Performing Malmquist DEA in hospitality industry

The Malmquist productivity index or more commonly malmquist DEA (Data Envelopment Analysis) was first incepted by the researcher Malmquist in 1953 as a quantity to be used in the analysis of consumption of inputs (Färe, Grosskopf, & Margaritis, 2011).

R. S. Fare in 1994, however, developed a DEA-based Malmquist productivity index to check the productivity change over time (Fuentes & Lillo-Bañuls, 2015). In addition, according to Färe et al., (2011); the index decomposed into two components, one measuring the change in the technology frontier and the other the change in technical efficiency. The Malmquist productivity index can measure the ratio of DEA efficiencies in two different time periods with shifting DEA efficiency frontiers (Coelli, 2008). Färe et al., (2011) mentions that Malmquist productivity index can theoretically divided into two components;“catch-up” and “frontier shift”. However, the catch-up measures how much closer to the frontier a Decision Making Unit (DMU) or organization moves, while the frontier does not move. Moreover, frontier is composed of DEA efficiency measure. However, DMUs’ among all firms in a time period; the frontier shift means change at industry level.

Key features of Malmquist DEA

Furthermore, in the following points key features of Malmquist DEA to differentiate it between Cost efficiency and Multistage DEA is discussed.

  • Best for productivity index testing along with efficiency measurement.
  • It only works for more than one time period for any given DMU.
  • Requires input and output variables for all the years.
  • Balanced data for all the years and firms.
  • Can perform both CRS (constant returns to scale) and VRS (variable returns to scale)DEA and input and output oriented DEA.

Applications of Malmquist DEA

  1. To check the timelines of change in efficiencies over the period which is given by the malmquist productivity index (Fuentes & Lillo-Bañuls, 2015).
  2. Assess the performance of the organizations of over more than one year (Färe et al., 2011).
  3. In addition, to contrast the performance measurement and efficiency and to check the consistency of the DMUs (Yoruk & Zaim, 2005).
  4. Consequently another application is that it can be used to measure the productivity growth over the time and its efficiency change and technological change (Liu & Wang, 2008).
  5. Finally, one major application and advantage over other models is that it can be used for regress and progress of a DMU in different periods with efficiency and technology variations without considering the present value of money (Liu & Wang, 2008).

Hospitality Industry in India; A case study

This study considered three renowned hospitals of India, namely; Apollo Hospital, Fortis Hospital and Wockhartd Hospitals. Furthermore, in this case study, the data extracted from the annual reports of the three hospitals available at their official website. However, the annual reports range is for the years 2014 to 2016 (3 years). Hence in this study three years of timeline is considered. Moreover, for relevance of the study the input and output variables from the research done by Bhat, Verma, & Reuben, (2001) on hospitality industry has been adopted. Consequently, the input variable were; Total Expenditure and Number of Doctors and Nurses, while the output variables are Average revenue per occupied bed per day and Revenue from operations. Furthermore, both the frontiers will be conducted; CRS (constant returns to scale) and VRS (variable returns to scale) for Malmquist DEA to understand the change of findings and results.

Extracting and presenting the data in Malmquist DEA

  • Extract data from the annual reports and present in MS Excel
Dataset in MS Excel for malmquist DEA

Dataset in MS Excel

  • Next, input the data in Notepad
Dataset in Notepad

Dataset in Notepad

  • Finally, open the instruction file and change the codes as follows
    1. Change the Time Period to 3 (Since this is a dataset with three years of information)
    2. Next, 0 for Input oriented
    3. Change to 0 for CRS-DEA
    4. Next, 2 for both Input and output
    5. Change to 2 for Malmquist DEA
    6. Finally add no. of firms to 3
Open the DEAP.exe file and enter the instruction file name and enter

Open the DEAP.exe file and enter the instruction file name and enter

Malmquist DEA is a model that is best used when there is more than one year of data and malmquist productivity index is to be found. However here efficiency evaluation of firms whereby financial data considered to conduct Malmquist DEA. Lastly, in the next article however, we will represent the findings and interpretations from evaluating Malmquist CRS-DEA.


Avishek Majumder

Avishek Majumder

Research Analyst at Project Guru
Avishek is a Master in Biotechnology and has previously worked with Lifecell International Private Limited. Apart from data analysis and biological research, he loves photography and reading. He loves to play football and basketball in his spare time with an avid interest in adventure and nature. He was also a member of the Scouts in his school and has attended Military training.
Avishek Majumder

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