A chance-constrained programming method with credibility measure for solving the multi-skill multi-mode resource-constrained project scheduling problem

This paper addresses a multi-skilled extension of the multi-mode resource-constrained project scheduling problem (MRCPSP) with preemption of activities and generalized precedence relations under uncertainty. The problem is formulated mathematically as a single objective optimization model to minimize the project makespan. Concerning real-world circumstances, amount of non-renewable resources and availability are considered as interval type-2 fuzzy numbers. Therefore, a type-2 fuzzy chance-constrained programming (TFCP) method is developed to tackle the problem. Four unique characteristics are taken into account in this paper concurrently: (i) multi-skilled resources; (ii) renewable and non-renewable resources; (iii) preemptable activities; and (iv) interval type-2 fuzzy parameters. The existence of these practical contributions causes projects schedule, especially construction projects, to be closer to the real-world conditions. The proposed mathematical model is validated and tested on instances from PSPLIB (j12, j16 and j18) and MMLIB (MM50 and MM100) datasets. In this study, the computational results for the first time demonstrate that the number of preemption points depend heavily on fluctuations of non-renewable resources and number of skills. It is also shown that considering multi-skill renewable resources is an effective factor in project makespan. In J20, there were both a four-unit reduction and increase in the number of preemption points achieving by increasing the average amount of available non-renewable resources by 23 units and decreasing it by 22 units, respectively. Additionally, when seven skills of renewable resources were reduced, the number of preemption points increased by seven units. In this problem instance, project is completed within 28 days considering multi-skill renewable resources, whereas the project makespan is reported 33 days without considering them. Various sensitivity analyses are presented to evaluate the proposed mathematical model and the overall solution approach. Comparative analysis is conducted to compare the schedule in crisp and uncertain conditions. Eventually, the importance of considering multi-skill resources in project scheduling is illustrated compared to not considering them.