Quantifying the Decision-Making of PPPs in China by the Entropy-Weighted Pareto Front: A URT Case from Guizhou
In recent years, value for money (VFM) evaluations using the Public Sector Comparator (PSC) method have gradually been adopted by governments worldwide in the field of public investment, and used as decision-making tools for public-private partnership (PPP) projects. However, there has been little research concerned with such emerging decision-making questions with VFM. This paper proposed a quantitative decision-making method of entropy-weighted Pareto front applied in the specific context of
... pecific context of Chinese PPPs, with a case study of an Urban Transit Railway (URT) PPP project from Guizhou province. Factor analysis was used to extract the qualitative indicators of VFM evaluation, associate them with the quantitative characteristics of the project, and thus help public sector decision-makers choose the proper quantitative decision variables. Jin et al.  developed a neuro-fuzzy decision support system (NFDSS) for the risk-allocation decision-making process in PPP projects by combining fuzzy synthesis decision-making and neural network techniques. Tang  built a risk allocation model on the framework of cumulative prospect theory to help the public and private sector reach consensus with each other. Yin et al.  designed a risk-sharing scheme for the PPP projects based on the cloud model, which was used to solve the problem of existing decision-making method that the opinions of a few experts who hold the right views are ignored, by grading on thickness of the 'cloud'. Song and Fei  provided one type of group-decision technique to moderate expectations of PPP participators by an iterative algorithm to provide a solution for the group's satisfaction. Xie and Ng  established a decision-making model using a Bayesian network (BN) to connect the decision items, evaluation criteria, and objectives with a weighted score approach applied to combine each objective of the stakeholders into a single value. Alireza et al.  identified that one of the key issues in a multi-objective problem of a PPP project was the most feasible and satisfactory solution of the allocation of excess costs among the public sector, private sector, and the users; then, a decision-making model was proposed and solved via a max-min composition algorithm. Xu et al.  developed a pricing model using the system dynamics (SD) technique based on a concession project pricing parameters, and then verified the effectiveness of the proposed model by a real toll tunnel project located in China. Xue et al. [11, 12] proposed a Bi-level Programming (BLP) decision model of the public bus system to determine the capacity and charge of a bus PPP project where the upper problem was to maximize the total surplus, including the value-of-time (VOT) of passengers as constrained by ticket fare; the lower problem was the passenger's surplus, which was constrained by service capability and the lowest return rate of the private sector. Liu et al.  analyzed the government guarantee of restrictive competition in PPP projects, and constructed an evaluation model with real option theory. Hu et al.  constructed a model of the operational pattern selection of a PPP project on an Support Vector Machine (SVM) classifier, taking investment scale, project VFM value, and the types of income as the three main factors. These research studies substantially developed the contemporary decision-making methodology with the introduction of the machine learning techniques and intelligent algorithms. However, only a few of these decision-making models referred to the specific requirement of a VFM evaluation of the PPP projects, which is accepted and promoted by more countries worldwide, especially in Asia. Besides, the decision-making of the PPPs is a typical multi-objective optimization problem providing many optimal solutions that are equally good from the perspective of the given objectives, which are known as the Pareto front and as non-dominated solutions (Pareto solutions)  . This paper proposed a quantitative decision-making method of entropy-weighted Pareto front for PPP projects in China, then illustrated how to use it via a real Urban Transit Railway (URT) PPP project case. Firstly, the factor analysis method was applied to extract the main factors associated with the quantitative characteristics of a URT PPP project from 15 qualitative indicators, which were used in 19 collected cases  . Secondly, entropy weights that were distributed to the net cost of the private sector, the public sector, and the users were calculated by the predicted operation income, general public budget, and passenger volume from the selected case. Thirdly, two types of multi-objective optimization models were built with the constraint that both the VFM and the returns of the private sector are positive; then, each of models was solved by a genetic algorithm solver to generate the Pareto front (the Pareto solution matrix). Finally, the entropy weights were applied to all of the elements in each of the Pareto solution sets. After that, the set with the minimum-weighted sum was picked out, and the best decision was determined. Furthermore, a sensitivity analysis of the net cost of the private sector and the public sector on the parameters in each optimization model were carried out. Author Contributions: F.L. contributed to the research design, data collection, implementation of model, and manuscript writing. J.L. and X.Y. acted as supervisory roles and contributed equally to problem analysis and the application of methodology.