Construction of Pseudo CRS frontier for a negative data using RTS model of Allahyar & A modified multiplier BCC model

Abstract

Performance measurement of Decision Making Units (DMU) possessing an array of positive and negative type of input and output data has been an extensively researched topic in Data Envelopment Analysis. However, assessment of Returns to Scale (RTS) under negative data problem has only been attainable after the deliberation of a Variable Returns to Scale assumption. Steps referred earlier were indeed purported a solution around the vicinity of the Decision Making Unit under examination to predict the nature of the Returns to Scale of a firm. The extant investigation extends the research of Allahyar and Malkhalifeh [Comput. Ind. Eng. 82 (2015) 78–81] to identify a Pseudo Constant Returns to Scale Frontier for a negative data problem along with the new origin based on the provided data. However, this approach seems to be ineffective to create a frontier for multiple input output scenario. In this regard, a new variation of Multiplier form of BCC model is proposed here to detect the new origin for the sake of designing the Pseudo CRS frontier. Small examples are added for the elaboration of the CRS efficient DMUs using methods described by Allahyar and Malkhalifeh [Comput. Ind. Eng. 82 (2015) 78–81] to identify the new origin from the Multiplier form of BCC model. This outcome is finally validated with the aid of the multiplier model of Sahoo et al. [Eur. J. Oper. Res. 255 (2016) 545–558].