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
References:
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China Water, URL:, , ().   Google Scholar

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Xiluodu, Chinese National Committee on Large Dams,, URL: , ().   Google Scholar

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E. Ammar, On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem,, Information Sciences, 178 (2008), 468.  doi: 10.1016/j.ins.2007.03.029.  Google Scholar

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O. Atli and C. Kahraman, Fuzzy resource-constrained project scheduling using taboo search algorithm,, International Journal of Intelligent Systems, 27 (2012), 873.  doi: 10.1002/int.21552.  Google Scholar

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H. Aytug, M. Lawley and et al., Executing production schedules in the face of uncertainties: A review and some future directions,, European Journal of Operational Research, 161 (2005), 86.  doi: 10.1016/j.ejor.2003.08.027.  Google Scholar

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S. Bag, D. Chakraborty and A. Roy, A production inventory model with fuzzy random demand and with flexibility and reliability considerations,, Computers and Industrial Engineering, 56 (2009), 411.  doi: 10.1016/j.cie.2008.07.001.  Google Scholar

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T. Bhaskar, M. Pal and et al, A heuristic method for RCPSP with fuzzy activity times,, European Journal of Operational Research, 208 (2011), 57.  doi: 10.1016/j.ejor.2010.07.021.  Google Scholar

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J. Cai, Hydropower in China,, Master Thesis, (2009).   Google Scholar

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W.Chen, R. Xiao and H. Lu, A chaotic PSO approach to multi-mode resource-constraint project scheduling with uncertainty,, International Journal of Computational Science and Engineering, 6 (2011), 5.   Google Scholar

[10]

J. Choi M. Realff and J. Lee, Dynamic programmingin a heuristically confined state space: astochastic resource-constrained project scheduling application,, Computers and Chemical Engineering, 28 (2004), 1039.   Google Scholar

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F. Deblaere, E. Demeulemeester and W. Herroelen, Proactive policies for the stochastic resource-constrained project scheduling problem,, European Journal of Operational Research, 214 (2011), 308.  doi: 10.1016/j.ejor.2011.04.019.  Google Scholar

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S. Elmaghraby, Activity Networks-Project Planning and Control by Network Models,, New York: Wiley, (1977).   Google Scholar

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R. Freeman, A generalized network approach to project activity sequencing,, IRE Transactions on Engineering Management, 7 (1960), 103.  doi: 10.1109/IRET-EM.1960.5007550.  Google Scholar

[14]

L. Gan and J. Xu, Control risk for multi-mode resource-constrained project scheduling problem under hybrid uncertainty,, Journal of Management in Engineering, (2013).   Google Scholar

[15]

Y. Gao, G. Zhang and et al., Particle swarm optimization for bi-level pricing problems in supply chains,, Journal of Global Optimization, 51 (2011), 245.  doi: 10.1007/s10898-010-9595-8.  Google Scholar

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S. He, Q. Wu and et al., A particle swarm optimizer with passive congregation,, BioSystems, 78 (2004), 135.  doi: 10.1016/j.biosystems.2004.08.003.  Google Scholar

[17]

W. Herroelen and R. Leus, Project scheduling under uncertainty: Survey and research potentials,, European Journal of Operational Research, 165 (2005), 289.  doi: 10.1016/j.ejor.2004.04.002.  Google Scholar

[18]

H. Ke and B. Liu, Project scheduling problem with stochastic activity duration times,, Applied Mathematics and Computation, 168 (2005), 342.  doi: 10.1016/j.amc.2004.09.002.  Google Scholar

[19]

B. Keller and G. Bayraksan, Scheduling jobs sharing multiple resources under uncertainty: A stochastic programming approach,, IIE Transactions, 42 (2009), 16.  doi: 10.1080/07408170902942683.  Google Scholar

[20]

J. Kennedy and R. Eberhart, Particle swarm optimization,, In Proceedings of the IEEE Conference on Neural Networks, (1995), 1942.  doi: 10.1109/ICNN.1995.488968.  Google Scholar

[21]

E. Klerides and E. Hadjiconstantinou, A decomposition-based stochastic programming approach for the project scheduling problem under time/cost trade-off settings and uncertain durations,, Computers and Operations Research, 37 (2010), 2131.  doi: 10.1016/j.cor.2010.03.002.  Google Scholar

