**3. Discussion and Conclusions**

In the proposed method of assembly works planning, an active and key role is played by the planner who, based on their experience, and the results of historical simulations, has the ability to change the input assumptions. The size, first in regards to the load capacity of cranes, is effectively assessed by the number of unmounted elements in the solutions of subsequent simulations. If the number is large, it is a signal to the planner to change the size of the cranes. The potential locations of cranes can be effectively determined by the planner, assuming that he has elementary knowledge about the relationships between load capacity, reach and lifting height. The planner also does the final crane selection and assembly schedule, however, the developed method supports the decision-maker by presenting many acceptable solutions.

It should also be mentioned that the aim of planning is not always to choose the best solution for a selected construction project, but to achieve the smallest possible cost of works through the prism of the production potential. Therefore, it is not their goal to carry out works quickly on one particular construction site, but to use the production potential, construction equipment and workers effectively. The method of assembly planning cannot therefore focus on choosing one optimal solution that presents the most favorable ratio of the pace of works to their cost. The planner's support consists of indicating available solutions, and assessing their quality. The final decision should always be left to the decision maker.

The method does not explicitly include collisions between cranes. Algorithmically, this problem is difficult to solve, because construction situations are unstable-they depend on many random factors. Therefore, other solutions are advised, e.g., planning cranes' locations at a safe distance from each other or using anti crane collision systems and limit switches. This should solve the problem of work safety and collision-free assembly. As the spans of prefabricated elements are large, the work zones of cranes may overlap, but it does not affect the pace of work significantly if the planner or crane operator locates the machine skillfully.

Such an approach to the assembly planning problem was made in this paper—the planner indicates the potential locations of cranes in a way that reduces the risk of collision, while the possible risk of collision is eliminated using the already available techniques.

There are still several open issues in the problem of assembly planning that should be considered in the course of further research. These include, but are not limited to, the following:

1. In the current formula, the planning tool prioritizes the order of assembly in accordance with the order proposed by the planner (order according to the list of elements to be mounted). Each assembled element is the predecessor of the next element to be assembled. In fact, this relationship primarily stems from the technological conditions and lets the planer decide freely about the order of assembly. The order of the elements to be mounted should be enriched by a matrix of dependency relations between the assembled elements and their predecessors, while decisions to move a mobile crane should be made after checking the possibility of assembling all elements for which the required predecessors have already been mounted. Such a solution would increase the effectiveness of the proposed method by reducing the number of necessary adjustments of mobile cranes.


The authors intend to use the proposed planning tool to plan assembly works in real planning situations. The practical application of the planning tool will be the subject of future publications

**Author Contributions:** Conceptualization, R.M. and M.B.; methodology, R.M. and M.B.; software, M.B.; validation, R.M. and M.B.; formal analysis, R.M.; resources, M.B.; writing—original draft preparation, M.B.; writing—review and editing, R.M.; supervision, R.M.; project administration, R.M.; funding acquisition, R.M. and M.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
