Proactive-reactive project scheduling with flexibility and quality requirements

1. Proactive-reactive project scheduling with flexibility and quality requirements Mario Brčić Prof. dr. sc. Damir Kalpić University of Zagreb, Faculty of Electrical Engineering and Computing August 2014

2. Overview • Introduction • Project scheduling under uncertainty • Previous research results • New model • Preliminary results • Conclusion

3. Introduction Increased services and products complexity • More • complex projects • High activity count • Subcontractors • Suppliers • Due dates Coordination

4. Introduction • Management • Planning • Scheduling • Control • Mostly NP-hard problems • Efficiency? Source: Standish CHAOS 2012 report

5. Introduction • Efficiency? • Boeing 787 Dreamliner • Large degree of outsourcing • Exceeding budget by ~150 % (>10 bn $) • Exceeding planned due dates by >60% (>3 years) • Billions of dollars of additional losses due to cancelled orders, delivery delay penalties and damage to the reputation • Lockheed Martin F-35 • Exceeing budget by >60% (>150 bn $) • Exceeding planned due dates by >60% (~7 years) • Still in execution

6. Introduction Historical sequence • Critical Path Method • Program evaluation and review technique (PERT) • Resource Constrained Project Scheduling Problems (RCPSP) • Critical Chain Project Management • RCPSP generalizations taking into account the uncertainty

7. Project Scheduling under Uncertainty • Stochastic Resource Constrained Project Scheduling Problems (SRCPSP) • probability distribution for uncertainty is known (described by events) • random variables model uncertain elements • Fuzzy Resource Constrained Project Scheduling Problems • degrees of fuzzy set memberships is known for uncertainty • fuzzy numbers model uncertain elements • Robust Resource Constrained Project Scheduling Problems • only possible outcomes of uncertain events are known • minimax, minimin, minimax regret, ....

8. Project Scheduling under Uncertainty • Baseline schedule • Coordination • Commiting between project collaborators • Prior to the project execution start

9. Project Scheduling under Uncertainty • Solutions: policies (strategies) • Functions that map from the states to the controls • Candidate solution evaluation often “too expensive” - simulation • Solution approaches • Predictive • Point estimates, no anticipation of variability • Proactive • Increasing the degree of robustness • Reactive • Dynamic changes • Baseline repairing • Completely online (dynamic) methods Static

10. RCPSP • Combinatorial problem defined by n-tuple (V,E,d,R,B,D,f) • Activities - V={0,...., n+1} V’=V/{0,n+1} • Precedence relations - • Directed acyclic graph G(A,E) • Activity durations - • Renewable resources - R={R1,..., Rr} • Resource availabilities - • Activity demands - • Objective/cost function - c:X→R Single execution mode

11. RCPSP with uncertain activity durations • Combinatorial problem defined by n-tuple (V,E,Ω,F,P,d,R,B,D,f) • Activities - V={0,...., n+1} V’=V/{0,n+1} • Precedence relations - • Directed acyclic graph G(A,E) • Activity durations - • Renewable resources - R={R1,..., Rr} • Resource availabilities - • Activity demands - • Objective/cost function - c:S×Π→R • Probability space - (Ω,F,P) Random variable More complex domain Information about uncertainty

12. Previous research results • Reactive procedures • Möhring et al. 1984 • Theoretical basis • Policy families • Parameterized policies • Choi 2007, Csaji 2008 – Markov decision process • Reinforcement learning • Offline computational burden

13. Previous research results • Proactive procedures • Protected baseline • Robustness measures • Quality robustness • Timely project completion probability • Expected due date exceeding cost • Schedule stability measure - Leus Herroelen, 2004 • Combined robustness measures • Bi-criteria measure of stability and quality

14. Previous research results • Proactive-reactive procedures • Combined measures : stability+quality • Van de Vonder et al., 2006 • Defined new reactive policy family • Offline policy calculation • Van de Vonder et al., 2007 • Baseline schedule repair policies • Sampling with point estimates • Don’t change baseline schedule • Online policy calculation

15. Previous research results • Deblaere et al., 2011 • Combined robustness measure • Expected due date penalty/bonus • Expected asymmetric schedule stability cost • Resource-based policies with release times • Priority vector • Release times vector • Simulation-based descend (SBD) • Offline computational burden • Integrated procedure for finding proactive schedule and reactive policy • The best performance so far

16. Previous research results • Baseline schedule fixed • Excessive commiting problem • Lambrechts, 2007 • Proactive rescheduling • Bi-criteria objective function • New schedule with increased proactivity • New schedule “close” to the preceding • Taboo search for uncertain resource availabilities • Moderate results! • Immediate instability costs outweigh the potential gains

17. Goal • Proactive rescheduling • Schedule stability measure “useless” • Unit cost identical for all changes over each activity • Changes over baseline not desirable • Implies long-term commiting • New robustness measures • Demeulemeester and Herroelen, 2011

18. New robustness measure • Robustness measure (CBF) which depends on: • Size of the schedule change • Temporal distance of the change from the present • More distant changes are more likely to cost less |x-y| t time min(x,y)-t

