Purpose 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. Design/methodology/approach 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. Findings 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. Practical implications The proposed model and algorithm can be used for scheduling activities of small- and large-size real-world projects. Originality/value 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.
PurposeThe purpose of this research is to study the Multi-Skill Resource-Constrained Multi-Project Scheduling Problem (MSRCMPSP), where (1) durations of activities depend on the familiarity levels of assigned workers, (2) more efficient workers demand higher per-day salaries, (3) projects have different due dates and (4) the budget of each period varies over time. The proposed model is bi-objective, and its objectives are minimization of completion times and costs of all projects, simultaneously.Design/methodology/approachThis paper proposes a two-phase approach based on the Statistical Process Control (SPC) to solve this problem. This approach aims to develop a control chart so as to monitor the performance of an optimizer during the optimization process. In the first phase, a multi-objective statistical model has been used to obtain control limits of this chart. To solve this model, a Multi-Objective Greedy Randomized Adaptive Search Procedure (MOGRASP) has been hired. In the second phase, the MSRCMPSP is solved via a New Version of the Multi-Objective Variable Neighborhood Search Algorithm (NV-MOVNS). In each iteration, the developed control chart monitors the performance of the NV-MOVNS to obtain proper solutions. When the control chart warns about an out-of control state, a new procedure based on the Conway’s Game of Life, which is a cellular automaton, is used to bring the algorithm back to the in-control state.FindingsThe proposed two-phase approach has been used in solving several standard test problems available in the literature. The results are compared with the outputs of some other methods to assess the efficiency of this approach. Comparisons imply the high efficiency of the proposed approach in solving test problems with different sizes.Practical implicationsThe proposed model and approach have been used to schedule multiple projects of a construction company in Iran. The outputs show that both the model and the NV-MOVNS can be used in real-world multi-project scheduling problems.Originality/valueDue to the numerous numbers of studies reviewed in this research, the authors discovered that there are few researches on the multi-skill resource-constrained multi-project scheduling problem (MSRCMPSP) with the aforementioned characteristics. Moreover, none of the previous researches proposed an SPC-based solution approach for meta-heuristics in order to solve the MSRCMPSP.
This paper addresses the Multi-Skill Resource-Constrained Project Scheduling Problem with Transfer Times (MSRCPSP-TT). A new model has been developed that incorporates the presence of transfer times within the multi-skill RCPSP. The proposed model aims to minimize project’s duration and cost, concurrently. The MSRCPSP-TT is an NP-hard problem; therefore, a Multi-Objective Multi-Agent Optimization Algorithm (MOMAOA) is proposed to acquire feasible schedules. In the proposed algorithm, each agent represents a feasible solution that works with other agents in a grouped environment. The agents evolve due to their social, autonomous, and self-learning behaviors. Moreover, the adjustment of environment helps the evolution of agents as well. Since the MSRCPSP-TT is a multi-objective optimization problem, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used in different procedures of the MOMAOA. Another novelty of this paper is the application of TOPSIS in different procedures of the MOMAOA. These procedures are utilized for: (1) detecting the leader agent in each group, (2) detecting the global best leader agent, and (3) the global social behavior of the MOMAOA. The performance of the MOMAOA has been analyzed by solving several benchmark problems. The results of the MOMAOA have been validated through comparisons with three other meta-heuristics. The parameters of algorithms are determined by the Response Surface Methodology (RSM). The Kruskal-Wallis test is implemented to statistically analyze the efficiency of methods. Computational results reveal that the MOMAOA can beat the other three methods according to several testing metrics. Furthermore, the impact of transfer times on project’s duration and cost has been assessed. The investigations indicate that resource transfer times have significant impact on both objectives of the proposed model
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