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:, , ().

[2]

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

[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.

[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.

[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.

[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.

[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.

[8]

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

[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.

[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.

[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.

[12]

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

[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.

[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).

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[25]

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

[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.

[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.

[28]

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

[29]

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

[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).

[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.

[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.

[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.

[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.

[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.

[36]

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

[37]

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

[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.

[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.

[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.

[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.

[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.

[43]

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

[44]

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

[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.

[46]

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

[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.

[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.

[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.

show all references

References:
[1]

China Water, URL:, , ().

[2]

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

[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.

[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.

[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.

[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.

[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.

[8]

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

[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.

[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.

[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.

[12]

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

[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.

[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).

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[25]

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

[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.

[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.

[28]

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

[29]

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

[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).

[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.

[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.

[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.

[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.

[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.

[36]

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

[37]

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

[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.

[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.

[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.

[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.

[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.

[43]

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

[44]

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

[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.

[46]

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

[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.

[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.

[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.

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