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5.   Fuad Selamzade: Measurement of the Efficiency of Azerbaijan Region Hotel
                          6.                                  Organization:  Window Analysis and Malmquist Index



                    By using a priori knowledge about the relative values of inputs and outputs for DEA
                    window model, the model including multiplier constraints to obtain definitive and
                    more realistic productivity estimates is suggested by Asmild et al. (2004). Here, the
                                                                                               i
                    dimensions sxL and rxL are included in the model, being used through the C  input
                         o
                    and C  output constraint matrices respectively. In this case, the formula (9) takes the
                    following form:

                                              Θkwt = minθ,λ,Zθ                                    (10)

                    The effect of adding these multiplier constraints to the DEA model is to eliminate
                    them by the constraints, although there are some old (or unconstrained) reference
                    points. This is done by adding flexibility to z`s. As a result, while the calculation of
                    the greater efficiency and Malmquist index for observations within the bounds, the
                    results of the small input activity scores, lower super-efficiency scores are obtained
                    for the observations out of bounds.

                    "Malmquist  Index Total  Factor Productivity"  (TFP) was  developed by  Malmquist
                    (1953) to determine how the efficiency changes over time in the evaluation process
                    of efficiencies. This index measures the change in TFP between two data points by
                    calculating the differences ratios of each data point by using common technology.
                    This measurement is performed with the distance function which is used to define
                    production  technologies  having  multiple  inputs  and  outputs  without  specifying
                    targets  such  as  cost  minimization  or  profit  maximization  (Griffel-Tatje  &  Lovell:
                    1995: 171).

                    When  a  technology  is  discussed  as  the  reference  technology  for  the  period  t,  the
                    output-oriented Malmquist TFP change index can be written for the s (base period)
                    and t periods as follows (Coelli, et al., 1998: 291);

                                                              
                                                              (      ,      )
                                            
                                           (   ,    ,    ,    ) =     (      ,      )                   (11)
                                                            0
                                                  
                                               
                                                        
                                                     
                                          0
                                                              
                                                            0

                    Alternatively, when discussing the period s as reference, the calculation changes as
                    follows:
                                                              
                                                              (      ,      )
                                           
                                                            0
                                          (   ,    ,    ,    ) =     (      ,      )                 (12)
                                              
                                                 
                                                        
                                                     
                                         0
                                                              
                                                            0

                                                                  s
                    As it can be seen from the equations above, d0 (yt,xt) notation shows the production
                    element from period t to period s. Malmquist TFP Index can be shown as the geometric
                    mean of different functions as follows (Kutlar, Yuksel and Bakirci, 2011: 139);

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