Qualifying Exam Presentation

Subcontractors Partnering in Resource Management A Cooperative Game Theoretic Approach

Sadegh AsgariPhD Student

Department of Civil Engineering and Engineering Mechanics Columbia University

Outline

• Introduction

• Problem Statement

• Game Theory

• Resource Management Model

• Illustrative Example

• Conclusion

• References

Introduction

Motivation!

Introduction

• Partnering (or cooperation):

– Long-term (Strategic) vs. Short-term– Vertical vs. Horizontal

Individual Planning << Collective Planning

Project Breakdown into Subprojects

Economies of Scale & Resource Sharing

“… a commitment between two or more organizations for the purpose of achieving specific business objectives by maximizing the effectiveness of each participant’s resources.” (CII, 1991)

Introduction• Partnering between GC & Subcontractor (or supplier) Barlow, J. (2000). “Innovation and learning in complex offshore construction projects.” Research

Policy, 29(7-8): 973-989.DeVilbiss, C. E. & Leonard, P. (2000). “Partnering is the foundation of a learning organization.”

Journal of Management in Engineering, 16(4): 47-57. Hartmann et al. (2009). “Relative Importance of Subcontractor Selection Criteria Evidence from

Singapore.” Journal of Construction Engineering and Management, 135, 826. Humphreys, P., Matthews, J., & Kumaraswamy, M. (2003). “Preconstruction project partnering:

From adversarial to collaborative relationships.” Supply Chain Management: An International Journal, 8(2), 166–178.

Eriksson, P. E. (2007). “Cooperation and partnering in facilities construction - empirical application of prisoner's dilemma.” Facilities, 25(1/2): 7-19

• Partnering between Contractors (or Subcontractors)Perng et al. (2005): investigating the possibility of improving profitability through coalition

formation by independent subcontractors. Hsueh and Yan (2011): applying cooperative game theory to allocate joint venture profits among its

members with respect to their contributions.

Outline

• Introduction


• Game Theory



• Conclusion

• References

Problem Statement

• Developing a model for resource management

• If cooperation is agreed, designing fair, efficient, and stable rules for allocating benefits among cooperative subcontractors

A resource leveling model

Partnering: A Cooperative Game

Joint resource management as a case of short-term partnering

Outline

• Introduction


• Game Theory



• Conclusion

• References

Game Theory

• Game Theory: the mathematical study of conflict and cooperation between rational, intelligent decision-makers.– Non-cooperative vs. Cooperative– A useful framework to investigate various aspects of construction

projects (Lazar, 2000).• Applications in Construction ManagementPeña-Mora and Wang (1998): a method for facilitating negotiations and conflict resolution in large-

scale civil engineering projects using game theory and negotiation theory. Ho and Liu (2004): a decision model for analyzing construction claims and examining the existence of

opportunistic bidding behavior based on game theory. Ho (2005): applying game theory to analyze the behavioral dynamics of competing bidders and

project owners. Ho (2006) developing a game theoretic model for government rescue dynamics to provide theoretic

foundations for examining the quality of public-private partnership policies. Medda (2007): examining the process of risk allocation between public and private sectors in

transport infrastructure agreements through a final offer arbitration game to analyze the behavior of the players when faced with opposite objectives in allocation of risks.

Game Theory

• Applications in Construction Management (continued) Shen et al. (2007); Hanaoka and Palapus, (2012): Applying game theory to identify a reasonable

concession period, one of the most important decision variables in arranging a build-operate-transfer (BOT) contract.

Sacks and Harel (2007): applying game theory to explain the influence of reliability degree of the planned schedule on subcontractors’ and project managers’ behaviors under traditional unit price contracting.

Eriksson (2007): Applying game theory to explain the lack of cooperation in buyer-supplier relationships within construction and facilities management, and found that long-term contracting provide cooperation incentives.

Yousefi et al. (2010): a systematic negotiation method for construction disputes based on non-cooperative game theory concepts and considering the attitudes of parties at two complementary levels of decision-making, i.e., strategic and tactical.

