# Multi-Objective Resource-Constrained Scheduling in Large and Repetitive Construction Projects
## 5 Discussion  
The resource-constrained scheduling problem is a multi-objective one with varying objective priorities in each project case and deployment environment. Thus, different optimization criteria should be developed in order to utilize those that better fit the individual problem objectives and characteristics. Focusing merely on a single sub-objective provides a partial view of the solution potential and typically prevents participants from making informed and concise decisions. In this work, an optimization model is developed for multi-objective resource-constrained scheduling aimed at large and repetitive projects. Several specific parameters (decision criteria) have been integrated in a multi-objective model that attempts to minimize the negative impact from not meeting the project priorities and constraints. These parameters are associated with (a) the exceedance of the daily resource availability and (b) the day-by-day fluctuations of resource needs. The above deviations result in direct financial losses, which can be assessed depending on the specificities of each particular project. On the other hand, the above sub-objectives are partly conflicting, meaning that a holistic evaluation, including single- and multi-criteria analysis is performed in any potentially productive way. The present study examines different objectives and criteria, either separately or in combination, to evaluate the degree to which each optimization structure facilitates certain or prevailing objectives in actual projects. To serve the needs for easy and practical application, which is important in scheduling operations of actual (construction) projects, the problem is structured in a spreadsheet form where scheduling and resource allocation calculations are made. Evolutionary algorithms have been found to perform well in such problem environments and the present work employs Genetic Algorithms in this direction. In addition, known general-purpose GA-solving commercial software has been employed. In construction industry practice, it is expected to use such type of assistance rather than developing an optimization model internally. Finally, due to the stochastic nature of evolutionary algorithms, it is recommended to implement multiple runs of a specific optimization setup to develop a clearer picture of the solution potential. Optimization is performed in the form of a weighted-sum function of several parameters (criteria) that can potentially be used in combination for providing global decision-making assistance. The weighted-sum structure perfectly fits the problem nature. This is because the weights represent (at least in some of the included parameters, RLE and RIO) explicit actual unit cost values of the corresponding resource inefficiencies. As such, the objective function provides a pure cost value that can undisputably be used for assessing the specific project schedule, which minimizes the total resource allocation cost. Among the decision parameters that have been considered, the STD, RLE, and MaxR promote the goals of resource leveling and resource overallocation prevention. In another optimization direction, the RIO parameter can better represent the adverse effect of resource movement in and out of the project. The analysis reveals that all criteria can potentially end up with comparatively enhanced solutions and, therefore, it is advised to perform runs with all criteria, either individually or collectively. It is also advised to make multiple runs with each set of criteria as the output of an evolutionary type of search is not deterministic. The experimentation with the case study example shows that the employment of such a global analysis generally is in favor of improved results. The case study results indicate that the optimization with the proposed strategy can provide rather effective resource allocation patterns, both in terms of resource overallocation and resource variations from day to day.