•We measure the efficiency of two-stage system with shared and reused resource.•We introduce additive and non-cooperative efficiency measures to this system.•A heuristic algorithm is suggested to ...transform nonlinear model into a linear one.•We prove the heuristic algorithm to be a good and effective approach.•The new approaches are applied to industrial production processes of China.
Data envelopment analysis (DEA) is an approach for measuring the performance of a set of homogeneous decision making units (DMUs). Recently, DEA has been extended to processes with two stages. Two-stage processes usually have undesirable intermediate outputs, which are normally considered be unrecoverable final outputs. In many real situations like industrial production however, many first-stage waste products can be immediately used or processed in the second stage to produce new resources which can be fed back immediately to the first stage. The objective of this paper is to provide an approach for analyzing the reuse of undesirable intermediate outputs in a two-stage production process with a shared resource. Shared resources are input resources that not only are used by both the first and second stages but also have the property that the proportion used by each stage cannot be conveniently split up and allocated to the operations of the two stages. Additive efficiency measures and non-cooperative efficiency measures are proposed to illustrate the overall efficiency of each DMU and respective efficiency of each sub-DMU. In the non-cooperative framework, a heuristic algorithm is suggested to transform the nonlinear model into a parametric linear one. A real case of industrial production processes of 30 provincial level regions in mainland China in 2010 was analyzed to verify the applicability of the proposed approaches.
•Renewable energy quotas incorporating equality and efficiency are allocated at regional level.•The methods combined entropy and ZSG-DEA models are proposed.•The quota allocation results have ...achieved the goal of transferring the responsibility of renewable energy quota from western to eastern.
Renewable energy policy plays an important role in achieving carbon neutrality which is main goal for climate change mitigation. China is striving to promote the implementation of renewable portfolio standards under the goal of carbon neutralization in 2060. Thus, based on the principles of equality and efficiency, we apply zero sum gains data envelopment analysis (ZSG-DEA) model combined with entropy model to allocate China's renewable energy quota from provincial perspectives. Further, we introduce an environmental Gini coefficient to evaluate the rationality of allocation results. The allocation results show that Guangdong, Jiangsu, Sichuan and Shandong are four provinces with the most renewable energy quota, while Hainan, Guizhou, Gansu, and Xinjiang are four provinces with the least quota. In addition, the quota allocation results have achieved the goal of transferring the responsibility of renewable energy quota from western provinces to eastern provinces. Last, managerial suggestions in promoting renewable energy development are discussed.
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•The platform’s combating effort has a non-monotonic effect on sellers’ profits.•Optimal combating effort level depends on the authentic firm’s production cost.•The authentic firm can ...be better off with a higher production cost.
In recent years, criticism of online marketplaces has been incessant because of the widespread presence of counterfeit goods. This study develops an analytical framework to investigate the interactions among an online marketplace, an authentic brand seller, and a counterfeiter of the brand. Both sellers exert efforts to attract sales for the brand, and the online platform determines its effort level in combating counterfeiters. Our analysis reveals several interesting insights. First, our analysis shows that the platform’s combating effort has a non-monotonic impact on both sellers’ profits. Second, the platform’s optimal combating effort level relies on the production cost of the authentic firm. The platform finds it optimal to exert maximum possible effort to combat counterfeiters when the unit cost of the authentic product is very low, and not to combat when the unit cost is very high. Third, interestingly, the authentic seller can be better off with a higher production cost due to the strategic reaction of the platform whose revenue derives from both types of sellers. The intuition and managerial implications of these insights are discussed.
•Previous studies on closest targets are not based on Hölder distance functions.•In addition, they are based on conceptual framework or a multi-stage procedure.•Mixed integer linear program (MILP) is ...proposed to find the closest targets.•The proposed model satisfies strong monotonicity on an extended facet.•A real case of universities in China's national “985 Project” is analyzed.
Within the framework of data envelopment analysis (DEA) methodology, the problem of determining the closest targets on the efficient frontier is receiving increased attention from both academics and practitioners. In the literature, the number of approaches to this problem are increasing, most of which are based on the computation of closest targets. Some of the existing approaches satisfy the important property of strong monotonicity. However, they tend to either propose a complex conceptual framework and multi-stage procedure or change the original definition of Hölder distance functions. Clearly, these approaches cannot be solved easily when there are many “extreme” efficient units with multiple inputs and multiple outputs. To solve this problem, we consider the notion of the extended facet production possibility set (EFPPS). In particular, we propose a Mixed Integer Linear Program (MILP) to find the closest efficient targets and that is related to a measure that satisfies the strong monotonicity property. Additionally, in this paper, the proposed approach is applied to real data from 38 universities involved in China's 985 university project.
