Portrait of Professor Steve Wenbin Liu

Professor Steve Wenbin Liu

Professor of Management Science and Computational Mathematics


Global and parallel optimisation methods, numerical simulation and modelling, simulation and optimisation of highly complex systems, production and operations management, productivity analysis.

Research interests

Global and parallel optimisation methods, numerical simulation and modelling, simulation and optimisation of highly complex systems, production and operations management, productivity analysis



Current Supervisees

  • Charles Turkson: Sustainability Assessment of Electricity Production and Consumption: Dea Systems Modelling Of Complex Internal Structures.
  • Giulio GiannettiDynamics of the Volatility-Leverage Connection under Varying Market Conditions
  • Yu Ye: Developing and Managing Performance Tree - A New Performance Management Framework

Past Supervisees

  • Ahmed Aljazea: Warranty Risk Management for the Consumer Durable Manufacturers
  • Darshana Sabhi Appanna: Reliability Modeling for Asset Management in the Southeast Water 
  • Yi Zheng: Theory and Action Research on a new Framework and Approach of Performance Management
  • Yang Song: Performance Management in Financial Organizations
  • Wei Wang: Performance Management in Public Hospitals in China
  • Evangelia Lipitakis: The Use of Bibliometric Methods in Evaluating Research Performance In Business and Management: A Study of Three UK Business Schools
  • Li Qi: Performance Management and Efficiency Analysis for Companies
  • Ross Wyatt: DEA Models
  • Fang Xu: Measuring Research Quality by using Bibliometric Methods
  • Lu Zhao: Performance Management of Supply Chain



Showing 50 of 143 total publications in the Kent Academic Repository. View all publications.


  • Sabhi Appanna, D. (2019). Reliability Modelling For Asset Management in South East Water.
    Over the years, the reliability modelling of water assets has generated increasing interest among both researchers and practitioners. Statistical methods and software packages for assessing asset reliability have been developed in order to improve asset availability, indirectly reduce water losses, and hence improve the efficiency of water assets. OFWAT, which is the economic regulator of the water sector in England and Wales, aims to ensure that water companies operate under their statutory functions and have sufficient financial means to perform these functions adequately. Water companies need to prepare a five-year business plan for OFWAT, in order to certify they have enough capital and are transparent when carrying out their statutory functions. Hence, this thesis aims to analyse the reliability of two selected types of assets at South East Water to help plan their future investments on vehicles and future maintenance costs on borehole assets.

    This thesis will provide an extensive literature review on reliability modelling in water distribution networks. An MS Excel-based decision support system will be developed for both vehicles and borehole assets, using data collected from South East Water. For the transport model, a block replacement policy will be developed by using Visual Basic, to obtain the optimum time of replacing a vehicle. Performance analysis will be conducted on the borehole data to pinpoint the worst performers among the 16 boreholes under analysis.


