Mixed-integer programming models for tower crane selection and positioning with respect to mutual interference

Abstract Cranes have a major impact on a construction project from both an operational and an economic perspective as they are the primary lifting equipment and among the most expensive construction equipment. In this research we, thus, focus on two inter-related decisions regarding tower cranes, namely their selection and their on-site location. On a given polygonal construction site, there are given polygonal supply and demand areas that have to be connected by tower cranes with given specifications such as operating radius, operating height and costs. Cranes have to be selected and their on-site locations have to be determined so that each demand area is connected to its supply area. The objective is to minimize overall cost. When locating cranes, infeasible areas, minimum distances between cranes and obstacles limiting the cranes’ slewing ranges, e.g. other cranes or existing structures, have to be respected. We provide a formal problem definition, analyze its computational complexity, and develop four different mixed-integer programming models. Finally, an extensive computational study investigates the performance of standard solver CPLEX using the model formulations.