Scheduling jobs sharing multiple resources under uncertainty: A stochastic programming approach

IIE Transactions (Institute of Industrial Engineers)

Volumn 42, Issue 1, 2010, Pages 16-30

  Keller, Brian ^a   Bayraksan, Güzin ^b  

^a BOOZ ALLEN HAMILTON   (United States)

^b University of Arizona   (United States)

Author keywords

Sampling; Stochastic integer programming; Stochastic scheduling

Indexed keywords

APPROXIMATE SOLUTION; BENDERS DECOMPOSITION; DUE DATES; ENGINEERING CONSULTING; EXACT SOLUTION; INTEGER PROGRAM; MULTIPLE CLASS; MULTIPLE RESOURCES; OPTIMAL SCHEDULE; POTENTIAL APPLICATIONS; RESOURCE CAPACITY; RESOURCE CONSUMPTION; SAMPLING-BASED; SCHEDULING JOBS; SCHEDULING PROBLEM; SEQUENTIAL SAMPLING; SERVICE INDUSTRIES; SOLUTION METHODOLOGY; SOLUTION METHODS; STOCHASTIC SCHEDULING; TEST PROBLEM; TWO STAGE; UNCERTAIN PROCESSING;

DYNAMIC PROGRAMMING; SCHEDULING; STOCHASTIC SYSTEMS;

INTEGER PROGRAMMING;

EID: 77649283579     PISSN: 0740817X     EISSN: 15458830     Source Type: Journal    
DOI: 10.1080/07408170902942683     Document Type: Article

References (46)