  • Turkson, C., Acquaye, A., Liu, W. and Papadopoulos, T. (2020). Sustainability assessment of energy production: A critical review of methods, measures and issues. Journal of Environmental Management [Online] 264. Available at: https://doi.org/10.1016/j.jenvman.2020.110464.
    Sustainable operations of energy production systems have become an increasingly important policy agenda globally because of the massive pressure placed on energy resources needed to support economic development and population growth. Due to the increasing research interest in examining the operational impacts of energy production systems on the society and the environment, this paper critically reviews the academic literature on the clean, affordable and secure supply of energy focussing on methods of assessments, measures of sustainability and emerging issues in the literature. While there have been some surveys on the sustainability of energy production systems they have either tended to focus on one assessment approach or one type of energy generation technology. This study builds on previous studies by providing a broader and comprehensive examination of the literature across generation technologies and assessment methods. A systematic review of 128 scholarly articles covering a 20-year period, ending 2018, and gathered from ProQuest, Scopus, and manual search is conducted. Synthesis and critical evaluation of the reviewed papers highlight a number of research gaps that exist within the sustainable energy production systems research domain. In addition, using mapping and cluster analyses, the paper visually highlights the network of dominant research issues, which emerged from the review.
  • Gong, W., Liu, W., Tan, Z. and Yan, N. (2019). A convergent adaptive finite element method for elliptic Dirichlet boundary control problems. IMA Journal of Numerical Analysis [Online] 39:1985-2015. Available at: https://doi.org/10.1093/imanum/dry051.
    This paper concerns the adaptive finite element method for elliptic Dirichlet boundary control problems in the energy space. The contribution of this paper is twofold. First, we rigorously derive efficient and reliable a posteriori error estimates for finite element approximations of Dirichlet boundary control problems. As a by-product, a priori error estimates are derived in a simple way by introducing appropriate auxiliary problems and establishing certain norm equivalence. Secondly, for the coupled elliptic partial differential system that resulted from the first-order optimality system, we prove that the sequence of adaptively generated discrete solutions including the control, the state and the adjoint state, guided by our newly derived a posteriori error indicators, converges to the true solution along with the convergence of the error estimators. We give some numerical results to confirm our theoretical findings.
  • Zhou, Z., Liu, X., Xiao, H., Ren, T. and Liu, W. (2018). Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset. Mathematical Problems in Engineering [Online] 2018. Available at: https://doi.org/10.1155/2018/7563093.
    The pre-commitment and time-consistent strategies are the two most representative investment strategies for the classic multi-period mean-variance portfolio selection problem. In this paper, we revisit the case in which there exists one risk-free asset in the market and prove that the time-consistent solution is equivalent to the optimal open-loop solution for the classic multi-period mean-variance model. Then, we further derive the explicit time-consistent solution for the classic multi-period mean-variance model only with risky assets, by constructing a novel Lagrange function and using backward induction. Also, we prove that the Sharpe ratio with both risky and risk-free assets strictly dominates that of only with risky assets under the time-consistent strategy setting. After the theoretical investigation, we perform extensive numerical simulations and out-of-sample tests to compare the performance of pre-commitment and time-consistent strategies. The empirical studies shed light on the important question: what is the primary motivation of using the time-consistent investment strategy.
  • Zhang, L., Gao, S., Qi, L., Liu, W., He, Y. and Li, Q. (2018). Wideband Circularly Polarized Tightly Coupled Array. IEEE Transactions on Antennas and Propagation [Online] 66:6382-6387. Available at: http://dx.doi.org/10.1109/TAP.2018.2867031.
    Tightly coupled arrays (TCA) have received considerable
    interests recently. Although various TCAs have been reported, they are
    limited to single or dual linear polarizations. Considering the importance of
    circular polarization (CP) in various wireless systems, it is meaningful to
    design a CP TCA with a simple configuration. This paper presents a
    circularly polarized tightly coupled crossed dipole array (CP-TCCDA) with
    wide overlapped impedance bandwidth and axial ratio (AR) bandwidth. A
    tightly coupled crossed dipole unit cell is investigated and the comparison
    with an isolated crossed dipole of the same size indicates that the VSWR<3
    bandwidth is increased from 3:1 to 7.1:1 while the 3-dB AR bandwidth is
    increased from 1.3:1 to 2.1:1. Analysisis given to explain the principles of AR
    bandwidth improvement and is verified by the comparison of radiated Efields
    between a CP-TCCDA and a conventional crossed dipole array. To
    verify the design concept, a 4×4 CP-TCCDA with feeding network is
    fabricated and measured. The measured results confirm that the proposed
    array achieves VSWR<3 bandwidth from 2.06GHz to 6.46 GHz (3.14:1) and
    3-dB AR bandwidth from 2.35GHz to 5.6GHz (2.38:1), which are much
    wider than the bandwidth of an isolated element and a conventional array
    using the same element.
  • Zhou, Z., Zeng, X., Xiao, H., Ren, T. and Liu, W. (2018). Multiperiod portfolio optimization for asset-liability management with quadratic transaction costs. Journal of Industrial & Management Optimization [Online] 15:1493-1515. Available at: https://doi.org/10.3934/jimo.2018106.
    This paper investigates the multiperiod asset-liability management problem with quadratic transaction costs. Under the mean-variance criteria, we construct tractability models with/without the riskless asset and obtain the pre-commitment and time-consistent investment strategies through the application of embedding scheme and backward induction approach, respectively. In addition, some conclusions in the existing literatures can be regarded as the degenerated cases under our setting. Finally, the numerical simulations are given to show the difference of frontiers derived by different strategies. Also, some interesting findings on the impact of quadratic transaction cost parameters on efficient frontiers are discussed.
  • Shen, W., Yang, G., Zhou, Z. and Liu, W. (2018). DEA models with Russell measures. Annals of Operations Research [Online]. Available at: https://doi.org/10.1007/s10479-018-2867-2.
    In real applications, data envelopment analysis (DEA) models with Russell measures are widely used although their theoretical studies are scattered over the literature. They often have seemingly similar structures but play very different roles in performance evaluation. In this work, we systematically examine some of the models from the viewpoint of preferences used in their Production Possibility Sets (PPS). We identify their key differences through the convexity and free-disposability of their PPS. We believe that this study will provide guidelines for the correct use of these models. Two empirical cases are used to compare their differences.
  • Liu, W., Mingers, J., wang, w and Zheng, Y. (2018). A Performance Management Framework for the Public Sector: The Balanced Stakeholder Model. Journal of the Operational Research Society [Online]. Available at: https://doi.org/10.1080/01605682.2018.1448247.
    Managing performance is a major concern within the public sector. Many systems for performance management, such as the balanced scorecard, have been developed in the private sector but these tend to focus on financial targets and a small range of stakeholders, primarily shareholders. The public sector has a much wider range of objectives and of stakeholders. Previous papers have developed a performance measurement and management system (the “3 E’s” methodology) based on SSM. In this paper the methodology has been further developed to help identify sets of relevant stakeholders, both internal and external, and then try to balance their particular interests which may be independent, complementary or conflicting. The methodology decomposes activities throughout the organization; identifies key stakeholders and their interests at each level; views these in terms of four perspectives – goal, operation, stakeholder, capability; and identifies KPIs if required. A case study of its application in a Chinese hospital is included.
