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In order to encourage the high-water-consumption (HWC) manufacturers to carry out water-saving transformation relying on self-strength or outsourcing to a water-saving service company (WSSC) during production processes, government subsidies are provided according to water-saving efforts (WSE) or investment cost. In this context, the authors derive the participant's equilibrium decisions and the manufacturer's water-saving strategy. Additionally, the effects of subsidies on WSE and stakeholders' profits are discussed.

Mathematical models including optimization model and Stackelberg game model are constructed under different subsidy schemes.

The study finds that (1) there exists a threshold related to the subsidy coefficient for the HWC manufacturer when choosing between self-saving and outsourcing-saving. (2) When the technological competitive advantage between WSSC and manufacturer is within a certain range, government's subsidy promotes HWC enterprises to choose outsourcing-saving. (3) Given a water-saving mode, subsidy on investment cost is more effective for the government to achieve more environmental performance.

First, subsidy endogeneity can be considered to explore the optimal interval for government subsidies to maximize social welfare. Second, in outsourcing-saving, other types of contract can be discussed. Another extension is about model uncertainties. Finally, other policies on improving water efficiency can be also examined.

The paper includes implication for HWC manufacturers to select the best water-saving mode under subsidy, and it allows policymakers to understand the efficiency of proposed subsidies.

Decisions on water-saving efforts, selection of water-saving modes and operational planning are also regarded as business strategies in the paper. Particularly, the influences of different government subsidies are also considered and compared.

The Public–Private Partnership (PPP) modality plays an important role in the procurement of global infrastructure projects. Regarding PPP's complex transaction structure, pricing of a PPP project is critical to both parties where the government pursues a high value for money (VFM) and the investor strives to maximize its financial gains. Despite the straightforward win–win principle, a formidable compromise is often the case to end up with a fairly acceptable price, subject to many determinants such as the risk profile, expected return, technological innovation and capacities of both parties. Among them, this study chooses to examine the “managing flexibility” (MF) capacity of investors in pricing of a PPP project, in light of the widely recognized importance of a real-option perspective toward the long term, complex and uncertain PPP arrangement. This study addresses two major questions: (1) how is MF in PPP projects to be valued and (2) how are PPP projects to be priced when considering a project's MF value.

A binomial tree model is used to evaluate the MF value in PPP projects. Based on the developed MF pricing model, net present value (NPV) and adjusted VFM value are then calculated. Finally, a multi-objective decision-making method (MODM) was adopted to determine the optimal level of returns based on invested capital (ROIC), return on operation maintenance (ROOM) and concession period.

The applicability and functionality of the proposed model is investigated using a real project case. For a given return, extended NPV and adjusted VFM value were calculated and analyzed using sensitivity analysis. Factor influence is shown by the model to be dependent on factor impact on cash flow. Subsequently, a multi-objective decision-making (MODM) model was adopted to determine the optimal level of returns, where the solution approximates the real-world bidding price. Results confirm that the pricing model provides a reliable and practical PPP proposal pricing tool.

This study proposes an integrated framework for valuing MF in PPP projects and thus more accurately determine optimal pricing of PPP projects than revealed in extant research. The model offers a practical tool to aid in the valuation of PPP projects.