مدل تجزیه و تحلیل عملکرد مبتنی بر مرز برای مدیریت زنجیره تامین:حالت هنر و دستورالعمل های پژوهش

Effective supply chain management relies on information integration and implementation of best practice techniques across the chain. Supply chains are examples of complex multi-stage systems with temporal and causal interrelations, operating multi-input and multi-output production and services under utilization of fixed and variable resources. Acknowledging the lack of system’s view, the need to identify system-wide and individual effects as well as incorporating a coherent set of performance metrics, the recent literature reports on an increasing, but yet limited, number of applications of frontier analysis models (e.g. DEA) for the performance assessment of supply chains or networks. The relevant models in this respect are multi-stage models with various assumptions on the intermediate outputs and inputs, enabling the derivation of metrics for technical and cost efficiencies for the system as well as the autonomous links. This paper reviews the state of the art in network DEA modeling, in particular two-stage models, along with a critical review of the advanced applications that are reported in terms of the consistency of the underlying assumptions and the results derived. Consolidating current work in this range using the unified notations and comparison of the properties of the presented models, the paper is closed with recommendations for future research in terms of both theory and application.

Supply chain management (SCM) was introduced as a common scientific and managerial term in 1982 (cf. Oliver & Webber, 1992) to describe a hierarchical control system for material, information and financial flows in a potentially multidirectional network of autonomous decision making entities. Although there is a lack of universally accepted definition (Otto & Kotzab, 1999), a well-used and typical definition of a supply chain is ‘a network of organizations that are involved, through upstream and downstream linkages in the different processes and activities that produce value in the form of products and services in the hand of the ultimate consumer’ Christopher (1998, p. 15). The management activity is consequently the coordination of this network, or ‘chain’, of independent processes as to achieve the overall goal in terms of value creation. Three elements are important in our context: the multi-level character of the network, the interdependency and the competitive objective. First, the underlying system is constituted of multiple layers, both horizontally (sequential processing) and vertically (control layers, levels of integration into firms, business units, joint ventures, information sharing, etc.). This implies that the systematic analysis of a supply chain must take into account the level of processing as well as the locus of control in order to understand the organization and its performance. Second, the ‘links’ in the chain form sequential processing stages that are interdependent with respect to potentially three types of flows; material flows in progressive processing, information flows specifying types and quantity of processes to be performed, and financial flows to reimburse or incentivize the units to devote time and resources to the joint activity. Third, a supply chain is not an arbitrary processing plan but it involves multiple independent organizations (conventionally at least three) cooperating under commercial conditions and subject to actual or potential future competition, both collectively in terms of the final output and individually for each processing stage. Taken together, the three observations underline that performance evaluation is of highest importance to assure continuity, competitiveness and, ultimately, survival of the network, but that this evaluation must take into account the specificities of the network character and the decision-making autonomy of the evaluated units. A wide range of metrics for supply chain performance have been proposed (cf. Melnyk et al., 2004 and Neely et al., 1995) using an equally diverse portfolio of methodologies (cf. Estampe, Lamouri, Paris, & Brahim-Djelloul, 2013). Whereas most SCM literature has been devoted to the elaboration and evaluation of absolute metrics, usually linked to the dimensions cost (profit), time (rates) and flexibility (change of rate), there has also been a growing awareness of the need to perform external benchmarking (Beamon, 1999), the lack of integration of metrics (Beamon, 1999 and Chan and Qi, 2003), the lack of system’s view (Holmberg, 2000) and the lack of non-cost indicators (Beamon, 1999 and De Toni and Tonchia, 2001). In response to this critique, several applications of non-parametric frontier analysis, such as Data Envelopment Analysis (DEA), have been proposed for supply chain management. The production-economic foundations and the capacity to derive a consistent set of informative performance metrics for a multi-input and multi-output setting qualify frontier analysis as a useful tool for operation management assessments. However, the interdependencies among evaluated units call for specific frontier models, in particular the multi-stage or network models (cf. Färe & Grosskopf, 1996b). These models explicitly take into account the network structure in the evaluation, deriving metrics that can evaluate both individual unit and chain-wide performance in the long and the short run. However, the rapid development of such models (e.g. Chen and Zhu, 2004, Chen et al., 2009, Chen et al., 2009, Chen et al., 2006, Färe and Grosskopf, 2000 and Zha and Liang, 2010) and their relevance to supply chain performance assessment have not yet been critically reviewed. It is to fill this need that this paper summarizes the state-of-the-art in frontier analysis models for supply chain management and their applications, along with identification of future research directions. We put emphasis on a special case of multi-level DEA, commonly called the two-stage process. The outline of this paper is organized as follows. In section 2, we discuss the relevant challenges with in SCM in terms of performance assessment. Section 3 is a short recapitulation of DEA definitions for readers not familiar with the models. In Section 4, we present a generic activity model for supply chain evaluation. In Section 5 we review the DEA-models including two-stage structures, models based on cooperative and non-cooperative game theory and the bi-level programming model. The paper is concluded in section 6 with a critical analysis of the reviewed work and some directions for future research.