  • Shen, W., Ge, L. and Liu, W. (2018). Stochastic Galerkin Method for Optimal Control Problem Governed by Random Elliptic PDE with State Constraints. Journal of Scientific Computing [Online] 78:157-1600. Available at: https://doi.org/10.1007/s10915-018-0823-6.
    In this paper, we investigate a stochastic Galerkin approximation scheme for an optimal control problem governed by an elliptic PDE with random field in its coefficients. The optimal control minimizes the expectation of a cost functional with mean-state constraints. We first represent the stochastic elliptic PDE in terms of the generalized polynomial chaos expansion and obtain the parameterized optimal control problems. By applying the Slater condition in the subdifferential calculus, we obtain the necessary and sufficient optimality conditions for the state-constrained stochastic optimal control problem for the first time in the literature. We then establish a stochastic Galerkin scheme to approximate the optimality system in the spatial space and the probability space. Then the a priori error estimates are derived for the state, the co-state and the control variables. A projection algorithm is proposed and analyzed. Numerical examples are presented to illustrate our theoretical results.
  • Gong, B., Liu, W., Tang, T., Zhao, W. and Zhou, T. (2017). An Efficient Gradient Projection Method for Stochastic Optimal Control Problems. SIAM Journal on Numerical Analysis [Online] 55:2982-3005. Available at: https://doi.org/10.1137/17M1123559.
    In this work, we propose a simple yet effective gradient projection algorithm for a class of stochastic optimal control problems. We first reduce the optimal control problem to an optimization problem for a convex functional by means of a projection operator. Then we propose a convergent iterative scheme for the optimization problem. The key issue in our iterative scheme is to compute the gradient of the objective functional by solving the adjoint equations that are given by backward stochastic differential equations (BSDEs). The Euler method is used to solve the resulting BSDEs. Rigorous convergence analysis is presented, and it is shown that the entire numerical algorithm admits a first order rate of convergence. Several numerical examples are carried out to support the theoretical finding.
  • Zhou, Z., Liu, C., Zeng, X., Jiang, Y. and Liu, W. (2017). Carbon emission performance evaluation and allocation in Chinese cities. Journal of Cleaner Production [Online] 172:1254-1272. Available at: http://dx.doi.org/10.1016/j.jclepro.2017.10.208.
    This paper presents a DEA approach with multiple abatement factors to evaluate CO2 emission performance and allocate CO2 emission quotas in Chinese cities. We first consider the difference of marginal abatement costs among cities, and construct the non-radial directional distance function with multiple abatement factors. The total-factor CO2 emission performance index and its dynamic change index are then proposed to measure CO2 emission performance. Considering equity and efficiency, we develop a composite index by the hybrid method to allocate emissions quota, which considers CO2 emissions as well as CO2 emission performance. Then we conduct an empirical study using inputs and outputs dataset of 71 Chinese cities in 2005–2012. Chinese cities have poor energy efficiency and still have high CO2 emissions. The eastern region outperforms the central region and the western region performs worst, whereas the dynamic CO2 emission performance of the central region has the largest increase. The change of CO2 emission performance is driven mainly by technological advances. As for the CO2 emission allocation, the composite index method encourages cities to reduce emissions and enhance emission performance through carbon trading market. It also motivates cities with high historical emissions to reduce their emissions by improving technology when they have poor CO2 emission performance.
  • Zhou, Z., Xiao, H., Jin, Q. and Liu, W. (2017). DEA Frontier Improvement and Portfolio Rebalancing: An Application of China Mutual Funds on Considering Sustainability Information Disclosure. European Journal of Operational Research [Online] 269:111-131. Available at: https://dx.doi.org/10.1016/j.ejor.2017.07.010.
    Data envelopment Analysis (DEA) has been a widely used methodology for evaluating the relative performance of portfolios. Extensive work has appeared for realizing the role of DEA in the aspect of assessing portfolio performance and deriving the relative rankings. However, the role of providing realizable benchmarks is not fully explored in the existing literatures. Most importantly, the DEA-based portfolio performance evaluation methods developed in the existing literatures can hardly provide support for fund managers in pursuing sustainability performance. In this paper, we first propose a DEA frontier improvement approach under the mean-variance framework. This approach provides investor with a rebalancing strategy as well as an improved DEA frontier which approximates the portfolio efficient frontier better than the traditional DEA model does. Then, this approach is extended to a general return-risk framework. Our in-sample simulation results verify the effectiveness of the proposed approach for a wide range of applications. In addition, the out-of-sample tests show that the rebalancing investment strategies can achieve higher Sharpe ratios and Sortino ratios than those of the original ones. Finally, we apply the proposed approach to evaluate mutual fund performance in China with the consideration of sustainability information disclosure. We construct a disclosure index to indicate the extent of sustainable information disclosure of each mutual fund. The results show that the proposed approach provides not only investment recommendations, but also references for constructing sustainable green funds.
  • Gong, B., Ge, L., Sun, T., Shen, W. and Liu, W. (2017). Stochastic Spline-Collocation Method for Constrained Optimal Control Problem Governed by Random Elliptic PDE. International Journal of Numerical Analysis and Modeling [Online] 14:627-645. Available at: http://www.math.ualberta.ca/ijnam/Volume-14-2017/No-4-17/2017-45-09.pdf.
    In this paper, we investigate a stochastic spline-collocation approximation scheme for an optimal control problem governed by an elliptic PDE with random field coefficients. We
    obtain the necessary and sufficient optimality conditions for the optimal control problem and establish a scheme to approximate the optimality system through the discretization with respect
    to the spatial space by finite elements method and the probability space by stochastic splinecollocation method. We further investigate Smolyak approximation schemes, which are effective
    collocation strategies for smooth problems that depend on a moderately large number of random variables. For more general control problems where the state may be non-smooth with respect
    to the random variables in some areas, we adopt a domain decomposition strategy to partition the random space into smooth and non-smooth parts and then apply Smolyak scheme and spline
    approximation respectively. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results.
  • Zhou, Z., Jin, Q., Xiao, H., Wu, Q. and Liu, W. (2017). Estimation of cardinality constrained portfolio efficiency via segmented DEA. Omega [Online] 76:28-37. Available at: https://dx.doi.org/10.1016/j.omega.2017.03.006.
    The cardinality constrained portfolio selection problem arises due to the empirical findings that investors tend to hold limited number of assets. Yet the lack of fast computational methods for frontier of cardinality constrained portfolio investments makes the performance evaluation of this problem a long-standing challenge. Classic Data Envelopment Analysis (DEA) models have been justified valid in evaluating and ranking portfolio performance. Unfortunately, when it comes to the cardinality constrained portfolio selection problem, the DEA models fail to approximate the portfolio efficiency (PE) since the real frontier is discontinuous and not concave. To solve this problem, we propose a segmented DEA approach based on data segment points. A searching algorithm is introduced to approach the real segment points and proved to be valid. In each segment, the frontier is continuous and concave; hence, classic DEA models can be applied to evaluate the PE. The simulation results further indicate that the segmented DEA approach proposed in this paper is effective and practical in evaluating the cardinality constrained portfolio performance.