[22]

A. Kovács and T. Kis, Constraint programming approach to a bilevel scheduling problem,, Constraints, 16 (2011), 317.  doi: 10.1007/s10601-010-9102-3.  Google Scholar

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G. Kopanos, L. Puigjaner and M. Georgiadis, A bi-level decomposition methodology for scheduling batch chemical production facilities,, Computer Aided Chemical Engineering, 1627 (2009), 681.  doi: 10.1016/S1570-7946(09)70334-7.  Google Scholar

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R. Kuo and C. Huang, Application of particle swarm optimization algorithm for solving bi-level linear programming problem,, Computers and Mathematics with Applications, 58 (2009), 678.  doi: 10.1016/j.camwa.2009.02.028.  Google Scholar

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H. Kwakernaak, Fuzzy random variables-I, definitions and theorems,, Information Sciences, 15 (1978), 1.  doi: 10.1016/0020-0255(78)90019-1.  Google Scholar

[26]

O. Lambrechts, E. Demeulemeester and W. Herroelen, Proactive and reactive strategies for resource-constrained project scheduling with uncertain resource availabilities,, Journal of Scheduling, 11 (2008), 369.  doi: 10.1007/s10951-007-0021-0.  Google Scholar

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O. Lambrechts, E. Demeulemeester and W. Herroelen, A tabu search procedure for developing robust predictive project schedules,, International Journal of Production Economics, 111 (2008), 493.  doi: 10.1016/j.ijpe.2007.02.003.  Google Scholar

[28]

J. Li and J. Xu, A novel selection model in a hybrid uncertain environment,, Omega, 37 (2009), 439.   Google Scholar

[29]

B. Liu and Y. Liu, Expected value of fuzzy variable and fuzzy expected value models,, IEEE Transactions on Fuzzy Systems, 10 (2002), 445.   Google Scholar

[30]

Y. Lu, Key technologies for the construction of the Xiluodu high arch dam on the Jinsha River in the development of hydropower in western China,, China Three Gorges Copporation, (2012).   Google Scholar

[31]

J. Nematian, K. Eshghi and A. Jahromi, A resource-constrained project scheduling problem with fuzzy random duration,, Journal of Uncertain Systems, 4 (2010), 123.   Google Scholar

[32]

H. Peng, Z. Chen and L. Sun, A bilevel program for solving project scheduling problems in network level pavement management system,, Journal of Tongji University (Natural Science), 38 (2010), 380.   Google Scholar

[33]

J. Peng and B. Liu, Birandom variables and birandom programming,, Computers and Industrial Engineering, 53 (2007), 433.  doi: 10.1016/j.cie.2004.11.003.  Google Scholar

[34]

H. Prade, Using fuzzy set theory in a scheduling problem: A case study,, Fuzzy Sets and Systems, 2 (1979), 153.  doi: 10.1016/0165-0114(79)90022-8.  Google Scholar

[35]

M. Puri and D. Ralescu, Fuzzy random variables,, Journal of Mathematical Analysis and Applications, 114 (1986), 409.  doi: 10.1016/0022-247X(86)90093-4.  Google Scholar

[36]

Y. Shi and R. Eberhart, Particle swarm optimization,, In Proc. IEEE Int. Conf. on Neural Networks, (1998), 69.   Google Scholar

[37]

B. Xiao, Key technical issues in design of Xiluodu project,, China Three Gorges Construction, 11 (2004), 34.   Google Scholar

[38]

J. Xu and C. Ding, A class of chance constrained multiobjective linear programming with birandom coefficients and its application to vendors selection,, International Journal of Production Economics, 131 (2011), 709.  doi: 10.1016/j.ijpe.2011.02.020.  Google Scholar

[39]

J. Xu and J. Gang, Multi-objective bilevel construction material transportation scheduling in large-scale construction projects under a fuzzy random environment,, Transportation Planning and Technology, 36 (2013), 352.  doi: 10.1080/03081060.2013.798486.  Google Scholar

[40]

J. Xu and Z. Zeng, A dynamic programming-based particle swarm optimization algorithm for an inventory management problem under uncertainty,, Engineering Optimization, (2012).  doi: 10.1080/0305215X.2012.709514.  Google Scholar

[41]