Supply chain management (SCM) covers several disciplines and is rapidly growing. Performance measurement is an important activity, both for planning and optimization purposes. DEA as a non-parametric technique for measuring efficiency continues to enjoy increasing popularity. Reviewing the multi- and two-level extensions published in the DEA literature reveals a considerable wealth of different models, based either on restrictions in the reference set, the weight system or the sequence of optimization of the DMU problems. However, the analysis also shows several open problems in the application of DEA to supply chain performance measurement. First, the existing models demonstrate the limitations of and the rigidity in the model specification process. Whereas supply chains by definition involve several stages (normally at least three) interacting independently with markets for raw materials and intermediate outputs, bulk of the extensions are limited by explicit or implicit restrictions to two-stage processes with no third-party interaction. In practice, this implies a strict dyadic buyer-seller dichotomy in which all intermediate outputs are consumed by a single entity. The assumption is very strong and in open contradiction to standard results in multi-stage supply chain planning models, where intermediate plants and distribution centers are expected to serve multiple downstream units, within and/or without the focal enterprise. Moreover, the lack of flexibility in the model structure is commonly motivated by the solution approach, derivations of joint metrics etc. that consequently hamper the generalization of the results to a realistic situation. Further work is necessary on this fundamental point to allow applications of frontier-based methods to real multi-stage supply chains. Second, most models lack a clear economic or technical motivation for the intermediate measures. Besides the multi-stage property, one of the underlying features distinguishing supply chain management from general operations management is the prevalence of decentralized decision making. In economics and management science, we tend to attribute these decision makers with some procedural rationality that renders them susceptible to mathematical modeling. A common assumption is that the decision makers maximize some profit or objective function subject to some rationally imposed constraints, e.g. resource allocation across a group. It is therefore necessary for any performance assessment to take into account the objectives of the underlying units in their assessment, if the resulting estimate is to have any relevance as an indication for the effectiveness of their decision making. We note that some suggested models tend to abstract from the economic or preferential reality of the evaluated units in assuming that their objectives per se should be related to, or even centered on, the very metric that analysts propose for their evaluation. In fact, most models dispose of this step by simply assuming that the objectives of the unit correspond to the maximization of some single-stage evaluation problem, such as the conventional CRS formulation. Already in a single-stage setting, the interpretation of productivity measures is associated with many limitations, cf. Agrell and West (2001). In the supply chain setting, considering the interdependencies between the levels and the ambiguous character of the input resource restrictions, this hurdle is even more delicate to solve, both conceptually and mathematically. Here we need careful and well-justified behavioral motivation for the submodels, as well as an economically well-founded framework for the centralized models. Further consolidation of the literature based on game-theoretical approaches may be way to address this shortcoming. Third, the existing literature largely neglects an explicit modeling of the power or governance structures within the supply chain. Given the absence of a centralized decision maker, the modeler faces a hierarchical multi-criteria problem without any clear preferential structure. Whereas conventional approaches in economics would use Stackelberg-type bi-level games or Nash bargaining concepts, the supply chain management literature frequently employs non-cooperative and cooperative game theoretical approaches. Although some models are founded on elements hereof, there is need of stringent models unifying the evaluation model structure with the underlying assumptions about the power or governance structure within the chain. Such work, founded on economic theory and decision theory, may also eliminate the too frequent resort to ad hoc technical and scaling parameters in the models without any methodological foundation. Fourth, the relevant literature mostly takes into account the predominance of multiplicative models. Multi-product networks, especially for dynamic approaches, involve relatively large dimensional output vectors and likely (correctly) zero-valued observations. Multiplicative approaches (radial efficiency metrics) here yield computationally poor results with efficiency scores in the presence of significant slack, i.e. weak technical efficiency. Additive models (seminal work by Charnes, Cooper, Golany, Seiford, & Stutz, 1985) are traditionally viewed as inferior, lacking translation- and unit invariance (cf. Ali & Seiford, 1990) and being difficult to decompose into relevant submeasures. However, the special structure for supply chain problems, in which measurement units often can be qualitatively homogenous (value, weight, energy contents, pieces) may enable simple, consistent and informative decompositions based on additive transformations as in Agrell and Bogetoft (2005). The use of additive approaches also opens for analyses of multi-output cases of more realistic dimensions in terms of cost- versus technical efficiency. More work is necessary to determine the properties and robustness of such models in generalized multi-stage settings. The work by Chang et al. (2011) based on the non-radial Tone and Tsutsui (2009) model is here particularly interesting, also from a conceptual viewpoint. Stating these areas of desired progress is in no way negating the positive and productive wealth of work in the areas of two-stage non-parametric frontier models. On the contrary, it is this energy and thrust that will unlock the force of the models to attack the so far unsolved, frustrating and decisive problems found in supply chain performance measurement.