1. Aytug, H., Lawley, M., McKay, K., Mohan, S. and Uzsoy, R. (2005) Executing production schedules in the face of uncertainties: a review and some future directions. European Journal of Operational Research, 161, 86-110.
2. Baker, K. and Trietsch, D. (2007) Safe scheduling, in Tutorials in Operations Research, INFORMS, Hanover, MD, pp. 79-101.
3. Bayraksan, G. and Morton, D. (2006) Assessing solution quality in stochastic programs. Mathematical Programming, 108, 495-514.
4. Bayraksan, G. and Morton, D. (2009) A sequential sampling procedure for stochastic programming. Operations Research, forthcoming.
5. Benders, J. (1962) Partitioning procedures for solving mixed-variable programming problems. Numerische Mathematik, 4, 238-252.
6. Birge, J. and Dempster, M. (1996) Stochastic programming approaches to stochastic scheduling. Journal of Global Optimization, 9(3-4), 417-451.
7. Birge, J. and Louveaux, F. (1997) Introduction to Stochastic Programming, Springer, New York, NY.
8. Brucker, P. (2001) Scheduling Algorithms, third edition, Springer, New York, NY.
9. Cai, X., Lee, C. and Li, C. (1998) Minimizing total completion time in two-processor task systems with prespecified processor allocations. Naval Research Logistics, 45, 231-242.
10. Chan, L., Muriel, A. and Simchi-Levi, D. (1998) Parallel machine scheduling, linear programming, and parameter list scheduling heuristics. Operations Research, 46, 729-741.
11. Chen, J. and Lee,C. (1999) Generalmultiprocessor task scheduling. Naval Research Logistics, 46, 57-74.
12. Cooper, D. (1976) Heuristics for scheduling resource constrained projects: An experimental comparison. Management Science, 22, 1186-1194.
13. Deblaere, F., Demeulemeester, E., Herroelen, W. and Van De Vonder, S. (2007) Robust resource allocation decisions in resource-constrained projects. Decision Sciences, 38, 5-37.
14. Denton, B. and Gupta, D. (2003) A sequential bounding approach for optimal appointment scheduling. IIE Transactions, 35, 1003-1016.
15. Drozdowski, M. (1996) Scheduling multiprocessor tasks-an overview. European Journal of Operational Research, 94, 215-230.
16. Dyer,M. andWolsey, L. (1990) Formulating the single machine sequencing problem with release dates as a mixed integer program. Discrete Applied Mathematics, 26, 255-270.
17. Herroelen, W. (2007) Generating robust project baseline schedules. in Tutorials in Operations Research, INFORMS, Hanover,MD, pp. 124- 144.
18. Herroelen,W. and Leus, R. (2005) Project scheduling under uncertainty: Survey and research potentials. European Journal of Operational Research, 165, 289-306.
19. Herroelen, W. and Reyck, B.D. (1999) Phase transitions in project scheduling. Journal of the Operational Research Society, 50, 148-156.
20. Herroelen, W., Reyck, B.D. and Demeulemeester, E. (1998) Resourceconstrained project scheduling: a survey of recent developments. Computers & Operations Research, 25(4), 279-302.
21. Higle, J. and Sen, S. (1996) Stochastic Decomposition: A Statistical Method for Large Scale Stochastic Linear Programming,Kluwer, Dordrecht, The Netherlands.
22. Hiriart-Urruty, J. and Lemaŕechal, C. (1993) Convex Analysis and Minimization Algorithms II. Comprehensive Studies in Mathematics, Springer-Verlag, Berlin.
23. Hoogeveen, J., Van De Velde, S. and Veltman, B. (1994) Complexity of scheduling multiprocessor tasks with prespecified processor allocations. Discrete Applied Mathematics, 55, 259-272.
24. Kiwiel,K. (1990) Proximity control in bundlemethods for convex nondifferentiable minimization. Mathematical Programming, 46, 105-122.
25. Kleywegt, A., Shapiro, A. and Homem-De-Mello, T. (2001) The sample average approximation method for stochastic discrete optimization. SIAM Journal of Optimization, 12, 479-502.
26. Kubale, M. (1987) The complexity of scheduling independent twoprocessor tasks on dedicated processors. Informations Processing Letters, 24, 141-147.
27. Lee, C. and Cai, X. (1999) Scheduling one and two-processor tasks on two parallel processors. IIE Transactions, 31, 445-455.
28. Leus, R. and Herroelen, W. (2004) Stability and resource allocation in project planning. IIE Transactions, 36, 667-682.
29. Linderoth, J. and Wright, S. (2003) Decomposition algorithms for stochastic programming on a computational grid. Computational Optimization and Applications, 24, 207-250.
30. Marchand, H. and Wolsey, L. (1999) The 0-1 knapsack problem with a single continuous variable. Mathematical Programming, 85, 15-33.
31. Miller, A.,Nemhauser,G. and Savelsbergh, M. (2000) On the capacitated lot-sizing and continuous 0-1 knapsack polyhedra. European Journal of Operational Research, 125, 298-315.
32. M̈ohring, R., Schultz, A., Stork, F. and Uetz, M. (2001) On project scheduling with irregular starting time costs. Operations Research Letters, 28, 149-154.
33. M̈ohring, R., Schultz, A., Stork, F. and M. Uetz (2003) Solving project scheduling problems byminimumcut computations. Management Science, 49, 330-350.
34. Morton, D. and Popova, E. (2004) A Bayesian stochastic programming approach to an employee scheduling problem. IIE Transactions, 36, 155-167.
35. Pascoe, T. (1966) Allocation of resources-CPM. Revue Française de Recherche Oṕerationnelle, 38, 31-38.
36. Patterson, J. (1976) Project scheduling: the effects of problem structure on heuristic performance. Naval Research Logistics, 23, 95-123.
37. Queyranne,M. and Schulz, A. (1994) Polyhedral approaches to machine scheduling. Preprint 408/1994, Department of Mathematics, Technical University of Berlin, Berlin, Germany.
38. Ruszczy ́ nski, A. (1986) A regularized decomposition method for minimizing a sum of polyhedral functions. Mathematical Programming, 35, 309-333.
39. Santoso, T., Ahmed, S., Goetschalckx, M. and Shapiro, A. (2005) A stochastic programming approach for supply chain network design under uncertainty. European Journal of Operational Research, 167, 96-115.
40. Shapiro, A. (2003) Monte Carlo sampling methods, in Handbooks in Operations Research and Management Science, Volume 10: Stochastic Programming, Ruszczý nski, A. and Shapiro, A. (eds), Elsevier, Amsterdam, pp. 353-425.
41. Van De Vonder, S. (2006) Proactive-reactive procedures for robust project scheduling. Ph.D. thesis, Department of Decision Sciences and Information Management, Katholieke Universiteit Leuven, Leuven, Belgium.
42. Van De Vonder, S., Demeulemeester, E. and Herroelen,W. (2007) A classification of predictive-reactive project scheduling procedures. Journal of Scheduling, 10, 195-207. (Pubitemid 46866610)
43. Van Slyke, R. and Wets, R. (1969) L-shaped linear programs with applications to optimal control and stochastic programming. SIAM Journal of Applied Mathematics, 17, 638-663.
44. Wolsey, L. (1990) Valid inequalities for 0-1 knapsacks and MIPs with generalised upper bound constraints. Discrete Applied Mathematics, 29, 251-261.
45. Wolsey, L. (1998) Integer Programming, Wiley, New York, NY.
46. Zhu, G., Bard, J. and Yu, G. (2007). A two-stage stochastic programming approach for project planning with uncertain activity durations. Journal of Scheduling, 10, 167-180.