Other Models and Issues

4.5.1 Other Models

DEA can be regarded as a body of concepts and methodologies that has evolved since the seminal work of Charnes, Cooper and Rhodes (1978). The CCR ratio model has been the focus of this dissertation to highlight the fundamental mechanisms that have propelled the application of DEA. It has yielded objective evaluations of efficiencies and thus inefficiencies of decision making units. By revealing the inadequacies of the non- performing units it provides a path for improvement. The flaw in the original model however, was the assumption that movements (toward efficiency) were at constant returns to scale. The CCR yields a piecewise linear constant RTS surface. CCR type models, under radial efficiency, do not take into account input excesses and output shortfalls, i.e. non-zero slacks. The slacks-based measure (SMB) addressed this by using the additive model “to give scalar measures from 0 to 1 that identify all of the inefficiencies that the model can identify” (Cooper, Seiford and Tone 2006, p. 104). The Banker-Charnes-Cooper (BCC) model (1984) distinguished between technical and scale inefficiencies. It estimated TE at given scales of operations by evaluating the benefits of using decreasing, increasing or constant returns-to-scale to enhance efficiency. The BCC yields a piecewise linear variable RTS envelopment surface.

The multiplicative models use piecewise log-linear or piecewise Cobb-Douglas envelopment instead of the traditional linear piecewise surface.

The additive and extended additive model relates to the CCR model but incorporates Pareto’s economic concept and Koopman’s earlier work.

An evolution of the DEA concept and methodologies in the first 15 years of this approach is detailed in Charnes et al. (1994, p.12), with other authors mentioned earlier (Emrouznejad and Thanassoulis 2005; DEAzone 2005) adding to this list in later years.

4.5.2 Other Issues

The body of knowledge surrounding DEA and its applications is growing steadily and becoming diverse. It is not expected that this paper can fully explore all the issues but some additional commentary may give a perspective of DEA’s applicability. The earlier models were implicit in the notion that more outputs and less inputs were positive achievements, and consequently were designed around this axiom with no provision for alternatives. In recent times the focus on operational efficiencies has broadened to include the impact of these efficiencies beyond the organisation. For example, increased productive output may be seen positively by stockholders, economists, and government and company staff, yet be frowned upon by the community. Increased output may mean increased waste, pollution or environmental damage consequent opun acheiving the perceived affordability of a decrease in the purchase cost per unit. Traditional DEA models could not accommodate such negative outputs. Consequently, strategies such as loading the inputs or inversing outputs to become inputs, e.g. pollution becomes an input cost to compensate, were adopted. Undesirable inputs/outputs in variable returns to scale (VRS) envelopment models have now been developed (Zhu 2003).

DEA purposely identifies the best-practice frontier and performance is measured against this. It is usual to have more than one DMU on the efficient frontier. If all the efficient DMUs define the frontier and occupy different positions on it, which is the best of the efficient DMUs? Fortunately a way of ranking efficient DMUs through a context- dependent analysis allows a form of first tier, second tier and so on, elimination until the ‘best of the best’ is left.

Congestion in economics refers to situations where reductions in inputs can actually increase outputs. For example, an oversupply of fertilizer may actually reduce output. The VRS model can be re-written to account for this and to include the impact of (input) slack on (input) congestion.

Supply chain efficiencies, in particular those value-adding processes that are available through an analysis of the total supply chain, have been elusive due to the existence of multiple and different measures that members of the chain use, and the adversarial nature of contractual negotiations. Zhu (2003) contends that traditional DEA fails to correctly

characterize the performance of the supply chain because the efficient performance of individual components of the chain may not be correctly identified. He presents models that can address this.

Non-discretionary inputs and outputs are those situations where exogenously fixed or non-management-controlled environments impact on possible efficiencies of the DMUs. Traditional DEA models assume that all inputs and outputs can be varied at the discretion of management or others, but ‘non-discretionary variables’ not subject to management control may be significant enough to be included in consideration. These variables may be as diverse as weather conditions for flying aircraft, the demographics of a regional customer bases, the age of storage facilities, etc. A mathematical treatment of the data to minimize the influence of non-discretionary input excesses or output slacks is possible and has been formulated for CCR and BCC models (Charnes et al. 1994).

4.6 Conclusion

This chapter has demonstrated that DEA is founded on a statistical base which defines productivity as a measure of efficiency represented by the ratio of inputs to outputs. The history and development of DEA shows a strong grounding in the study of the efficiencies represented by these ratios, in organisations which are traditionally not regarded as profit driven commercial enterprises and so a limited choice of suitable PM processes. The commercial organisations on the other hand, through their profit motivated missions, have had a plethora of PM instruments at their disposal.

Nevertheless, the growth in DEA has demonstrated its acceptance as not only an effective diagnostic tool for non-commercial organizations, but more recently as a valuable addition to measuring efficiencies and efficiency-like relationships in a variety of commercial environments.

The production or efficiency frontier displayed by DEA, in so far as it can be displayed in simple two-dimensional graphical models, shows that there are conditions where the achievable efficiencies under existing conditions are as good as can be expected, while maintaining a Pareto optimality.

Technical and allocative efficiencies with input and output orientations show how efficiencies are calculated, and subsequently how inefficiencies can be improved in non- performing units.

The weighting of factors and its significance was discussed, together with suggestions as to how this could be addressed in the future. It was also highlighted that this study would not pursue the course of formulating a strategy for calculating weights since the DEA algorithm’s assignment of values for these weightings provides a solution that is regarded as conservative.

DEA is not without weaknesses. These were delineated with suggestions that could help ameliorate the difficulties they present. Alternatively the strengths of DEA were highlighted to show why such an optimization technique is appropriate and ideal for any analysis of efficiencies which represent performance. And, while DEA is not the only model that is capable of these revelations, it is one that is finding support in areas as diverse as SCM and CG.

Finally, the DEA application is linked to the study of CG through one of its dimensions – that of CSR. The CSR study is presented in the next chapter, along with how it was applied using the successful procedural steps advanced by Golany and Roll in 1989.