Abstract
In this paper, we study a class of two-stage stochastic optimization for insuring critical path problems, in which the first-stage objective is to minimize the Value-at-Risk, and the second-stage objective is to maximize the insured task durations. Subsequently, we turn the proposed problem into its equivalent form. For general task duration distributions, the problem is also very complex, so we cannot solve it by conventional optimization methods. We use stochastic simulation method to estimate Value-at-Risk. Furthermore, we employ a hybrid binary particle swarm optimization algorithm (BPSO) to solve it, where the dynamic programming method (DPM) is used in the second-stage problem. Finally, we conduct some numerical experiments to illustrate the feasibility and effectiveness of the designed algorithm.
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References
Moder JJ, Phillips CR, Davis EW (1983) Project management with CPM PERT and precedence diagramming. 3rd edn, vol 1, Van Nostrand Reinhold, New York, pp 345–362
Chen YL, Rinks D, Tang K (1997) Critical path in an activity network with time constraints. Eur J Oper Res 100:122–133
Guerriero F, Talarico L (2010) A solution approach to find the critical path in a time-constrained activity network. Comput Oper Res 37:1557–1569
Bowman RA (1995) Efficient estimation of arc criticalities in stochastic activity networks. Manage Sci 41:58–67
Mitchell G, Klastorin T (2007) An effective methodology for the stochastic project compression problem. IIE Trans 39:957–969
Shen S, Smith JC, Ahmed S (2010) Expectation and chance-constrained models and algorithms for insuring critical paths. Manage Sci 56:1794–1814
Kennedy J, Eberhart RC (1995) Particle swarm optimization. Proceedings of IEEE international conference on neural networks, vol 1. Piscataway, pp 1942–1948
Liu Y, Wu X, Hao F (2012) A new chance-variance optimization criterion for portfolio selection in uncertain decision systems. Expert Syst Appl 39:6514–6526
Kageyama M, Fujii T, Kanefuji K, Tsubaki H (2011) An extension of risk measures using non-precise a-priori densities. J Uncertain Syst 5:314–320
Birge JR, Louveaux F (2011) Introduction to stochastic programming. 2nd edn, vol 1. Springer Science + Business Media LLC, New York, pp 678–692
Bellman RE (1957) Dynamic programming, vol 1. Princeton University Press, New Jersey, pp 256–284
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No.60974134), and the Natural Science Foundation of Hebei Province (No.A2011201007).
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Li, Z., Liu, Y., Zang, W. (2013). Stochastic Insuring Critical Path Problem with Value-at-Risk Criterion. In: Yang, Y., Ma, M. (eds) Proceedings of the 2nd International Conference on Green Communications and Networks 2012 (GCN 2012): Volume 3. Lecture Notes in Electrical Engineering, vol 225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35470-0_1
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DOI: https://doi.org/10.1007/978-3-642-35470-0_1
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