J. Xu and Z. Zhang, A fuzzy random resource-constrained scheduling model with multiple projects and its application to a working procedure in a large-scale water conservancy and hydropower construction project,, Journal of Scheduling, 15 (2012), 253.  doi: 10.1007/s10951-010-0173-1.  Google Scholar

[42]

J. Xu and X. Zhou, A class of multi-objective expected value decision-making model with bi-random coefficients and its application to flow shop scheduling problem,, Information Sciences, 179 (2009), 2997.  doi: 10.1016/j.ins.2009.04.009.  Google Scholar

[43]

L. Yan, Chance-constrained portfolio selection with bi-random returns,, Modern Applied Science, 3 (2009), 161.   Google Scholar

[44]

H. Zhang and C. Tam, Multimode project scheduling based on particle swarm optimization,, Computer-Aided Civil and Infrastructure Engineering, 21 (2006), 93.   Google Scholar

[45]

T. Zhang T. Hu and et al., An improved particle swarm optimization for solving bilevel multiobjective programming problem,, Journal of Applied Mathematics, 21 (2012).  doi: 10.1155/2012/626717.  Google Scholar

[46]

Z. Zhang, Bi-level Multi-objective Resource-constrained Project Scheduling Models under Complex Random Phenomena and the Application,, Doctoral Dissertation, (2011).   Google Scholar

[47]

Z. Zhang and J. Xu, A multi-mode resource-constrained project scheduling model with bi-random coefficients for drilling grouting construction project,, International Journal of Civil Engineering, 11 (2013), 1.   Google Scholar

[48]

G. Zhu, J. Bard and G. Yu, A branch-and-cut procedure for the multimode resource-constrained project-scheduling problem,, INFORMS Journal on Computing, 18 (2006), 377.  doi: 10.1287/ijoc.1040.0121.  Google Scholar

[49]

G. Zhu, J. Bard and G. Yu, A two-stage stochastic programming approach for project planning with uncertain activity durations,, Journal of Scheduling, 10 (2007), 167.  doi: 10.1007/s10951-007-0008-x.  Google Scholar

show all references

References:
[1]

China Water, URL:, , ().   Google Scholar

[2]

Xiluodu, Chinese National Committee on Large Dams,, URL: , ().   Google Scholar

[3]

E. Ammar, On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem,, Information Sciences, 178 (2008), 468.  doi: 10.1016/j.ins.2007.03.029.  Google Scholar

[4]

O. Atli and C. Kahraman, Fuzzy resource-constrained project scheduling using taboo search algorithm,, International Journal of Intelligent Systems, 27 (2012), 873.  doi: 10.1002/int.21552.  Google Scholar

[5]

H. Aytug, M. Lawley and et al., Executing production schedules in the face of uncertainties: A review and some future directions,, European Journal of Operational Research, 161 (2005), 86.  doi: 10.1016/j.ejor.2003.08.027.  Google Scholar

[6]

S. Bag, D. Chakraborty and A. Roy, A production inventory model with fuzzy random demand and with flexibility and reliability considerations,, Computers and Industrial Engineering, 56 (2009), 411.  doi: 10.1016/j.cie.2008.07.001.  Google Scholar

[7]

T. Bhaskar, M. Pal and et al, A heuristic method for RCPSP with fuzzy activity times,, European Journal of Operational Research, 208 (2011), 57.  doi: 10.1016/j.ejor.2010.07.021.  Google Scholar

[8]

J. Cai, Hydropower in China,, Master Thesis, (2009).   Google Scholar

[9]

W.Chen, R. Xiao and H. Lu, A chaotic PSO approach to multi-mode resource-constraint project scheduling with uncertainty,, International Journal of Computational Science and Engineering, 6 (2011), 5.   Google Scholar

[10]

J. Choi M. Realff and J. Lee, Dynamic programmingin a heuristically confined state space: astochastic resource-constrained project scheduling application,, Computers and Chemical Engineering, 28 (2004), 1039.   Google Scholar

[11]

F. Deblaere, E. Demeulemeester and W. Herroelen, Proactive policies for the stochastic resource-constrained project scheduling problem,, European Journal of Operational Research, 214 (2011), 308.  doi: 10.1016/j.ejor.2011.04.019.  Google Scholar

[12]

