Data Envelopment Analysis
7.1 Model Specifications
7.1.3 Incorporating non-discretionary input factors
these results are based on a relatively small experimental data set,the negative developments in the Austrian hotel industry during 1991 and 1996 described earlier (see pp. 81–82) are observed. In the Malmquist analysis the total factor productivity index is decomposed to efficiency and technical change indices.
The favourable course of the efficiency change index between 1993 and 1996 indicates the efforts of the industry to balance the drop in demand with improved efficiency (e.g. profit improvement programmes).
Malmquist indices for individual hotels can be used to assist hotel manag- ers in benchmarking their performance against the decomposed industry performance indicators. A complete listing of the Malmquist indices for all companies in the database is given in Appendix Table A.8. For an example consider Fig. 7.3 in which the solid lines represent the performance of com- pany no. 688. Overall,the manager of hotel no. 688 experienced unfavourable conditions between 1991 and 1997. In spite of 1994,the productivity change index is always clearly below the cumulative index,which indicates a poor productivity compared to the performance of the industry.
The decomposition of the productivity index allows multiple insights. One can assess whether the bad overall performance refers solely to inefficiencies in operations or involves poor anticipation of technological changes in the industry by the management of the company. Comparing the development of the technical change index with the cumulative function reveals that hotel no. 688 anticipated technological changes fairly well,thus leaving the primary explanation of the poor performance to the relative inefficiencies, which especially occurred between the periods 1991–1993 and 1996–1997.
The Malmquist extension to DEA has several merits compared to the window analysis approach demonstrated in the previous section. The major benefit is that it permits total factor productivity to be decomposed into techni- cal change and technical efficiency change. It also has methodological merits;
it neither requires the parameterization of a window width nor does it have idiosyncratic characteristics like the multiple representation of one and the same company in each window.
The disadvantage of the Malmquist extension is that there are no peer groups which derive automatically from the analysis as is possible with traditional DEAs. The dynamic version of the efficiency score,the efficiency index,is defined by two vectors ofλs,one for the efficiency score evaluation in periodt,and one for the efficiency score evaluation int+ 1. It is still unclear from the literature how these two vectors can be combined to form one common reference vector for all periods of observation.
subjects into more homogeneously defined subgroups and performing the analysis on each of the clusters separately. The other option is the inclusion of background (or moderator) variables.
There are several performance studies in the literature where DEA has been applied iteratively to a predefined number of subject clusters. In a study of education in California,for instance,Sengupta and Sfeir (1986) split high-school districts into rural and urban; similar adjustments were made by Grosskopf and Valdmanis (1987) in an evaluation of hospital performance. In Ganley and Cubbin (1992) clusters based on recognized administrative groups of local education authorities largely amount to a distinction between rural and urban schooling.
An objection that typically arises in conjunction with clustering subjects in performance studies relates to the criteria chosen for defining clusters.
Ganley and Cubbin express this problem when they say:
Generally speaking, empirical clustering criteria have been rather crude and cannot exclude the possibility that a peer drawn from the same cluster may nevertheless be quite unlike the inefficient DMU [decision making unit11] for which it has been chosen. This will always be true in a trivial sense because every DMU is likely to have some unique characteristics (e.g. location).
(Ganley and Cubbin, 1992: 135)
Ganley and Cubbin also argue that,notwithstanding this problem,the effects of clustering on efficiency remain valuable in clarifying the discriminating power of DEA in terms of its ability to identify meaningful targets and peer groups.
In response to this criticism,more rigorous procedures for clustering have begun to emerge in DEA literature. For example,Bankeret al. (1989) developed an F-statistic that allows a test of the internal homogeneity. They tested this approach on a sample of 111 government-supported hospitals in North Carolina. They concluded that clustering can embody attainable targets by setting more demanding ‘tight’ targets for higher-performing groups and
‘looser’ targets (e.g. 90% of best-practice attainments) for the remaining group. They argue that this procedure,by making targets more equitable,will assist in acceptance of DEA assessment.
Another approach to deal with non-discretionary effects in DEA is the inclusion of moderator variables into the model. Although the inclusion of background variables is widely recognized in efficiency studies,there remains some dispute in the literature as to the effects of non-controllable variables on efficiency (e.g. Banker and Morey,1986a,b; Golany,1988; Ray,1988,
11 In 1981, Charneset al. introduced the generic term ‘Decision Making Units’ (DMUs) to describe the collection of departments, divisions or administrative units that have common inputs and outputs and are being assessed for efficiency. In the following, this expression has been used by many authors on studies on productivity and efficiency analysis. In this book the author decided to use the terms firm, company and business interchangeably instead of the artificial term DMU.
1991; Ruggiero,1996,1998). A DEA model which incorporated the effects of uncontrollable inputs where reductions cannot be achieved was introduced by Charnes and Cooper (1985). The theoretical foundation and mathematical treatment by linear programming was discussed on pp. 71–73. In the follow- ing the effects of including environmental input variables are tested on the AHRP data set.