  • Shen, W., Zhang, D., Liu, W. and Yang, G. (2016). Increasing discrimination of DEA evaluation by utilizing distances to anti-efficient frontiers. Computers and Operations Research [Online] 75:163-173. Available at: http://dx.doi.org/10.1016/j.cor.2016.05.017.
    This paper develops three DEA performance indicators for the purpose of performance ranking by using the distances to both the efficient frontier and the anti-efficient frontier to enhance discrimination power of DEA analysis. The standard DEA models and the Inverted DEA models are used to identify the efficient and anti-efficient frontiers respectively. Important issues like possible intersections of the two frontiers are discussed. Empirical studies show that these indicators indeed have much more discrimination power than that of standard DEA models, and produce consistent ranks. Furthermore, three types of simulation experiments under general conditions are carried out in order to test the performance and characterization of the indicators. The simulation results show that the averages of both the Pearson and Spearman correlation coefficients between true efficiency and indicators are higher than those of true efficiency and efficiency scores estimated by the BCC model when sample size is small
  • Gong, B., Sun, T., Shen, W. and Liu, W. (2016). A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Random Parabolic PDE with Constrained Control. International Journal of Computational Methods [Online] 13. Available at: http://dx.doi.org/10.1142/S0219876216500286.
    A stochastic Galerkin approximation scheme is proposed for an optimal control problem governed by a parabolic PDE with random perturbation in its coefficients. The objective functional is to minimize the expectation of a cost functional, and the deterministic control is of the obstacle constrained type. We obtain the necessary and sufficient optimality conditions and establish a scheme to approximate the optimality system through the discretization with respect to both the spatial space and the probability space by Galerkin method and with respect to time by the backward Euler scheme. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results.
  • Du, N., Wang, H. and Liu, W. (2015). A Fast Gradient Projection Method for a Constrained Fractional Optimal Control. Journal of Scientific Computing [Online] 68:1-20. Available at: https://doi.org/10.1007/s10915-015-0125-1.
    Optimal control problems governed by a fractional diffusion equation tends to provide a better description than one by a classical second-order Fickian diffusion equation in the context of transport or conduction processes in heterogeneous media. However, the fractional control problem introduces significantly increased computational complexity and storage requirement than the corresponding classical control problem, due to the nonlocal nature of fractional differential operators. We develop a fast gradient projection method for a pointwise constrained optimal control problem governed by a time-dependent space-fractional diffusion equation, which requires the computational cost from O(MN3)O(MN3) of a conventional solver to O(MNlogN)O(MNlog?N) and memory requirement from O(N2)O(N2) to O(N) for a problem of size N and of M time steps. Numerical experiments show the utility of the method.
  • Simper, R., Hall, M., Liu, W., Zelenyuk, V. and Zhou, Z. (2015). How relevant is the choice of risk management control variable to non-parametric bank profit efficiency analysis? The case of South Korean banks. Annals of Operations Research [Online] 250:105-127. Available at: https://dx.doi.org/10.1007/s10479-015-1946-x.
    Adopting a profit-based approach to the estimation of the efficiency of South Korean banks over the 2007Q3 to 2011Q2 period, we systematically analyse, within a non-parametric DEA analysis, how the choice of risk management control variable impacts upon such estimates. This is in recognition of previous findings that such estimates are dependent on the choice of risk management control variable and the lack of guidance from such studies on the optimal choice of risk control variable. Using the model of Liu et al. (Ann Operat Res 173:177–194, 2010), we examine the dependency of the estimated efficiency scores on the chosen risk control variables embracing loan loss provisions and equity as good inputs and non-performing loans as a bad output. We duly find that, both for individual banks and banking groups, the mean estimates are indeed model dependent although, for the former, rank correlations do not change much at the extremes. Based on the application of the Simar and Zelenyuk (Econom Rev 25:497–522, 2006) adapted Li (Econom Rev 15: 261–274, 1996) test, we then find that, if only one of the three risk control variables is to be included in such an analysis, then it should be loan loss provisions. We also show, however, that the inclusion of all three risk control variable is to be preferred to just including one, but that the inclusion of two such variables is about as good as including all three. We therefore conclude that the optimal approach is to include (any) two of the three risk control variables identified. The wider implication for research into bank efficiency is that the optimal choice of risk management control variable is likely to be crucial to both the delivery of risk-adjusted estimates of bank efficiency and the specification of the model to be estimated.
  • Wang, W., Liu, W. and Mingers, J. (2015). A Systemic Method for Organisational Stakeholder Identification and Analysis Using Soft Systems Methodology (SSM). European Journal of Operational Research [Online] 246:562-574. Available at: http://dx.doi.org/10.1016/j.ejor.2015.05.014.
    This paper presents a systemic methodology for identifying and analysing the stakeholders of an organisation at many different levels. The methodology is based on soft systems methodology and is applicable to all types of organisation, both for profit and non-profit. The methodology begins with the top-level objectives of the organisation, developed through debate and discussion, and breaks these down into the key activities needed to achieve them. A range of stakeholders are identified for each key activity. At the end, the functions and relationships of all the stakeholder groups can clearly be seen. The methodology is illustrated with an actual case study in Hunan University.
  • Liu, W., Xu, F. and Mingers, J. (2015). New Journal Classification Methods Based on the Global h-Index. Information Processing and Management [Online] 51:50-61. Available at: http://dx.doi.org/10.1016/j.ipm.2014.10.011.
    In this work we develop new journal classification methods based on the h-index. The introduction of the h-index for research evaluation has attracted much attention in the
    bibliometric study and research quality evaluation. The main purpose of using an h-index is to compare the index for different research units (e.g. researchers, journals, etc.) to differentiate their research performance. However the h-index is defined by only comparing citations counts of one’s own publications, it is doubtful that the h index alone should be used for reliable comparisons among different research units, like researchers or journals. In this paper we propose a new global h-index (Gh-index), where the publications in the core are selected in comparison with all the publications of the units to be evaluated. Furthermore, we introduce some variants of the Gh-index to address the issue of discrimination power. We show that together with the original h-index, they can be used to evaluate and classify academic journals with some distinct advantages, in particular that they can produce an automatic classification into a number of categories without arbitrary cut-off points. We then carry out an empirical study for classification of operations research and management science (OR/MS) journals using this index, and compare it with other well-known journal ranking results such as the Association of Business Schools (ABS) Journal Quality Guide and the Committee of Professors in OR (COPIOR) ranking lists.
  • Xu, F., Liu, W. and Rousseau, R. (2014). Introducing sub-impact factor (SIF-) sequences and an aggregated SIF-indicator for journal ranking. Scientometrics [Online] 102:1577-1593. Available at: http://dx.doi.org/10.1007/s11192-014-1401-9.
    The main methods for ranking academic journals are peer review based approaches and applications of various bibliometric indicators, or a mixture of the two. Such rankings are used to assess the overall quality of journals, although their real meaning remains unclear as long as the notion of “quality’ is not precisely defined. In our approach we examine journal evaluation from the perspective of knowledge accumulation taking the citation distribution into account. A new indicator, the sub-impact factor denoted as SIF, derived sub-impact factor sequences and an aggregated SIF-indicator are proposed. An empirical study is performed on 64 journals in the area of operations research and management science, illustrating the use of these indicators.