Unsal and Taylor (2011): integrating an agent-based simulation model with game theory to examine the hold-up problem in project networks.

Perng et al. (2005): investigating the possibility of improving profitability through coalition formation by independent subcontractors.

Hsueh and Yan (2011): applying cooperative game theory to allocate joint venture profits among its members with respect to their contributions.

Game Theory

• Cooperative Game Theory– How to divide a pie based on the people’s contribution! – Example:

• Feasibility of cooperative allocation solutions:– No player or coalition can do better off by leaving the grand coalition– The Core (Gillies, 1953): set of all (infinite) feasible solutions according

to individual and coalitional rationality.

V(A,B,C)= 3

V(A,B)= 0 V(B,C)= 2V(A)= 0

V(B)= 0V(C)= 0

V(A,C)= 1

The rationale: C > B > A

Game Theory

• Unique solution concepts based on different notions of fairness:– Nash-Harsanyi bargaining solution (Harsanyi, 1959 and 1963) – Nucleolus (Schmeidler, 1969): minimizes the maximum dissatisfaction– Shapley value (Shapley, 1953): the weighted average of the marginal

contributions– τ-value (Tijs, 1981): a feasible compromise between minimum right

and utopia

• Acceptability of cooperative allocation solutions: – Social choice rules or voting theory methods: Plurality rule– Quantitative stability evaluation methods: Propensity to Disrupt

Outline

• Introduction


• Game Theory



• Conclusion

• References

Resource Management Model• Coalition of Subcontractors • Constructing the payoff function of possible coalitions:

– Hariga M. & El-Sayegh S.M. (2011): A resource leveling model– Splitting some activities is allowed– Integer-Linear Programming: always Optimal result– Categorizing the construction resources:

• Constant resources: uniform resource histograms• Temporary resources: available at anytime such as open shop workers

• Objective Function of the Optimization Problem: – Constant resource cost– Temporary resource cost – Acquiring/releasing cost: (e.g. additional orientation)– Splitting cost: (e.g. startup and restarting costs)

Outline

• Introduction


• Game Theory



• Conclusion

• References

Illustrative Example• Example Information

Subcontractors' available resources and overlapping periods Overlapped period with

Atp Availability Period M1 M2 M3 SW OW Subcontractor

1Subcontractor

2Subcontractor

3Sum of overlapped

PeriodSubcontractor 1 day 1 - day 15 1 1 0 4 0 12 days 10 days 22 daysSubcontractor 2 day 4 - day 25 0 3 0 2 0 12 days 15 days 27 daysSubcontractor 3 day 6 - day 20 1 1 0 1 0 10 days 15 days 25 days

Status-quo Gantt charts of subcontractors (individual leveling) Cooperative Gantt chart of subcontractors (leveling by the grand coalition)

Resulted overall cost: $222,540

Grand coalition cost:$190,980

Illustrative ExampleConstant resource profiles

sum of individual cases the grand coalition

Illustrative Example• The Result

Values of the objective function and its components for all possible coalitions ($)Coalition

{1} {2} {3} {1, 2} {1, 3} {2, 3} {1, 2, 3}

Constant resources cost 36,000 6,600 52,500 30,600 60,000 54,600 52,500Idle resources returns 6,660 5,100 6,900 10,140 6,060 10,500 8,060Temporary resource costs 39,150 54,900 44,650 94,050 83,800 99,550 13,8700Acquiring\releasing costs 2,500 2,800 2,100 4,400 4,700 4,900 6,900Splitting costs 0 0 0 200 220 160 940

Total Cost 70,990 59,200 92,350 119,110 142,660 148,710 190,980Incremental benefit of cooperation 0 0 0 11,080 20,680 2,840 31,560

The Argument is verified! Total costs of Subcontractors (Individual Planning): $-222,540 << $-190,980 (Collective Planning)

