minimise the LCC. One means for such an optimisation is to use the so called Linear Programming (LP), technique. One drawback with LP models is that they must be entirely linear and therefore two variables cannot be, for example, multiplied with each other. The costs for building retrofits are, however, not very often linear but instead ‘steps’ are present in their cost functions. This calamity can, at least to a part, be solved by introducing binary integers, i.e., variables that only can assume 2 values, 0 or 1. In this paper it is described how to design such a Mixed Integer Linear Programming (MILP), model of a building and how different cost elements of the climate shield influence the optimal solution.