Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis

7STRONG COMPLEMENTARY SLACKNESS CONDITIONS

7.1 INTRODUCTION

This chapter¹ discusses the importance of strong complementary slackness conditions (SCSCs) in DEA. The use of SCSCs will be extended in Chapter 25 for an assessment on energy utility firms. The methodological concern of Chapter 25 is how to reduce the number of efficient organizations by applying both SCSCs and DEA‐DA (discriminant analysis). See Chapter 11 on DEA‐DA. Thus, this chapter provides a mathematical basis for Chapter 25 (ranking analysis).

To initiate this chapter, we return to Table 6.1 in which at least one DEA model(s) satisfies desirable properties related to OE, except unique projection for efficiency comparison and property of aggregation. The aggregation property, which not all models satisfy, may not be a serious problem in a practical perspective of DEA. An exception may be found in restructuring of industrial organizations, including merger and acquisition (M & A), where the sum of production factors needs to be examined by comparing it with their original achievements by separated firms. This type of managerial issue is very important from a business perspective, but difficult for us to discuss the issue by DEA because it needs to examine the corporate governance of an aggregated organization in a time horizon. A practical approach for discussing the industrial organization issue can be found in Charnes et al. (1988) and Sueyoshi (1991) that discussed how to examine a large‐scale industrial organization ...