The Fair Allocation of Benefits: Sub {1} > Sub {3} > Sub {2}

Sub (1}’s Contribution in {1,2} and (1,3}


Allocation of cooperative gains based on four cooperative game theory methodsMethod

Nash-Harsanyi Nucleolus Shapley Value τ-Value

Subcontractor 1

Allocated Cost ($) 60,470 59,910 56,123 55,854

Cost difference with respect to the non-cooperative case (%) 15% 16% 21% 21%

Resulted benefits ($) 10,520 11,080 14,867 15,136

Subcontractor 2

Allocated Cost ($) 48,680 53,760 53,253 53,502



Subcontractor 3

Allocated Cost ($) 81,830 77,310 81,603 81,624




Preference orders of the subcontractors over the four game theory solutionsMethod


Subcontractor 1 1 2 3 4Subcontractor 2 4 1 3 2Subcontractor 3 1 4 3 2Total score 6 7 9 8

Propensity to disrupt of the subcontractors under different cooperative game theory solutionsMethod


Subcontractor 1 1.73 1.59 0.93 0.90Subcontractor 2 0.03 1.00 0.83 0.91Subcontractor 3 0.95 0.36 0.91 0.91Maximum Propensity to disrupt 1.73 1.59 0.93 0.91

PTD of a player is essentially the ratio of what the other players will lose if the player refuses to cooperate and leaves the grand coalition, to what player will lose by leaving the grand coalition.

Outline

• Introduction


• Game Theory



• Conclusion

• References

Conclusion • Contributions of this study:

– There are financial incentives for cooperation. (10 - 20% savings in resource costs)

– A general framework for “Joint Resource Management”– Designing fair, feasible, and stable schemes for sharing the benefits of

cooperation using cooperative game theory methods• Challenges in practice

– Legal issues – Lack of trust & transparency and Incomplete flow of information

among parties avoid investigating these opportunities– Competition: Successful case of cooperation between Peugeot ,

Toyota, and Citroën (Brandenburger and Nalebuff, 1996)– Uncertainties & unpredictable changes: Short-term planning– Modeling always involves simplifications

Conclusion • Next step

– Evaluating the sensitivity of critical parameters on feasibility of cooperation and stability of solutions

– Capturing other aspects of construction problems (e.g, budget limitations, timing issues, material ordering and storage)

– Non-transferrable utility problems: Exchanging (bartering) common resources

Outline

• Introduction


• Game Theory



• Conclusion

• References

References Barlow, J. (2000). “Innovation and learning in complex offshore construction projects.” Research Policy, 29(7-8):

973-989.Brandenburger, A. M., & Nalebuff, B. J. (1996). Co-opetition. Currency, New York, N.Y.Construction Industry Institute (CII). (1991). “In search of partnering excellence”. Special Publication No. 17-1,

Rep., Partnering Task Force of CII, Austin, TX.DeVilbiss, C. E. & Leonard, P. (2000). “Partnering is the foundation of a learning organization.” Journal of

Management in Engineering, 16(4): 47-57. Hartmann et al. (2009). “Relative Importance of Subcontractor Selection Criteria Evidence from Singapore.”

Journal of Construction Engineering and Management, 135, 826. Humphreys, P., Matthews, J., & Kumaraswamy, M. (2003). “Preconstruction project partnering: From adversarial

to collaborative relationships.” Supply Chain Management: An International Journal, 8(2), 166–178.Eriksson, P. E. (2007). “Cooperation and partnering in facilities construction - empirical application of prisoner's

dilemma.” Facilities, 25(1/2): 7-19Gillies, D. B. (1959). “Solutions to general non-zero-sum games.” Contributions to the Theory of Games, Pages

47-85 in A. W. Tucker and D. R. Luce (Eds.) Princeton University Press, Princeton, NJ. Hariga M. & El-Sayegh S.M. (2011). “Cost Optimization Model for the Multiresource Leveling Problem with

Allowed Activity Splitting.” Journal of Construction Engineering and Management, 137, 56-64. Harsanyi, J. C. (1959). “A bargaining model for the cooperative n-person game.” Contributions to the Theory of

Games, Pages 324–356 in A. W. Tucker and D. R. Luce (Eds.) Princeton University Press, Princeton, NJ. Harsanyi, J. C. (1963). “A simplified bargaining model for the n-person game.” International Economic Review,

4:194-220.

