Discretized Cell Modeling for Optimal Layout of Multiple Tower Cranes

Multiple tower crane layout planning (MTCLP) refers to the selection of the types, quantities, and positions of tower cranes and material storage positions. In a construction project, choosing tower cranes with a larger covering radius and lifting capacity can reduce the transportation time of materials. However, it can also simultaneously raise the rental cost and the risk of crane crashes. Determining an optimal multiple tower crane layout plan to achieve high construction efficiency with low cost is still a challenge. Mathematically, MTCLP is a complex combinatorial problem controlled by a number of variables, such as site configuration, building layout, material storage positions, and workload. To precisely describe irregular shaped sites and buildings, this research partitioned the site into unit cells and proposed a cell-based optimization model. For the optimal crane layout plan, the problem was formulated as a mixed integer linear problem (MILP). The model’s mathematical constraints comprised coverage of the given positions, the crane’s safety distance, sufficient crane capacity, and the utilization ratio. The objectives were to increase the crane coverage ratio while reducing the cost and the working areas overlapped by more than two cranes. Two case studies are presented to demonstrate the effectiveness of the model. The first construction project consisted of seven buildings with irregular shapes. By strictly forbidding the areas to be overlapped by more than three tower cranes, the model successfully obtained the optimal crane layout plan using the Gurobi Optimizer. Compared with the contractor’s layout plan, the optimal plan reduced the rental cost by 10.7% and the area overlapped by more than three tower cranes by 4.56%. In the second project, alternative plans were identified by the Gurobi Optimizer and $\epsilon$-constraint method to enhance confidence in selecting the ultimate crane layout plan. The optimization procedure involved (1) optimizing the layout plan with minimum crane cost and maximum coverage ratio, (2) identifying all possible layouts as the Pareto fronts when the coverage ratio could not be raised without increasing the crane cost, and (3) minimizing the areas of crane overlap covered by more than three tower cranes. The effectiveness of the proposed model is also proved by comparing the differences in layout plans caused by “regular” and “urgent” lifting demands.