S. Elmaghraby, Activity Networks-Project Planning and Control by Network Models,, New York: Wiley, (1977).   Google Scholar

[13]

R. Freeman, A generalized network approach to project activity sequencing,, IRE Transactions on Engineering Management, 7 (1960), 103.  doi: 10.1109/IRET-EM.1960.5007550.  Google Scholar

[14]

L. Gan and J. Xu, Control risk for multi-mode resource-constrained project scheduling problem under hybrid uncertainty,, Journal of Management in Engineering, (2013).   Google Scholar

[15]

Y. Gao, G. Zhang and et al., Particle swarm optimization for bi-level pricing problems in supply chains,, Journal of Global Optimization, 51 (2011), 245.  doi: 10.1007/s10898-010-9595-8.  Google Scholar

[16]

S. He, Q. Wu and et al., A particle swarm optimizer with passive congregation,, BioSystems, 78 (2004), 135.  doi: 10.1016/j.biosystems.2004.08.003.  Google Scholar

[17]

W. Herroelen and R. Leus, Project scheduling under uncertainty: Survey and research potentials,, European Journal of Operational Research, 165 (2005), 289.  doi: 10.1016/j.ejor.2004.04.002.  Google Scholar

[18]

H. Ke and B. Liu, Project scheduling problem with stochastic activity duration times,, Applied Mathematics and Computation, 168 (2005), 342.  doi: 10.1016/j.amc.2004.09.002.  Google Scholar

[19]

B. Keller and G. Bayraksan, Scheduling jobs sharing multiple resources under uncertainty: A stochastic programming approach,, IIE Transactions, 42 (2009), 16.  doi: 10.1080/07408170902942683.  Google Scholar

[20]

J. Kennedy and R. Eberhart, Particle swarm optimization,, In Proceedings of the IEEE Conference on Neural Networks, (1995), 1942.  doi: 10.1109/ICNN.1995.488968.  Google Scholar

[21]

E. Klerides and E. Hadjiconstantinou, A decomposition-based stochastic programming approach for the project scheduling problem under time/cost trade-off settings and uncertain durations,, Computers and Operations Research, 37 (2010), 2131.  doi: 10.1016/j.cor.2010.03.002.  Google Scholar

[22]

A. Kovács and T. Kis, Constraint programming approach to a bilevel scheduling problem,, Constraints, 16 (2011), 317.  doi: 10.1007/s10601-010-9102-3.  Google Scholar

[23]

G. Kopanos, L. Puigjaner and M. Georgiadis, A bi-level decomposition methodology for scheduling batch chemical production facilities,, Computer Aided Chemical Engineering, 1627 (2009), 681.  doi: 10.1016/S1570-7946(09)70334-7.  Google Scholar

[24]

R. Kuo and C. Huang, Application of particle swarm optimization algorithm for solving bi-level linear programming problem,, Computers and Mathematics with Applications, 58 (2009), 678.  doi: 10.1016/j.camwa.2009.02.028.  Google Scholar

[25]

H. Kwakernaak, Fuzzy random variables-I, definitions and theorems,, Information Sciences, 15 (1978), 1.  doi: 10.1016/0020-0255(78)90019-1.  Google Scholar

[26]

O. Lambrechts, E. Demeulemeester and W. Herroelen, Proactive and reactive strategies for resource-constrained project scheduling with uncertain resource availabilities,, Journal of Scheduling, 11 (2008), 369.  doi: 10.1007/s10951-007-0021-0.  Google Scholar

[27]

O. Lambrechts, E. Demeulemeester and W. Herroelen, A tabu search procedure for developing robust predictive project schedules,, International Journal of Production Economics, 111 (2008), 493.  doi: 10.1016/j.ijpe.2007.02.003.  Google Scholar

[28]

J. Li and J. Xu, A novel selection model in a hybrid uncertain environment,, Omega, 37 (2009), 439.   Google Scholar

[29]

B. Liu and Y. Liu, Expected value of fuzzy variable and fuzzy expected value models,, IEEE Transactions on Fuzzy Systems, 10 (2002), 445.   Google Scholar

[30]

Y. Lu, Key technologies for the construction of the Xiluodu high arch dam on the Jinsha River in the development of hydropower in western China,, China Three Gorges Copporation, (2012).   Google Scholar