References Ho, S. P. (2005). “Bid compensation decision model for projects with costly bid preparation.” Journal of

Construction Engineering and Management, 131(2), 151-159.Ho, S. P. (2006). “Model for financial renegotiation in public-private partnership projects and its policy

implications: game theoretic view.” Journal of Construction Engineering and Management, 132(7), 678-688.

Ho, S. P. & Liu, L. Y. (2004). “Analytical Model for Analyzing Construction Claims and Opportunistic Bidding.” Journal of Construction Engineering and Management, 130(1): 94-104.

Hsueh, S. L. & Yan, Min-Ren. (2011). “Contribution-based profit-sharing scheme for joint ventures.” Technological and Economic Development of Economy, 17:3, 445-458.

Kumaraswamy, M. M. & Matthews J. D. (2000). “Improved Subcontractor Selection Employing Partnering Principles.” Journal of Management in Engineering, 16(3): 47-57.

Lazar, Frederick D. (2000). “Project Partnering: Improving the Likelihood of Win/Win Outcomes.” Journal of Management in Engineering, 16(2): 71-83.

Medda, F. (2007). “A game theory approach for the allocation of risks in transport public private partnerships.” International Journal of Project Management, 25(3), 213–218.

Pena-Mora, F. & Wang, C.Y. (1998). “Computer-supported collaborative negotiation methodology.” Journal of Computing in Civil Engineering, 12 (2) (1998), pp. 64–81.

Perng,Yeng-Horng, Chen, Shu-Ju & Lu, Hui-Jung. (2005). “Potential benefits for collaborating formwork subcontractors based on co-operative game theory.” Building and Environment, 40:239–244.

Rahman, M. M. & Kumaraswamy, M.M. (2004). “Contracting Relationship Trends and Transitions,” Journal of Management in Engineering, 20(4), 147-161.

References Sacks, R., & Harel, M. (2006). “An Economic Game Theory Model of Subcontractor Resource Allocation

Behavior”, Construction Management & Economics, Vol. 24 No. 8 pp. 869-881.Schmeidler, D. (1969). “The nucleolus of a characteristic function game.” SIAM Journal on Applied

Mathematics, 17, pp. 1163-1170. Shapley, L.S. (1953). “A Value for n-Person Games.” Contributions to the Theory of Games, H. W. Kuhn and A.

W. Tucker, eds.,N. II, Annals of Math. Studies, 28. Princeton University Press, pp. 307-317. Shen, L. Y., Bao, H. J., Wu, Y. Z., & Lu, W. S. (2007). “Using bargaining-game theory for negotiating concession

period for BOT-type contract.” Journal of Construction Engineering and Management, 133(5), 385–392.Tijs, S. H. (1981). “Bounds for the core of a game and the τ-value.” Game Theory and Mathematical Economics,

O. Moeschlin and D. Pallaschke. eds, North-Holland, Amsterdam.Unsal, H. I. & Taylor, J. E. (2011a). “Modeling Interfirm Dependency: Game Theoretic Simulation to Examine the

Holdup Problem in Project Networks.” Journal of Construction Engineering and Management, 137(4), 284-293.

Unsal, H. I. & Taylor, J. E. (2011b). “An empirical investigation of opportunistic behaviour in project networks and its impact on market efficiency.” Engineering Project Organization Journal, 1:2, 95-106.

von Neumann, J. & Morgenstern, O. (1947). “Theory of Games and Economic Behavior.” Princeton University Press, Princeton, NJ.

Yousefi, S., Hipel, K.W., & Hegazy, T. (2010). “Attitude-Based Negotiation Methodology for the Management of Construction Disputes.” Journal of Management in Engineering, 26:144-122.

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