The Chinese government has proposed a dual credit policy (DCP) as a substitute for electric vehicle (EV) subsidies, which fluctuates the auto market. To investigate the policy substitution influences ...for the production and pricing strategies, we use Stackelberg game paradigms to model a two-stage auto supply chain. The manufacturer regulated by the DCP produces both EV and internal combustion engine vehicles (ICEV). The retailer sells them to heterogeneous consumers. By backward induction, the optimal production and pricing strategies are derived for the subsidy policy only (scenario B) and with a joint subsidy policy and DCP (scenario DS). Our findings show, 1) different with only one case in scenario B, the manufacturer and the retailer have three corresponding optimal production and pricing strategies in scenario DS, according to the manufacturer’s Corporate Average Fuel Consumption credit (CAFC credit); 2) the demand for the ICEV may also decline like EV as the subsidies are phased out in scenario DS when the manufacturer’s CAFC credit is in balance case; 3) the changes of DCP rules may have different effects on the optimal production and pricing strategies in different CAFC cases.
•We studied optimal production and pricing when DCP is substituted for subsidy.•We characterized equilibriums in scenario B and scenario DS.•Phased out subsidies may have opposite impacts on ICEV sales in two scenarios.•Rules of the DCP impact differently on production and pricing in three cases.•Impacts of the NE credit price follow one threshold in case Ⅱ.
•New approach for common equilibrium efficient frontier selection is proposed.•The new approach considers each DMU’s minimum and maximum efficiencies.•A new Max-min model based on satisfaction degree ...is proposed.•An effective algorithm is proposed to solve the non-linear Max-min model.
As a non-parametric programming approach, Data envelopment analysis (DEA) has been extended to consider the situation of fixed-sum outputs, which causes competition among the evaluated decision making units (DMUs). Minimum reduction strategy of the fixed-sum output has been proposed to form a common equilibrium efficient frontier to solve the problem. However, the non-uniqueness of the common equilibrium efficient frontier problem has reduced the usefulness of this extended method. Aiming at solving the problem, we propose an extended secondary goal approach to further narrow the scope of the common equilibrium efficient frontier. Compared with traditional secondary goal approaches, the new approach has considered each DMU’s minimum and maximum inefficiency value. Specially, a Max-min model based on satisfaction degree is proposed to reflect each DMU’s satisfaction on achieving its final efficiency value. In addition, two effective algorithms are given to solve the non-linear Max-min model and further guarantee the uniqueness of common equilibrium efficient frontier. Last, we use a numerical example to illustrate our proposed models.
Carbon-economic inequality (CEI) occurs due to the unequal exchange between embodied CO2 emissions and value-added in interregional trade. How to reduce CEI has become an urgent task to realize the ...Sustainable Development Goals. In this study, we quantify the CEI in bilateral and regional trade in China using the embodied CO2 emission and value-added during 2012–2017. Then, we analyze the drivers of CEI changes using the multiplicative structural decomposition analysis. Finally, we measure national CEI using an extended Gini coefficient and further identify the sources of inequality using the Shapley decomposition approach. The results indicate that 1) inequalities in bilateral trade mainly occur between the three north regions (North, Northwest, and Northeast) and eastern coastal regions (Beijing–Tianjin, South coast, and Central coast), and the inequalities generally exhibit worsening trends during 2012–2017. In regional trade, the Northwest suffers the worst and widening inequalities, while the Southwest has obtained an expanded advantage. 2) the decomposition results show that coal efficiency and input structure disparities are the main factors that exacerbate CEI in bilateral trade between the three north and Beijing–Tianjin/South coast regions. Improved input structure is the leader in helping the Southwest reduce CEI in bilateral and regional trade. 3) the overall CEI continues to deteriorate, with the Gini coefficient increasing from 0.260 to 0.305 during 2012–2017, where regional gap and intra-regional inequality, coal-induced CO2 emission, and the electricity production industry are the leading causes. This exacerbated CEI calling for optimizing regional trade patterns and providing holistic solutions for sustainable development.
