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Frontiers of Engineering Management    2020, Vol. 7 Issue (3) : 413-425     https://doi.org/10.1007/s42524-019-0045-0
RESEARCH ARTICLE
Real option-based optimization for financial incentive allocation in infrastructure projects under public–private partnerships
Shuai LI1(), Da HU1, Jiannan CAI2, Hubo CAI2
1. Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN 37996, USA
2. Lyles School of Civil Engineering, Purdue University, West Lafayette, IN 47907, USA
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Abstract

Financial incentives that stimulate energy investments under public–private partnerships are considered scarce public resources, which require deliberate allocation to the most economically justified projects to maximize the social benefits. This study aims to solve the financial incentive allocation problem through a real option-based nonlinear integer programming approach. Real option theory is leveraged to determine the optimal timing and the corresponding option value of providing financial incentives. The ambiguity in the evolution of social benefits, the decision-maker’s attitude toward ambiguity, and the uncertainty in social benefits and incentive costs are all considered. Incentives are offered to the project portfolio that generates the maximum total option value. The project portfolio selection is formulated as a stochastic knapsack problem with random option values in the objective function and random incentive costs in the probabilistic budget constraint. The linear probabilistic budget constraint is subsequently transformed into a nonlinear deterministic one. Finally, the integer non-linear programming problem is solved, and the optimality gap is computed to assess the quality of the optimal solution. A case study is presented to illustrate how the limited financial incentives can be optimally allocated under uncertainty and ambiguity, which demonstrates the efficacy of the proposed method.

Keywords financial incentives      public–private partnerships      energy infrastructure projects      real option      optimization      uncertainty     
最新录用日期:    在线预览日期:    发布日期: 2020-08-06
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Shuai LI
Da HU
Jiannan CAI
Hubo CAI
引用本文:   
Shuai LI,Da HU,Jiannan CAI, et al. Real option-based optimization for financial incentive allocation in infrastructure projects under public–private partnerships[J]. Front. Eng, 2020, 7(3): 413-425.
网址:  
https://journal.hep.com.cn/fem/EN/10.1007/s42524-019-0045-0     OR     https://journal.hep.com.cn/fem/EN/Y2020/V7/I3/413
Fig.1  Methodology overview.
Symbol Definition
S Social benefits
Q Probability measure
μ Drift rate
σ Volatility
dt Length of time interval
Bt Standard Brownian motion
θ Density generators
Θ Set of density generators
α Decision-makers’ attitude toward ambiguity
Wt Present value of social benefits
r Discount rate
Vt Value of providing financial incentives
I Public costs of financial incentives
W* Critical value between postponing and exercising the provision of financial incentives
pj Given real numbers
ε Degree of uncertainty
η Symmetrically distributed random variable with zero mean and support [−1,1]
φ Positive parameter corresponding to the probabilistic guarantee
B Deterministic budget limit
Um Expectation of empirical distributions
z* Optimal solution value
Lm Objective value
G Optimality gap
G ¯( n) Mean of the optimality gap
SG2(n) Variance of the optimality gap
Tab.1  Definition of key parameters
Project ID Social benefit GMB Ambiguity Investment cost
Mean Standard deviation Drift rate Volatility Mean Degree of uncertainty
1 175 5 0.05 0.05 0.2 1550 0.05
2 180 4 0.05 0.05 0.2 1600 0.15
3 25 3 0.06 0.08 0.5 500 0.4
4 200 20 0.03 0.06 0.25 1650 0.35
5 155 35 0.06 0.1 0.25 1900 0.15
6 50 4 0.08 0.15 0.1 950 0.15
7 300 7.5 0.03 0.10 0.5 2150 0.1
8 225 15 0.07 0.09 0.35 1550 0.5
9 330 60 0.04 0.05 0.45 2850 0.2
10 125 5 0.1 0.05 0.4 2000 0.3
11 220 5 0.05 0.07 0.1 1800 0.1
12 280 10 0.06 0.08 0.2 3300 0.25
13 120 15 0.07 0.05 0.75 1200 0.2
14 250 50 0.08 0.1 0.25 3350 0.05
15 360 15 0.1 0.1 0.1 4500 0.05
Tab.2  Social benefits and public investment data of candidate projects
Fig.2  Timing and option values with varying ambiguity.
Fig.3  Option value distributions with varying ambiguity under pessimism.
Fig.4  Option value distributions with varying ambiguity under optimism.
Project ID α
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
1 1 1 0 0 0 0 1 1 1 1
2 1 0 1 1 1 1 1 1 1 1
3 0 0 0 0 0 1 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0
6 1 1 1 1 1 1 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0
8 1 1 1 1 1 1 1 1 1 1
9 0 0 0 0 0 0 0 0 0 0
10 1 1 1 1 1 1 1 1 1 1
11 1 1 1 1 1 1 1 1 1 1
12 0 0 0 0 0 0 0 0 0 0
13 1 0 0 0 0 0 0 0 0 0
14 0 1 1 1 1 1 1 1 1 1
15 1 1 1 1 1 1 1 1 1 1
Tab.3  Optimal solutions with various probabilistic budget guarantees under pessimism
Fig.5  Optimal value and the optimality gap when decision-maker is pessimistic.
Project ID α
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
1 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0
3 1 1 0 0 0 1 1 1 1 0
4 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 1
6 0 0 1 1 1 1 1 1 1 0
7 1 1 1 1 1 1 1 1 1 1
8 1 1 1 1 1 1 1 1 1 1
9 0 0 0 0 0 0 0 0 0 0
10 1 1 1 1 1 1 1 1 1 1
11 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0
13 1 1 1 1 1 1 1 1 1 1
14 1 1 1 1 1 1 1 1 1 1
15 1 1 1 1 1 1 1 1 1 1
Tab.4  Optimal solutions with various probabilistic budget guarantees under optimism
Fig.6  Optimal value and the optimality gap when decision-maker is optimistic.
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