  • Yang, G., Shen, W., Zhang, D. and Liu, W. (2014). Extended Utility and DEA Models without Explicit Input. Journal of the Operational Research Society [Online] 65:1212-1220. Available at: https://dx.doi.org/10.1057/jors.2013.68.
    In this paper, we discuss the relationship between multi-attribute utility theory and data envelopment analysis (DEA) models without explicit inputs (DEA-WEI), including dual models and some theoretical analysis of DEA-WEI models. We then propose generic DEA-WEI models with quadratic utility terms. Finally, we provide illustrative examples to show that DEA-WEI with suitable quadratic utility terms are able to reflect some value judgments that the standard DEA models cannot.
  • Ning, D., Liang, G. and Liu, W. (2014). Adaptive Finite Element Approximation for an Elliptic Optimal Control Problem with Both Pointwise and Integral Control Constraints. Journal of Scientific Computing [Online] 60:160-183. Available at: http://dx.doi.org/10.1007/s10915-013-9790-0.
    In this paper, we study the adaptive finite element approximation for a constrained optimal control problem with both pointwise and integral control constraints. We first obtain the explicit solutions for the variational inequalities both in the continuous and discrete cases. Then a priori error estimates are established, and furthermore equivalent a posteriori error estimators are derived for both the state and the control approximation, which can be used to guide the mesh refinement for an adaptive multi-mesh finite element scheme. The a posteriori error estimators are implemented and tested with promising numerical results.
  • Ma, C., Liu, D., Zhou, Z., Zhao, W. and Liu, W. (2014). Game cross efficiency for systems with two-stage structures. Journal of Applied Mathematics [Online] 2014. Available at: http://dx.doi.org/10.1155/2014/747596.
    Data envelopment analysis (DEA) is a nonparametric approach for measuring the relative efficiencies of peer decision-making units (DMUs). For systems with two-stage structures, where all the outputs from the first stage are the only inputs to the second stage, the centralized model, which is based on the concept of cooperative game theory, has been widely used to examine the efficiencies of such systems. We define the cross efficiencies of systems with two-stage structures. Since the centralized model may lead to multiple and unacceptable cross efficiencies and rankings of DMUs due to its high flexibility in choosing optimal weights on input and output factors, we develop a game model to obtain a unique cross efficiency measure, which is constructed from the perspective of noncooperative game. An iterative algorithm is then proposed to obtain the game cross efficiencies for the overall systems and subsystems. We use the proposed game model to evaluate the performance of top 30 US commercial banks. The results show that the game model can lead to a unique reasonable cross efficiency for each DMU.
  • Yang, G., Yang, J., Liu, W. and Li, X. (2013). Cross-efficiency aggregation in DEA models using the evidential-reasoning approach. European Journal of Operational Research [Online] 231:393-404. Available at: http://dx.doi.org/10.1016/j.ejor.2013.05.017.
    Cross-efficiency in data envelopment analysis (DEA) models is an effective way to rank decision-making units (DMUs). The common methods to aggregate cross-efficiency do not consider the preference structure of the decision maker (DM). When a DM's preference structure does not satisfy the "additive independence" condition, a new aggregation method must be proposed. This paper uses the evidential-reasoning (ER) approach to aggregate the cross-efficiencies obtained from cross-evaluation through the transformation of the cross-efficiency matrix to pieces of evidence. This paper provides a new method for cross-efficiency aggregation and a new way for DEA models to reflect a DM's preference or value judgments. Additionally, this paper presents examples that demonstrate the features of cross-efficiency aggregation using the ER approach, including an empirical example of the evaluation practice of 16 basic research institutes in Chinese Academy of Sciences (CAS) in 2010 that illustrates how the ER approach can be used to aggregate the cross-efficiency matrix produced from DEA models.
  • Zhou, Z., Wang, M., Ding, H., Ma, C. and Liu, W. (2013). Further study of production possibility set and performance evaluation model in supply chain in DEA. Annals of Operations Research [Online] 206:585-592. Available at: http://dx.doi.org/10.1007/s10479-013-1365-9.
    Performance evaluation is an importance issue in supply chain management. Yang et al. (Ann. Oper. Res. 38(6):195–211, 2011) defined two types of supply chain production possibility sets and proved the equivalence between them. Based on the sub-perfect CRS production possibility set, they proposed a supply chain DEA model to appraise the overall technical efficiency of supply chains. The relationship among efficiency scores of the proposed model, CCR models of system and subsystems are discussed. However, we find that the equivalence between the two types of supply chain production possibility sets is not correct. The proofs of their three theorems are all problematic. In this paper, we correct some results and give three new proofs.
  • Zhou, Z., Sun, L., Yang, W., Liu, W. and Ma, C. (2013). A bargaining game model for efficiency decomposition in the centralized model of two-stage systems. Computers and Industrial Engineering [Online] 64:103-108. Available at: http://dx.doi.org/10.1016/j.cie.2012.09.014.
    Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). The centralized model has been widely used to examine the efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Since there may exist some flexibility in decomposing the overall efficiency between the two stages when multiple optimal weights exist, we develop a Nash bargaining game model to obtain a fair efficiency decomposition for the two stages while keeping the overall efficiency unchanged under this circumstance. The minimal achievable efficiencies for the two stages are used as the breakdown point and the unique bargaining decomposition of the overall efficiency is obtained subsequently. The Nash bargaining game model is applied to evaluate the performance of 10 branches of China Construction Bank.
  • Xu, F., Zhang, D., Yang, G. and Liu, W. (2013). Game perspectives of DEA models and their duals. Journal of Applied Mathematics [Online] 2013. Available at: http://dx.doi.org/10.1155/2013/879325.
    We present a series of two-person games, which lead to various DEA models. The relationship between the DEA models and the games is explicit in our setting, although the Nash equilibrium solutions do not generally exist. Besides the classic DEA models, we also establish an explicit relationship between the games and some extended DEA models, such as free disposable hull DEA models and "negative" or "inverted" DEA models.
  • Du, N., Shi, J. and Liu, W. (2013). An effective gradient projection method for stochastic optimal control. International Journal of Numerical Analysis and Modeling [Online] 10:757-774. Available at: http://www.math.ualberta.ca/ijnam/Volume-10-2013/No-4-13/2013-04-01.pdf.
    In this work, we propose a simple yet effective gradient projection algorithm for a class of stochastic optimal control problems. The basic iteration block is to compute gradient projection of the objective functional by solving the state and co-state equations via some Euler methods and by using the Monte Carlo simulations. Convergence properties are discussed and extensive numerical tests are carried out. Possibility of extending this algorithm to more general stochastic optimal control is also discussed.
  • Liu, W., Meng, W., Mingers, J., Tang, N. and Wang, W. (2012). Developing a Performance Management System Using Soft Systems Methodology: A Chinese Case Study. European Journal of Operational Research [Online] 223:529-540. Available at: http://dx.doi.org/10.1016/j.ejor.2012.06.029.
