proactive-reactive project scheduling with flexibility and quality requirements mario brčić prof....

Proactive-reactive project scheduling with flexibility and quality requirements

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

OverviewOverview

• Introduction

• Project scheduling under uncertainty

• Previous research results

• New model

• Preliminary results

• Conclusion

2

IntroductionIntroduction

3

Coordination

Increased services and

products complexity

More complex projects• High activity

count• Subcontracto

rs• Suppliers• Due dates


4Source: Standish CHAOS 2012 report

• Management– Planning– Scheduling – Control

• Mostly NP-hard problems

• Efficiency?


5

• 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

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

Project Scheduling under UncertaintyProject 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, ....

7


• Baseline schedule– Coordination

• Commiting between project collaborators– Prior to the project execution start

8


• 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

9

Static

RCPSPRCPSP

• 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

10

AAE

2 nd N

rB NrnD )2(N Single execution

mode

RCPSP with uncertain activity durationsRCPSP 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) 11

AAE

rB NrnD )2(N

2: nd N Random variable

More complex domainInformation about uncertainty

Previous research resultsPrevious 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

12


• 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

13


• 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

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• 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 far15


• 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

16

GoalGoal

• 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

17

New robustness measureNew 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

18

time

t

min(x,y)-t

|x-y|

Stability - simplifiedStability - simplified

19

distance

price

Stability measure

distance

price

Asymmetric stability measure(Deblaere et al.

2011.)

Computational studyComputational study

20

• 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 %100

||

Debl

NewDebl

C

CC

Preliminary performancePreliminary performance

21

• 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

ConclusionConclusion

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• 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

QuestionsQuestions

23

LiteratureLiterature

[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. 24

LiteratureLiterature[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

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proactive-reactive project scheduling with flexibility and quality requirements mario brčić prof....

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