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Learning process on priority rules to solve the RCMPSP


The priority rules are extensively used as a useful decision making technique for managers in single and multiple projects with limited resources, mainly because of their speed and simplicity. However, the question of which priority rule to use has been discussed without conclusive guidance. There is not any rule which performs better than any other in all instances. In this paper we propose an easy and quick learning process to determine which priority rule is the best for each instance. The analysis was carried out with 34 popular priority rules in 26 benchmarking problems. However, the process is capable of using any set of priority rules. As expected, every instance has its own best priority rule. It is also demonstrated that the selection of the most appropriate priority rule is extremely relevant, even when any meta-heuristic is used to solve the problem. In particular, we focus on genetic algorithms because of their high performance in scheduling problems. Our results show that a wrong choice of priority rule is not compensated by the high performance of the meta-heuristic.

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  1. The extension to the dynamic RCMPSP is immediate.

  2. The parents are selected according to a spin of a roulette wheel which is weighted according to the fitness values. High-fit string has more area assigned to it on the wheel and hence, a higher probability of ending up as the choice when the biased roulette wheel is spun.

  3. Two-points indicate the positions in the string to create a parents’ substring. Parent 1 substrings are directly inherited by children 1. The remaining genes of children 1 are inherited from parent 2. For more details about operators:

  4. Two values exchange their positions in the string.


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Correspondence to E. Pérez Vázquez.



See Appendix Tables 3, 4, 5, 6 and 7.

Table 3 Priority rules
Table 4 Tie breakers
Table 5 Main characteristic of the instances
Table 6 Instances, optimum, PRs and TBs for the solution of minimizing \(C_{max}\) when using PR, when using learning on PR and when using learning on PR + GA
Table 7 Instances, optimum,PRs and TBs for the solution of minimizing average percent delay when using PR, when using learning on PR and when using learning on PR + GA

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Vázquez, E.P., Calvo, M.P. & Ordóñez, P.M. Learning process on priority rules to solve the RCMPSP. J Intell Manuf 26, 123–138 (2015).

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  • Project scheduling
  • Priority rules
  • Resource constrained multi-project scheduling
  • Learning process
  • Genetic algorithm