    The economic crisis created major problems for a successful, hi-tech Chinese company – Tonsan. They already had in place a performance management system based around the balanced scorecard which worked successfully in times of growth and high demand. However, with the world downturn they suddenly found that their current system was not able to cope with the demands placed on it. The authors were called in and decided to design a new, strategic performance management system to overhaul all the key business processes. The approach taken to develop the PM system was based around soft systems methodology (SSM), a well established systems-based approach to problem solving and organizational design. The methodology progressed from the development of key strategic objectives (using the BSC and strategy maps), through a structured decomposition of necessary organizational activities, the construction of key performance indicators, the specification of targets, to communication and future planning. It involved significant levels of participation and communication throughout the organization. The results were judged by senior management to have been very successful, and the company has grown significantly.
  • Chen, Y., Huang, F., Yi, N. and Liu, W. (2011). A Legendre–Galerkin Spectral Method for Optimal Control Problems Governed by Stokes Equations. SIAM Journal on Numerical Analysis [Online] 49:1625-1648. Available at: http://dx.doi.org/10.1137/080726057.
    In this paper, we study the Legendre–Galerkin spectral approximation of distributed optimal control problems governed by Stokes equations. We show that the discretized control problems satisfy the well-known Babuška–Brezzi conditions by choosing an appropriate pair of discretization spaces for the velocity and the pressure. Constructing suitable base functions of the discretization spaces leads to sparse coefficient matrices. We first derive a priori error estimates in both $H^1$ and $L^2$ norms for the Legendre–Galerkin approximation of the unconstrained control problems. Then both a priori and a posteriori error estimates are obtained for control problems with the constraints of an integral type, thanks to the higher regularity of the optimal control. Finally, some illustrative numerical examples are presented to demonstrate the error estimates.
  • Zhang, D., Banker, R., Li, X. and Liu, W. (2011). Performance Impact of Research Policy at the Chinese Academy of Sciences. Research Policy [Online] 40:875-885. Available at: http://dx.doi.org/10.1016/j.respol.2011.03.010.
    We present evidence on productivity improvement experienced by the research institutes of the Chinese
    Academy of Sciences (CAS) after its implementation of the Knowledge Innovation Program (KIP). Using
    a balanced panel of data on R&D inputs and outputs of 59 research institutes in CAS, we analyze the
    productivity, technological and efficiency changes from 1997 to 2005.Wedocument that the CAS research
    institutes have a productivity growth of 12.5% from 1998 to 2005, which can be further decomposed into
    8.8% attributed to technological progress and 3.3% to efficiency improvement. Results of regional analysis
    show that institutes in Beijing and Shanghai, performed better than institutes in other regions during the
    same period.
  • Liu, W., Zhang, D., Meng, W., Li, X. and Xu, F. (2011). A Study of DEA Models without Explicit Inputs. Omega [Online] 39:472-480. Available at: http://dx.doi.org/10.1016/j.omega.2010.10.005.
  • Liu, W., Cheng, Z., Mingers, J., Qi, L. and Meng, W. (2010). The 3E Methodology for Developing Performance Indicators for Public Sector Organizations. Public Money & Management [Online] 30:305-312. Available at: http://dx.doi.org/10.1080/09540962.2010.509180.
  • Xu, F., Liu, W. and Mingers, J. (2010). Modifications of the g-index to improve its discriminatory power. Geomatics and Information Science of Wuhan University 35:23-28.
  • Mingers, J., Liu, W. and Meng, W. (2009). Using SSM to Structure the Identification of Inputs and Outputs in DEA. Journal of the Operational Research Society [Online] 60:168-179. Available at: http://dx.doi.org/10.1057/palgrave.jors.2602542.
    This paper reports on an innovative combination of hard and soft methods-soft systems methodology (SSM) with data envelopment analysis (DEA). Problems in defining and agreeing appropriate inputs and outputs for DEA led to the use of SSM as a way or producing a comprehensive and systemic database of performance indicators. The contributions of the paper are: the use of SSM to improve DEA specifications; conceptual clarifications within both SSM and DEA; and an innovative example of multimethodology. These developments are illustrated through a study evaluating the performance of the basic research institutes of the Chinese Academy of Sciences.
  • Liu, W., Gong, W. and Yan, N. (2009). A new finite element approximation of a state-constrained optimal control problem. Journal of Computational Mathematics 27:97-114.
    In this paper, we study numerical methods for an optimal control problem with point-wise state constraints. The traditional approaches often need to deal with the delta-singularity in the dual equation, which causes many difficulties in its theoretical analysis and numerical approximation. In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state, whose optimality condition is characterized by a fourth order elliptic variational inequality. Then direct numerical algorithms (nonconforming finite element approximation) are proposed for the inequality, and error estimates of the finite element approximation are derived. Numerical experiments illustrate the effectiveness of the new approach.
  • Liu, W. and Yan, N. (2009). LOCAL A POSTERIORI ERROR ESTIMATES FOR CONVEX BOUNDARY CONTROL PROBLEMS. SIAM Journal on Numerical Analysis [Online] 47:1886-1908. Available at: http://dx.doi.org/10.2307/27862714.
    In this paper, we derive some improved a posteriori error estimates for finite element
    approximation of Neumann boundary control problems. We first establish local upper a posteriori error estimates for both the state and the control approximation of the general convex boundary control problems. We then derive local upper and lower a posteriori error estimates for a class of control problems that frequently appear in applications.
  • Liu, W., Meng, W. and Zhang, D. (2008). Two-Level DEA Approaches in Research Institute Evaluation. Omega [Online] 36:950-957. Available at: http://dx.doi.org/10.1016/j.omega.2007.12.005.
    It is well known that the discrimination power of data envelopment analysis (DEA) models will be much weakened if too many input or output indicators are used. It is a dilemma if decision makers wish to select comprehensive indicators, which often have some hierarchical structures, to present a relatively holistic evaluation using DEA. In this paper we show that it is possible to develop DEA models that utilize hierarchical structures of input–output data so that they are able to handle quite large numbers of inputs and outputs. We present two approaches in a pilot evaluation of 15 institutes for basic research in the Chinese Academy of Sciences using the DEA models.
  • Liu, W., Meng, W. and Zhang, D. (2008). A study of Multi-level DEA Models and Applications. Chinese Journal of Management Science 16:148-154.
  • Feng, T., Yan, N. and Liu, W. (2008). Adaptive Finite Element Methods for the Identification of Distribution Parameters in Elliptic Equation. Advances in Computational Mathematics [Online] 29:27-53. Available at: http://dx.doi.org/10.1007/s10444-007-9035-6.
    In this paper, adaptive finite element method is developed for the estimation
    of distributed parameter in elliptic equation. Both upper and lower error bound
    are derived and used to improve the accuracy by appropriate mesh refinement.
    An efficient preconditioned project gradient algorithm is employed to solve the
    nonlinear least-squares problem arising in the context of parameter identification
    problem. The efficiency of our error estimators is demonstrated by some numerical
  • Yang, D., Chang, Y. and Liu, W. (2008). A priori error estimate and superconvergence analysis for an optimal control problem of bilinear type. Journal of Computational Mathematics 26:471-487.
    In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L-2-norm error estimates and the almost optimal L-infinity-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.
  • Chen, Y., Yi, N. and Liu, W. (2008). Legendre-Galerkin Spectral Method for Optimal Control Problems Governed by Elliptic Equations. SIAM Journal on Numerical Analysis [Online] 46:2254-2275. Available at: http://dx.doi.org/10.1137/070679703.
    In this paper, we study the Legendre-Galerkin spectral approximation for a constrained optimal control problem. We first derive a priori error estimates for the spectral approximation of optimal control problems. Then a posteriori error estimates are obtained for both the state and the control approximation. A preconditioning projection algorithm is proposed with some numerical tests.

