Optimal configurations for modular systems at the example of crane bridges

The aim of this paper is to optimize modular systems which cover the construction of products that can be assembled on a modular basis. Increasing the number of different variants of individual components on the one hand decreases the cost of oversizing the assembled product, while on the other hand the cost for maintaining the modular system increases. For the minimization of the overall cost a mixed-integer model is derived. However, this model cannot simply be passed to a solver for mixed-integer optimization, since certain dependency structures of the variables occur. We propose a solution approach for this complicating structure using binary variables to transform the problem into a mixed-integer optimization problem, which can be solved deterministically. In a numerical study, this formulation is investigated using the example of a modular system for crane bridges.