# Multi-Objective Resource-Constrained Scheduling in Large and Repetitive Construction Projects
## 1 Introduction  
The resource-constrained scheduling problem (RCSP) has been thoroughly investigated over the past few decades and continues to be a topic of considerable interest for researchers due to its vital importance in project management. The purpose of project scheduling analysis is to create optimal time plans and resource selection and allocation strategies while still finishing the project on schedule. This is a classical combinatorial problem with application in several production-based processes, including in the construction industry. While there have been plenty of research efforts in developing methods and algorithms for the typical RCSP, most of them have been evaluated with rather small and simple project structures. It is known, however, that construction projects are typically large (in terms of the number of activities) and complex (work interdependence), while they are often developed in a repetitive structure of identical sub-projects. In real-world environments, daily work planning is frequently required for a set of repetitive projects (i.e., construction projects that contain recurrent units). These units/sub-projects are made up of a common work structure. Three types of repetitive construction projects can be defined based on the direction of the workflow succession along the sub-projects:  
* Horizontal/linear repetitive projects, which have a linear geometrical layout (e.g., highways, pipelines, and tunnels). In this case, sub-projects may be executed in parallel;* Vertical repetitive projects, which involve the repetition of a sub-project network in a non-linear way (e.g., high-rise buildings). The sub-projects can be executed in a serial manner;
* Multiple repetitive projects, which consist of both horizontal and vertical repetitive processes (e.g., wide-area multistorey buildings). The resource-constrained scheduling problem typically aims to smooth out resource usage over time and avoid resource overallocation throughout the project life cycle or during project phases. The benefits of such a process are multiple. First, there is a relatively constant resource usage, avoiding the need for continuous resource incoming and outcoming or resources being idle at the construction site. In terms of human resources, the condition of occasional working acts negatively in both their performance and morale. Further, if resource constraints exist (this is typical in construction work), the resource imbalance and variation in time lead to project delays and cost overruns. Finally, in multi-project cases, poor resource usage in one project substantially affects the performance of other projects in which the construction company is involved. Resource leveling, with or without resource constraints, has been widely analyzed in the past. The majority of existing works use simple statistical criteria, such as the standard deviation of the resource usage values in time, to assess the resource allocation effectiveness. Although this is a useful criterion for some theoretical analysis, it holds two major deficiencies. First, it is not connected with some type of measure that can provide a practical outcome of the loss associated with the observed deviations from the optimal solution (e.g., cost). Most importantly, although it provides a measure of the resource allocation variability extent, it cannot provide a robust indication of the day-by-day resource allocation variability. The focus of this work is to assess the potential of evolutionary-type optimization methods in obtaining near-optimal resource allocation schemes in large and repetitive projects from a practical point of view (i.e., in real-life applications). With this aim, two decision parameters with direct cost representation of the resource allocation imbalances are considered to provide an objective assessment of the resource allocation success in actual projects.