Book section

  • Liu, W. and Sirlantzis, K. (2009). SSC Minimization Algorithms. In: Floudas, C. and Pardalos, P. eds. Encyclopaedia of Optimization (2nd ed.). Springer Verlag, pp. 3662-3665.


  • Liu, W., Mingers, J. and Xu, F. (2009). Modifications to the G-Index to Improve Its Discriminatory Power. University of Kent Canterbury.
  • Mingers, J., Liu, W., Chen, Z., Li, Q. and Meng, W. (2009). The 3E Methodology for Developing Performance Indicators for Public Sector Organisations. University of Kent Canterbury. Available at: http://dx.doi.org/10.1080/09540962.2010.509180.


  • Aljazea, A. (2020). Warranty Risk Management For the Consumer Durable Manufacturers.
    Warranty is a contractual obligation for maintenance upon failures of sold items during a warranty period. Warrantors utilise warranty as a strong promotional tool. Although warranty can bring some benefits, it involves various types of risks that may lead to negative impact (such as economic loss) on the warrantor. Systematic analysis of such risks can protect warrantors from potential losses. Based on a critical and comprehensive analysis of the existing warranty literature, very few studies discuss warranty risk management (WaRM). This thesis therefore aims to investigate WaRM from several perspectives and it makes contributions to the literature and practice, as shown below.
    Firstly, a WaRM framework was developed. The framework was thoroughly analysed.
    Secondly, a questionnaire was designed to gain an in-depth understanding of WaRM. From analysing the survey in the UK automotive industry, the following findings were obtained:
    (a) the most commonly used tool for identifying warranty hazards is the root cause analysis technique;
    (b) the most commonly used tool for assessing warranty risks is the failure mode effect and criticality analysis technique;
    (c) the top contributors to warranty incidents and costs were human error related, which mainly include: (1) human error at different stages of the product life cycle; (2) product modification at suppliers and original equipment manufacturer (OEM); (3) customers' fraud (4) insufficient collaboration between parties (suppliers, OEM and warranty services providers). Based on these findings, two generic warranty hazard taxonomies were designed.
    Thirdly, the selection of methods to mitigate WaR (warranty risk) is important but includes uncertainty. The thesis investigates the warranty risk mitigation process and analyses the main criteria that can be influenced. A selection method is developed based on the joint application of the cumulative prospect theory (CPT) and the analytic hierarchy process method (AHP). The new method can guide decision makers to the selection of mitigation methods over their conflicting views and their attitudes towards risks.
    Fourthly, a warranty policy includes both warranty price and duration. Optimisation of warranty policies is therefore vitally important. The thesis also developed a CPT-based warranty model to optimise warranty price considering the warrantor's and buyers' risk attitudes. A numerical example is provided to illustrate the proposed models and the sensitivity of the profit to different risk attitudes for the parties. Accordingly, the main findings are: (1) The warrantor's risk attitude has less impact on the profit compared to the buyers' risk attitudes; (2) the increase in the repair cost may lead buyers to accept higher warranty price; and (3) the higher the buyers perceive the product failure rate, the more likely they will be willing to buy the extended warranty.
    The theoretical implications of this thesis are listed as follows:
    (a) Develop a framework for WaRM.
    (b) Determine the top contributors to warranty hazards and hence two taxonomies were developed.
    (c) Develop a decision model to select the optimal mitigation plan to respond to the emergent warranty risk.
    (d) Develop a mathematical model to optimise warranty price considering the buyer and warrantor point of views towards the expected repair cost and claims cost, respectively.
    The practical implications of this thesis are listed as follows:
    (a) The WaRM framework will provide warranty practitioners with the required guidelines to manage warranty risks.
    (b) The result of using the streaming data as an early warning tool has shown its efficiency in highlighting the warranty issues.
    (c) The warranty hazards taxonomies might help warranty practitioners in improving the process, procedures or technologies which are required to reduce the occurrence of warranty risks.
    (d) The development of WaRM-CPT model may aid the decision makers in selecting the optimal mitigation plan to respond to an emergent warranty risk.
    (e) The determination of the optimal warranty price can be achieved when the warrantor and buyers views are considered. To this end, a mathematical model is provided.
  • Zhao, L. (2017). Performance Management in Small and Medium Size Enterprises in China.
    The recent development and issues of small and medium size enterprises (SMEs) attract increasing attention from many researchers. However, the existing literature mainly focus on general management issues of SMEs, such as human resource and marketing etc.. There is little study conducted from the perspective of performance management for SMEs. Thus in this thesis, we focus on performance management in SMEs in China, and try to explore the possible effective performance management models for them.
    We firstly review the key issues commonly discussed in the existing SME studies. Based on the literature, we identify several main issues that are related to performance management of SMEs. We also notice that effective performance management models are often closely related to organizational structure. Thus we carry out reviews of organizational structure theories, especially Minzberg's configuration theory. Adjustments and refinements of the performance management six steps are carry out with the help of literature reviews of SME issues and Minzberg's configuration theory. After that, a further focused exploratory research is carried out. A questionnaire is designed and distributed in an industrial-based area of China, 300 local SMEs were participated in the survey. The questionnaire is mainly designed to investigate the actual performance management practice of SMEs as well as their current issues. Both qualitative and quantitative data is collected and analyzed. The analysis result shows that performance management practices in fast-growing SMEs are largely consistent with our adjusted performance management six steps. Meanwhile, we also identify some emerging issues in many sample SMEs through open questions of the questionnaire. After further discussions with some SME executives, we found that the management issues of '90s employees' are quiet severe in local SMEs, and traditional performance management approaches failed to deal with these issues. However, some new management approaches are reported to be helpful to improve the situation but not yet been studied academically. Thus we carry out a follow up study in order to explore the new approaches and try to explain the mechanism by leader member exchange theory. A semi-structured interview is designed and carried out in a local SME which adopted the new management approaches. The result provides some evidence for the proposed mechanism, which could be helpful for further studies.
  • Zheng, Y. (2017). Theory and Action Research on a New Framework and Approach of Performance Management.
    Today, the activities relevant to performance management (PM) can be found in every corner of business, and its importance could be described by a famous business motto that whether a company measures its workforce in hundreds or thousands, its success relies solely on performance. Despite its importance as an enabler of successful business, some issues and shortcomings still exist in the performance management research and its implementation, which can be largely categorized into two main challenges.
