# American Institute of Mathematical Sciences

April  2016, 12(2): 565-593. doi: 10.3934/jimo.2016.12.565

## Bi-level multiple mode resource-constrained project scheduling problems under hybrid uncertainty

 1 School Economics & Management, Nanjing University of Science and Technology, Nanjing 210094, China 2 State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610064

Received  June 2014 Revised  February 2015 Published  June 2015

This study focuses on the multi-mode resource-constrained projects scheduling problem (MRCPSP), which considers the complex hierarchical organization structure and hybrid uncertainty environment in the decision making process. A bi-level multi-objective MRCPSP model with fuzzy random coefficients and bi-random coefficients is developed for the MRCPSP. In the model, construction contractor, the upper level decision maker (ULDM), aims to minimize the consumption of resources and maximize the quality level of project. Meanwhile, outsourcing partner, the lower level decision maker (LLDM), tries to schedule the activities under resource allocation with the objective of minimizing the total tardiness penalty cost. To deal with the uncertainty variables, the fuzzy random parameters are transformed into the trapezoidal fuzzy variables, which are de-fuzzified by the expected value subsequently. For the bi-random parameters, the expected value operator is employed. After obtaining the equivalent crisp model, the passive congregation-based bi-level multiple objective particle swarm optimization algorithm (PC-based BL-MOPSO) is designed to obtain the Pareto solutions. Finally, a practical application is presented to verify the practicability of the proposed bi-level multi-objective MRCPSP model and the efficiency of algorithm.
Citation: Zhe Zhang, Jiuping Xu. Bi-level multiple mode resource-constrained project scheduling problems under hybrid uncertainty. Journal of Industrial & Management Optimization, 2016, 12 (2) : 565-593. doi: 10.3934/jimo.2016.12.565
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