Mixed integer programming for dynamic tower crane and storage area optimization on construction sites

Construction site layout planning, the arrangement of temporary facilities and equipment on site, is a fundamental part of construction preparation. In construction, the operation of tower cranes has a great impact on construction process execution and preparation costs. Therefore, tower cranes should be chosen and placed such that they enable smooth construction processes at minimal cost. Since the majority of loads on site are transported either from or to a storage area, the transport routes taken between tower cranes and storage areas have a high impact. This paper presents a mathematical model that computes cost-optimal positions for both tower cranes and storage areas. The model consists of two linked mixed integer programs, allowing for the detailed quality assessment of the obtained solutions. Time dependency is considered by subdividing the construction process into several construction phases. Conditions on site and construction elements can be retrieved from a building information model. Particular advantages of our approach include the close approximation of complex shapes via convex hulls. Available positions on site are represented by a fine grid and calculated during runtime, which allows for freer placement instead of restricting to a fixed number of possible locations given as input. Using mixed integer programming offers tremendous modeling possibilities and a rigorous quality guarantee for the obtained solutions. In contrast to existing heuristic approaches, the returned solutions are provably optimal up to the chosen optimality gap. A case study is provided to demonstrate the practical applicability of the proposed model.