    The first challenge is reflected in the PM dilemma of SMEs. Most existing PM frameworks focus on mechanistic organisations of significant size, yet small and medium enterprises, which comprise 99 percent of business in the UK and 94.15 percent in China, benefit little from the extant PM research. The second PM challenge is combining PM with business and management process innovations. Even for an organisation with simple operating cores, current PM frameworks provide little guidance on how to introduce innovations during performance management system (PMS) building up and management. This issue further causes difficulties in managing performance in complex operating cores, which is exemplified by the challenges of carrying out PM in an R&D unit.
    The above challenges are quite typical and should be dealt with in the level of performance management framework. We believe that existing PM frameworks are not built around an organisation's performance generation processes and therefore may not be able to handle many issues effectively, including those outlined above. Thus, the research objectives of this thesis are to develop a PM framework that is built around performance generation and also has mechanisms to address the above issues. Furthermore, we need to develop implemental approaches within the framework that can effectively deal with these challenges in real business cases.
    To accomplish the aforementioned research objectives, a comprehensive typological literature review was carried out to analyze the characteristics and features of the existing PM frameworks. Next, based on the literature research, a new PM framework, namely as the performance tree (PT) framework was introduced in Chapter five, which focuses on the performance generation processes of organisations and also contains mechanisms to accommodate different approaches for a wide range of organisations. In addition, two implemental approaches of PT frameworks were developed in the thesis for the sake of solving the pressing PM issues in SMEs and R&D unit.
    This research has the following four main contributions:
    1. A significant research gap was identified that the existing PM frameworks largely ignored the procedures of performance generation which could lead organisations to be near-sighted, unsustainable, and even experience strategic failure.
    2. A new performance management framework, PT framework was developed in this thesis. The PT framework adopts a performance-based perspective to explain performance generation and management processes; also it contains mechanisms to accommodate different approaches for a wide range of organisations seeking to handle the pressing PM issues
    3. An implemental approach of PT for classic Chinese manufacturer SMEs was developed in the thesis. Comparing with the existing PM approaches, the new one fully considers the managerial and operational characteristics of SMEs, such as fast-changing organisational chart and high demand for organisational adjustments.
    4. An implemental approach of PT for Chinese R&D units under was developed in the thesis. The approach considers both the characteristics of R&D management and the specific PM needs, and hence a PMS in accordance with core operation of R&D units can be developed under its guidance. Meanwhile, a behavioural evidence-based performance measurement system is accommodated in the approach to better measure and evaluate R&D staff's performance.
  • Song, Y. (2016). Performance Management in Chinese Commercial Banks.
    This dissertation aims to design and implement a tailored performance management framework for Chinese commercial banks in order to deal with some of the bank problems. Chinese commercial banks are experiencing rapid development from both internal management and external environments. With increasingly fierce competition, more strict risk management requirements and ongoing reform of process-oriented bank, many issues emerged regarding to the banks management and operations. Performance management is believed to be an effective tool to deal with some of the bank problems. However, the current performance management frameworks used in Chinese commercial banks are mostly designed for general organizations.There is lack of a systematic performance management framework specially designed for Chinese commercial banks considering features of banking operations and their current situations. Thus in this study, the main features of Chinese commercial banks are firstly discussed, which include risk management and external supervisory institutions. Then a performance management review is carried out including key definitions and current developments of performance management theories as well as some performance management methods. The commonly applied six steps performance management framework is adopted in this research since it is consistent with the research purpose. After that, the current performance management studies and practices in Chinese commercial banks are reviewed and discussed. Meanwhile, recent studies show that suitable performance management models are closely related to organizational structure. Therefore a review of organizational structure theories, especially the Minzberg's configuration theory, is carried out. The configuration theory suggests applying different management approaches for different parts of an organization, which assists to identify different structures in Chinese commercial banks and then design proper performance management activities. Based on the above review, a performance management framework for Chinese commercial bank is developed. This framework initially follows the six steps framework and integrates the bank features in management and operations into the performance management activities. The configuration theory is also applied in this framework in order to identify performance management targets as well as design proper performance management approaches. The main contingency factors related to this framework are discussed, especially the factor of stable organizational structure, since a rapid changing organizational structure requires further adjustments of the framework. This framework is applied in a case study which is carried out in a Chinese commercial bank located in Henan province. A performance management system is designed and implemented according to the framework based on the banks current situation. Feedback is collected after the implementation, and generally is positive. The framework is then adjusted by introducing performance tree method in order to deal with rapidly changing organizational structure. Compared with other methods, Performance tree method does not rely on the current organizational structure (e.g. Department structure) to carry out the strategy decomposition and deployment. It is also powerful in looking for innovative improvements in operations. The adjusted framework is applied in another case study carried out in a commercial bank located in Zhejiang province. This bank is experiencing rapid change in both management and operations due to process-oriented banking reform. Traditional performance management approach is found failed to deal with their current situation. A performance management system is designed for this bank based on the adjusted framework. Moreover, we also assist to develop a digital mission monitoring system to track and carry out their daily performance management activities. The feedback is positive after the implementation, and the bank is praised for good progress in building of process-oriented bank. The main contribution of this dissertation is the design and implementation of the tailored performance management framework for Chinese commercial banks, especially the adjustments in framework by introducing the performance tree method. It enriches theories and practices of performance management system in a rapid changing organizational structure. Further studies are suggested to look for more applications of performance tree method in different type of organizations.
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