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Optimal gainshare/painshare in alliance projects

  • Special Issue Paper
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Journal of the Operational Research Society

Abstract

Alliances are popularly used in delivering infrastructure. However, discussion is ongoing as to what is the optimal gainshare/painshare arrangement. This paper derives a result for the optimal gainshare/painshare between risk-averse parties, where the level of aversion may range from very large to being risk neutral. The derivation is based on solving an optimization problem using concepts from agency theory. The influence of the parties’ level of risk aversion and outcome uncertainty is examined. Practitioners were engaged in a designed exercise in order to validate the approach and propositions. The paper shows that: (i) the optimal gainshare/painshare arrangement in alliances is linear in the project outcome; (ii) the optimal gain/pain share to the contractor should decrease with increasing contractor level of risk aversion and/or decreasing owner level of risk aversion; and (iii) the outcome uncertainty has no influence on the optimal gainshare/painshare. The paper provides those who write alliance contracts with recommendations on gainshare/painshare. This study casts new light on establishing optimal alliance arrangements in the construction industry.

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Correspondence to D G Carmichael.

Appendix

Appendix

Derivation of the solution to the maximization problem presented in expression (5)

Consider both the owner and contractor to be risk-averse, though the level of aversion may range from very large to being risk neutral. Risk aversion is characterized by a concave utility function. Exponential, power and linear-exponential are candidate functions (Kirkwood, 2004). Here, the exponential utility function, because it has been popularly adopted (Holmstrom and Milgrom, 1987; Kirkwood, 2004), is used, and for the owner and the contractor, respectively, have the form,

Here r o and r c are the owner's and the contractor's level of risk aversion, respectively. The shapes of the owner and contractor utility functions change with r o and r c . Substituting Equations (A.1) and (A.2) into expression (5), differentiating the result with respect to Fee, setting to zero, and simplifying,

from which an expression for λ can be obtained. Taking the derivative of Equation (A.3) with respect to x gives,

Substituting λ from Equation (A.3) into Equation (A.4),

Equation (A.5) shows that the optimal gainshare/painshare contract depends on both the owner's and contractor's levels of risk aversion. Integrating Equation (A.5) with respect to x gives the optimal gain/pain sharing model, Equations (6) and (7).

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Hosseinian, S., Carmichael, D. Optimal gainshare/painshare in alliance projects. J Oper Res Soc 64, 1269–1278 (2013). https://doi.org/10.1057/jors.2012.146

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