Algorithm for optimizing project resource allocation considering fuzzy expert recommendations on task start times

This article proposes an algorithm for evaluating project resource allocation that takes into account various fuzzy expert recommendations regarding the start times of tasks within float constraints, aiming to select the optimal set of expert suggestions. To determine the float constraints for task start and finish times, the classical critical path method is used. Expert recommendations on task start times are modeled as fuzzy trapezoidal or triangular numbers defined along the time axis. Based on the fuzzy start and finish times of project tasks, a fuzzy representation of the probability that a task will be performed at a specific moment is constructed. Building alpha-cuts for this fuzzy probability representation allows the identification of intervals, within float constraints, during which a task is likely to be performed at a certain level of fuzzy probability, thus enabling resource planning for those periods. The obtained results allow for: evaluating the expert recommendations that are optimal in terms of resource distribution; minimizing subcontracting needs for task execution; and calculating the associated subcontracting costs. The proposed algorithmic and software solution can serve as an effective decision support tool in the implementation of multi-component projects.

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