•Carbon-economic inequality embodied in China's interregional trade is analyzed.•China's national inequality is measured using an extended carbon Gini coefficient.•The source of overall inequality is analyzed using a Shapley decomposition method.•Multiple factors driving the changes in carbon-economic inequality are identified.•China's national carbon-economic inequality continues to worsen from 2012 to 2017.
•We address the issue of eco-design for transportation in SSCM.•DEA is extended to construct a nonlinear model to seek Pareto Optimal solutions.•A tractable linear algorithm is developed to solve the ...model.•A heuristic Joint Transportation Policy is resulted from the research.•The Joint Transportation Policy has been theoretically proved to be sustainable.
This study addresses the issue of eco-design for transportation in sustainable supply chain management (SSCM). Data envelopment analysis (DEA) is adopted and extended to construct a model for this application. This proposed model, together with the tractable algorithm developed in this research, can provide stakeholders with a Pareto Optimal transportation strategy. This derived transportation strategy can help stakeholders realize certain transportation goals with less resource consumption and pollution emission. The discussion presented leads to a heuristic Joint Transportation Policy and concludes with two useful suggestions for putting the strategy into practice. The proposed model was used in an empirical study of design sustainable transportation mechanism for one air-condition manufacturer in China to transport its products as well, the analysis further demonstrating the theoretical and practical value of this research.
In many real applications, there exist situations where some independent and decentralized entities will construct a common platform for production processes. A natural and essential problem for the ...common platform is to allocate the fixed cost or common revenue across these entities in an equitable way. Since there is no powerful central decision maker, each decision-making unit (DMU) might propose an allocation scheme that will favor itself, giving itself a minimal cost and/or a maximal revenue. It is clear that such allocations are egoistic and unacceptable to all DMUs except for the distributing DMU. In this paper, we will address the fixed cost allocation problem in this decentralized environment. For this purpose, we suggest a non-egoistic principle which states that each DMU should propose its allocation proposal in such a way that the maximal cost would be allocated to itself. Further, a preferred allocation scheme should assign each DMU at most its non-egoistic allocation and lead to efficiency scores at least as high as the efficiency scores based on non-egoistic allocations. To this end, we integrate a goal programming method with data envelopment analysis methodology to propose a new model under a set of common weights. The final allocation scheme is determined in such a way that the efficiency scores are maximized for all DMUs through minimizing the total deviation to goal efficiencies. Finally, both a numerical example from prior literature and an empirical study of nine truck fleets are provided to demonstrate the proposed approach.
•We propose a cross-efficiency evaluation approach based on Pareto improvement.•Our approach generates Pareto-optimal cross efficiencies for the DMUs.•Our approach has good power of improving the ...cross-efficiencies of the DMUs.•The cross-efficiency of each DMU will be equal to its self-evaluated efficiency.•The cross-efficiencies of all DMUs can be generated by only a common set of weights.
Cross-efficiency evaluation, as an extension tool of data envelopment analysis (DEA), has been widely applied in evaluating and ranking decision making units (DMUs). Unfortunately, the cross-efficiency scores generated may not be Pareto optimal, which has reduced the effectiveness of this method. To solve this problem, we propose a cross-efficiency evaluation approach based on Pareto improvement, which contains two models (Pareto optimality estimation model and cross-efficiency Pareto improvement model) and an algorithm. The Pareto optimality estimation model is used to estimate whether the given set of cross-efficiency scores are Pareto-optimal solutions. If these cross-efficiency scores are not Pareto optimal, the Pareto improvement model is then used to make cross-efficiency Pareto improvement for all the DMUs. In contrast to other cross-efficiency approaches, our approach always obtains a set of Pareto-optimal cross efficiencies under the predetermined weight selection principles for these DMUs. In addition, if the proposed algorithm terminates at its step 3, the evaluation results generated by our approach unify self-evaluation, peer-evaluation, and common-weight-evaluation in DEA cross-efficiency evaluation. Specifically, the self-evaluated efficiency and the peer-evaluated efficiency converge to the same common-weight-evaluated efficiency when the algorithm stops. This will make the evaluation results more likely to be accepted by all the DMUs.
