Modeling of the time-dependent multi-skilled RCPSP considering learning effect: An evolutionary solution approach

The purpose of this paper is to propose a new mixed-integer formulation for the time-dependent multi-skilled resource-constrained project scheduling problem (MSRCPSP/t) considering learning effect. The proposed model extends the basic form of the MSRCPSP by three concepts: workforces have different efficiencies, it is possible for workforces to improve their efficiencies by learning from more efficient workers and the availability of workforces and resource requests of activities are time-dependent. To spread dexterity from more efficient workforces to others, this study has integrated the concept of diffusion maximization in social networks into the proposed model. In this respect, the diffusion of dexterity is formulated based on the linear threshold model for a network of workforces who share common skills. The proposed model is bi-objective, aiming to minimize make-span and total costs of project, simultaneously.

The MSRCPSP is an non-deterministic polynomial-time hard (NP-hard) problem in the strong sense. Therefore, an improved version of the non-dominated sorting genetic algorithm II (IM-NSGA-II) is developed to optimize the make-span and total costs of project, concurrently. For the proposed algorithm, this paper has designed new genetic operators that help to spread dexterity among workforces. To validate the solutions obtained by the IM-NSGA-II, four other evolutionary algorithms – the classical NSGA-II, non-dominated ranked genetic algorithm, Pareto envelope-based selection algorithm II and strength Pareto evolutionary algorithm II – are used. All algorithms are calibrated via the Taguchi method.

Comprehensive numerical tests are conducted to evaluate the performance of the IM-NSGA-II in comparison with the other four methods in terms of convergence, diversity and computational time. The computational results reveal that the IM-NSGA-II outperforms the other methods in terms of most of the metrics. Besides, a sensitivity analysis is implemented to investigate the impact of learning on objective function values. The outputs show the significant impact of learning on objective function values.

The proposed model and algorithm can be used for scheduling activities of small- and large-size real-world projects.

Based on the previous studies reviewed in this paper, one of the research gaps is the MSRCPSP with time-dependent resource capacities and requests. Therefore, this paper proposes a multi-objective model for the MSRCPSP with time-dependent resource profiles. Besides, the evaluation of learning effect on efficiency of workforces has not been studied sufficiently in the literature. In this study, the effect of learning on efficiency of workforces has been considered. In the scarce number of proposed models with learning effect, the researchers have assumed that the efficiency of workforces increases as they spend more time on performing a skill. To the best of the authors’ knowledge, the effect of learning from more efficient co-workers has not been studied in the literature of the RCPSP. Therefore, in this research, the effect of learning from more efficient co-workers has been investigated. In addition, a modified version of the NSGA-II algorithm is developed to solve the model.