[31]

J. Nematian, K. Eshghi and A. Jahromi, A resource-constrained project scheduling problem with fuzzy random duration,, Journal of Uncertain Systems, 4 (2010), 123.   Google Scholar

[32]

H. Peng, Z. Chen and L. Sun, A bilevel program for solving project scheduling problems in network level pavement management system,, Journal of Tongji University (Natural Science), 38 (2010), 380.   Google Scholar

[33]

J. Peng and B. Liu, Birandom variables and birandom programming,, Computers and Industrial Engineering, 53 (2007), 433.  doi: 10.1016/j.cie.2004.11.003.  Google Scholar

[34]

H. Prade, Using fuzzy set theory in a scheduling problem: A case study,, Fuzzy Sets and Systems, 2 (1979), 153.  doi: 10.1016/0165-0114(79)90022-8.  Google Scholar

[35]

M. Puri and D. Ralescu, Fuzzy random variables,, Journal of Mathematical Analysis and Applications, 114 (1986), 409.  doi: 10.1016/0022-247X(86)90093-4.  Google Scholar

[36]

Y. Shi and R. Eberhart, Particle swarm optimization,, In Proc. IEEE Int. Conf. on Neural Networks, (1998), 69.   Google Scholar

[37]

B. Xiao, Key technical issues in design of Xiluodu project,, China Three Gorges Construction, 11 (2004), 34.   Google Scholar

[38]

J. Xu and C. Ding, A class of chance constrained multiobjective linear programming with birandom coefficients and its application to vendors selection,, International Journal of Production Economics, 131 (2011), 709.  doi: 10.1016/j.ijpe.2011.02.020.  Google Scholar

[39]

J. Xu and J. Gang, Multi-objective bilevel construction material transportation scheduling in large-scale construction projects under a fuzzy random environment,, Transportation Planning and Technology, 36 (2013), 352.  doi: 10.1080/03081060.2013.798486.  Google Scholar

[40]

J. Xu and Z. Zeng, A dynamic programming-based particle swarm optimization algorithm for an inventory management problem under uncertainty,, Engineering Optimization, (2012).  doi: 10.1080/0305215X.2012.709514.  Google Scholar

[41]

J. Xu and Z. Zhang, A fuzzy random resource-constrained scheduling model with multiple projects and its application to a working procedure in a large-scale water conservancy and hydropower construction project,, Journal of Scheduling, 15 (2012), 253.  doi: 10.1007/s10951-010-0173-1.  Google Scholar

[42]

J. Xu and X. Zhou, A class of multi-objective expected value decision-making model with bi-random coefficients and its application to flow shop scheduling problem,, Information Sciences, 179 (2009), 2997.  doi: 10.1016/j.ins.2009.04.009.  Google Scholar

[43]

L. Yan, Chance-constrained portfolio selection with bi-random returns,, Modern Applied Science, 3 (2009), 161.   Google Scholar

[44]

H. Zhang and C. Tam, Multimode project scheduling based on particle swarm optimization,, Computer-Aided Civil and Infrastructure Engineering, 21 (2006), 93.   Google Scholar

[45]

T. Zhang T. Hu and et al., An improved particle swarm optimization for solving bilevel multiobjective programming problem,, Journal of Applied Mathematics, 21 (2012).  doi: 10.1155/2012/626717.  Google Scholar

[46]

Z. Zhang, Bi-level Multi-objective Resource-constrained Project Scheduling Models under Complex Random Phenomena and the Application,, Doctoral Dissertation, (2011).   Google Scholar

[47]

Z. Zhang and J. Xu, A multi-mode resource-constrained project scheduling model with bi-random coefficients for drilling grouting construction project,, International Journal of Civil Engineering, 11 (2013), 1.   Google Scholar

[48]

G. Zhu, J. Bard and G. Yu, A branch-and-cut procedure for the multimode resource-constrained project-scheduling problem,, INFORMS Journal on Computing, 18 (2006), 377.  doi: 10.1287/ijoc.1040.0121.  Google Scholar

[49]

G. Zhu, J. Bard and G. Yu, A two-stage stochastic programming approach for project planning with uncertain activity durations,, Journal of Scheduling, 10 (2007), 167.  doi: 10.1007/s10951-007-0008-x.  Google Scholar

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