Optimal Positioning of Mobile Cranes on Construction Sites Using Nonlinear Programming with Discontinuous Derivatives

Abstract

Mobile cranes represent conventional construction machinery that is indispensable for the erection of most prefabricated buildings, especially those containing heavy components. However, it is also common knowledge that the engagement of these machines has a significant influence on the environment, various social aspects of the construction process, and its economic benefits. Optimal positioning of the mobile crane on the construction site, primarily driven by the contractor’s interest to perform assembly operations with expensive machinery as effectively as possible, considerably reduces not only the costs of engaging such a machine but indirectly also its negative impacts on construction sustainability. This paper discusses an exact nonlinear model for the optimization task. The optimization model consists of a cost objective function that is subject to various duration and positioning constraints for the mobile crane, including bounds on its degrees of freedom of movement and stop positions. Because the model formulation includes discontinuous and non-smooth expressions, nonlinear programming with discontinuous derivatives (DNLP) was employed to ensure the optimal solution was reached. The model provides the mobile crane operator with exact key information that enables the complete and optimal assembly of the building structure under consideration. Additionally, the information gained on the optimal distribution of the mobile crane rental period to assembly operations allows for a detailed duration analysis of the entire process of building structure erection, which can be used for its further improvement. An application example is given in this study to demonstrate the advantages of the proposed approach.