Project Scheduling Problem with Uncertain Variables

Liang Lin, Ting Lou, Ni Zhan

College of Science, Guilin University of Technology, Guilin, China.

DOI: 10.4236/am.2014.54066                

Abstract

Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling problem with uncertain variables. First, two types of single-objective programming models with uncertain variables as uncertain chance-constrained model and uncertain maximization chance-constrained model are established to meet different management requirements, then they are extended to multi-objective programming model with uncertain variables.

Keywords

Project Scheduling Problem; Uncertain Variable; Single-Objective Programming; Multi-Objective Programming

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Kelley Jr., J.E. (1961) Critical Path Planning and Scheduling: Mathematical Basis. Operations Research, 9, 296-320. http://dx.doi.org/10.1287/opre.9.3.296
[2]	Kelley Jr., J.E. (1963) The Critical Path Method: Resources Planning and Scheduling. Industrial Scheduling, 13, 347365.
[3]	Freeman, R.J. (1960) A Generalized PERT. Operations Research, 8, 281. http://dx.doi.org/10.1287/opre.8.2.281
[4]	Freeman, R.J. (1960) A Generalized Network Approach to Project Activity Sequencing. IRE Transactions on Engineering Management, 7, 103-107. http://dx.doi.org/10.1109/IRET-EM.1960.5007550
[5]	Charnes, A. and Cooper, W.W. (1956) Chance-Constrained Programming. Management Science, 6, 73-79. http://dx.doi.org/10.1287/mnsc.6.1.73
[6]	Golenko-Ginzburg, D. and Gonik, A. (1997) Stochastic Network Project Scheduling with Non-Consumable Limited Resources. International Journal of Production Economics, 48, 29-37.
[7]	Ke, H. and Liu, B.D. (2005) Project Scheduling Problem with Stochastic Activity Duration Times. Applied Mathematics and Computation, 168, 342-353. http://dx.doi.org/10.1016/j.amc.2004.09.002
[8]	Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
[9]	Prade, H. (1979) Using Fuzzy Set Theory in a Scheduling Problem: A Case Study. Fuzzy Sets and Systems, 2, 153-165. http://dx.doi.org/10.1016/0165-0114(79)90022-8
[10]	Ke, H. and B.D. Liu (2004) Project Scheduling Problem with Fuzzy Activity Duration Times. Proceedings of IEEE International Conference on Fuzzy Systems, 2, 819-823.
[11]	Ke, H. and Liu, B.D. (2007) Project Scheduling Problem with Mixed Uncertainty of Randomness and Fuzziness. European Journal of Operational Research, 183, 135-147. http://dx.doi.org/10.1016/j.ejor.2006.09.055
[12]	Kwakernaak, H. (1978) Fuzzy Random Variables—I: Definitions and Theorems. Information Sciences, 15, 1-29. http://dx.doi.org/10.1016/0020-0255(78)90019-1
[13]	Kwakernaak, H. (1979) Fuzzy Random Variables—II: Algorithms and Examples for the Discrete Case. Information Sciences, 17, 253-278. http://dx.doi.org/10.1016/0020-0255(79)90020-3
[14]	Puri, M.L. and Ralescu, D.A. (1986) Fuzzy Random Variables. Journal of Mathematical Analysis and Applications, 114, 409-422. http://dx.doi.org/10.1016/0022-247X(86)90093-4
[15]	Kruse, R. and Meyer, K.D. (1987) Statistics with Vague Data. Springer, Berlin. http://dx.doi.org/10.1007/978-94-009-3943-1
[16]	Liu, Y.K. and Liu, B. (2003) Fuzzy Random Variables: A Scalar Expected Value Operator. Fuzzy Optimization and Decision Making, 2, 143-160. http://dx.doi.org/10.1023/A:1023447217758
[17]	Liu, B.D. (2002) Random Fuzzy Dependent-Chance Programming and Its Hybrid Intelligent Algorithm. Information Sciences, 141, 259-271. http://dx.doi.org/10.1016/S0020-0255(02)00176-7
[18]	Liu, B.D. (2007) Uncertainty Theory. 2nd Edition, Springer-Verlag, Berlin.
[19]	Kolmogorov, A.N. (1933) Grundbegriffe der Wahrscheinlichkeitsrechnung. Julius Springer, Berlin. http://dx.doi.org/10.1007/978-3-642-49888-6
[20]	Liu, Y.H. (2013) Uncertain Random Variables: A Mixture of Uncertainty and Randomness. Soft Computing, 17, 625634.