19. Stability - simplified price Stability measure distance price Asymmetric stability measure (Deblaere et al. 2011.) distance

20. Computational study • Setting similar to Deblare et al., 2011 (smaller scale) 50*6 PSPLIB 30-activity projects + 50*6 PSPLIB 60-activity projects • 1000 scenarios per project • Benchmark – Deblaere et al., 2011. • Mean cost and variance

21. Preliminary performance • 30-activity projects • Improvement in both performance and variance • ...but greater computation time • 60-activity projects • Even greater improvement in both performance and variance • ...again paying with even greater computation time

22. Conclusion • Complex projects • Multiple collaborators - coordination • Due dates • Stability measure • Excessive commitment • Fixed baseline • Proactive rescheduling • Cost-based flexibility • Simulation-based algorithm • Improvement over the best available alternative

23. Questions

24. Literature [1] The Standish Group International, “CHAOS Summary 2009,” 2009. [2] D. Gates, “Boeing celebrates 787 delivery as program’s costs top $32 billion,” The Seattle Times. [Online]. Available: http://seattletimes.com/html/businesstechnology/2016310102_boeing25.html. [Accessed: 10-Mar-2014]. [3] P. Giblin, “F-35 behind schedule, over budget,” azcentral.com. [Online]. Available: http://www.azcentral.com/news/arizona/articles/20140208fighter-plane-behind-schedule-over-budget.html. [Accessed: 10-Mar-2014]. [4] E. Demeulemeester and W. Herroelen, Robust Project Scheduling. Now Publishers Inc, 2011. [5] R. H. Möhring, F. J. Radermacher, and G. Weiss, “Stochastic scheduling problems I — General strategies,” Z. Für Oper. Res., vol. 28, no. 7, pp. 193–260, Nov. 1984. [6] R. H. Möhring and F. J. Radermacher, “Introduction to Stochastic Scheduling Problems,” in Contributions to Operations Research, P. D. K. Neumann and P. D. D. Pallaschke, Eds. Springer Berlin Heidelberg, 1985, pp. 72–130. [7] F. Stork, “Stochastic resource-constrained project scheduling,” PhD Thesis, Technical University at Berlin, Berlin, Germany, 2001. [8] F. Ballestín and R. Leus, “Resource‐Constrained Project Scheduling for Timely Project Completion with Stochastic Activity Durations,” Prod. Oper. Manag., vol. 18, no. 4, pp. 459–474, Jul. 2009. [9] B. Ashtiani, R. Leus, and M.-B. Aryanezhad, “New competitive results for the stochastic resource-constrained project scheduling problem: exploring the benefits of pre-processing,” J Sched., vol. 14, no. 2, pp. 157–171, Apr. 2011. [10] B. C. Csáji and L. Monostori, “Adaptive stochastic resource control: a machine learning approach,” J. Artif. Intell. Res., vol. 32, no. 1, pp. 453–486, 2008.

25. Literature [11] J. Choi, M. J. Realff, and J. H. Lee, “A Q-Learning-based method applied to stochastic resource constrained project scheduling with new project arrivals,” Int. J. Robust Nonlinear Control, vol. 17, no. 13, pp. 1214–1231, Sep. 2007. [12] C. Artigues, R. Leus, and F. Talla Nobibon, “Robust optimization for resource-constrained project scheduling with uncertain activity durations,” Flex. Serv. Manuf. J., vol. to appear, pp. 1–31, 2012. [13] R. Leus and W. Herroelen, “Stability and resource allocation in project planning,” IIE Trans., vol. 36, no. 7, pp. 667–682, 2004. [14] F. Deblaere, E. Demeulemeester, W. Herroelen, and S. Van de Vonder, “Robust Resource Allocation Decisions in Resource‐Constrained Projects,” Decis. Sci., vol. 38, no. 1, pp. 5–37, Feb. 2007. [15] S. Van de Vonder, E. Demeulemeester, R. Leus, and W. Herroelen, “Proactive-Reactive Project Scheduling Trade-Offs and Procedures,” in Perspectives in Modern Project Scheduling, vol. 92, J. Józefowska and J. Weglarz, Eds. Springer US, 2006, pp. 25–51. [16] S. Van de Vonder, F. Ballestin, E. Demeulemeester, and W. Herroelen, “Heuristic procedures for reactive project scheduling,” Comput. Ind. Eng., vol. 52, no. 1, pp. 11–28, 2007. [17] F. Deblaere, E. Demeulemeester, and W. Herroelen, “Proactive policies for the stochastic resource-constrained project scheduling problem,” Eur. J. Oper. Res., vol. 214, no. 2, pp. 308–316, Oct. 2011. [18] O. Lambrechts, “Robust project scheduling subject to resource breakdowns,” PhD Thesis, Faculty of Business and Economics, Katholieke Universiteit Leuven, Leuven, Belgium, 2007. [19] M. Brcic, D. Kalpic and M. Katic, “Proactive Reactive Scheduling in Resource Constrained Projects with Flexibility and Quality Robustness Requirements” in Lecture Notes in Computer Science vol. 8596, 2014., pp. 112-124