As stated earlier,initially,the inclusion of non-discretionary variables was omitted. Now such variables are defined by denoting X1–X3 as being uncontrollable to the manager. Recall thatX1is the total number of beds,X2
is the total number of seats in the F&B area of the hotel andX3is the number of opening days. The key to understanding which input variable is defined as discretionary and which is defined as non-discretionary lies in the observation that information about the extent to which a non-discretionary input variable may be reduced is not meaningful for the hotel manager. Note that this decision may not be the same for each manager for a given data set and that this may vary according to the manager’s operational flexibility (which is again constrained by the environment).
Analysis and results
As the special software package DEAP did not support the processing of mixtures of controllable and uncontrollable variables,in the following,DEA problems were solved with Holger Scheel’s Efficiency Measurement System (EMS),which uses Csaba Mészáros’s state-of-the-art BPMPD linear program solver.12 This allows one to efficiently estimate various forms of DEA models (input/output-oriented; radial/additive distance; constant/variable/
non-increasing/non-decreasing returns to scale) and offers a variety of additional options (non-discretionary variables; calculation of Andersen and Petersen’s ‘superefficiency’ scores; weight restrictions).
For the AHRP application an input-oriented variable returns to scale model was used. The complete results of the DEA runs with non-discretionary and discretionary inputs are listed in Appendix Table A.9. In comparison to Fig. 7.1,Fig. 7.4 shows the operating profit plotted against the DEA efficiency score distinguishing between discretionary and non-discretionary input variables for each of the 61 hotels in 1997. Again,the hotels deemed efficient and given a score of 1 are plotted along the right border. Comparing this plot with the plot in Fig. 7.1 clearly shows much higher inefficiencies for hotels which were run unprofitably or even experienced a loss in gross profit. In general,a strong positive correlation between gross profit and efficiency scores can be observed from the pictorial presentation in Fig. 7.1.
Hotel no. 2223,which is an 87-bed property,was selected for more detailed analysis and interpretation. In the year under consideration hotel no. 2223 achieved?978,500 F&B revenue and?328,600 room revenue, and
12 www.sztaki.hu/~meszaros/bpmpd/
spent?958,500 for operating expenses. The gross profit was ?348,700, or 27% of the total revenue. The occupancy rate was 50.9%.
By using DEA with uncontrollable input factors it was found that four of the remaining 60 hotels (hotels no. 1061,no. 1353,no. 2336 and no. 2786) constitute a peer group for the company under evaluation. However,as is typically the case,the characteristics of the peer-group members do not perfectly match those of the unit being evaluated.
To account for the difficulty in comparing actual property-operation characteristics,the linear program builds a weighted composite of the four efficient peer-group members identified that perfectly match the levels of outputs and the operating environment of the unit being evaluated. Thus a composite,efficient benchmark hotel is derived to develop what may now be called a ‘scorecard’. It shows the resource-expenditure targets for hotel no. 2223 based on the management achieving at least the same total room revenues,F&B revenues,and occupancy rate in the same or an even more difficult environment. With the benchmarking figures listed in Table 7.5,it is possible to calculate the efficiency score for hotel no. 2223. Dividing the total expenditures of the composite benchmarking partners by hotel no. 2223’s expenditures results in the efficiency score of 0.880.
The peer group is matched to hotel no. 2223 based both on the non- controllable factors and on the levels of all outputs in so far as the Fig. 7.4. Profitability versus DEA efficiency with non-discretionary input
variables for 61 Austrian hotels in 1997.
environmental factors in the benchmarking group are either equal or less favourable compared to the one of hotel no. 2223. In the case of the output factors,the virtual benchmarking company either performs equal to or better than the hotel under evaluation. The benchmark output figures are approximately the same as hotel no. 2223’s figures,however,the operational expenditures are considerably less when compared with the hotel under evaluation.
The benchmarks that are most potentially interesting for management are those for the eight resource expenditures. They constitute a set of targets for hotel no. 2223 to work toward. If hotel no. 2223 utilizes its resources more efficiently,it should be able to achieve the same output with lower expendi- tures. The DEA analysis indicates that hotel no. 2223 has the potential to improve its output by?134,200 (improvement of about 38.5%), when it reduces it expenditures to?843,700 (a decrease of about 12%).
Figure 7.5 depicts the ideal direction for hotel no. 2223 to move to be more efficient and profitable,as well as showing the position of the four bench- marking partners as suggested earlier in a related context. The identity of the four peer properties can be made available to hotel no. 2223 so that the management can ascertain from them (perhaps through site visits) the details of the processes and practices that enable them to perform better.
t= 1997 m= 35
(no. 2223) m= 20
(no. 1061) m= 27
(no. 1353) m= 40
(no. 2336) m= 48
(no. 2785) BMb Number of beds
Number of seats Number of opening days
958,587.9 958,120.9 958,365.9
1,958,130.9 1,958,127.9 1,958,265.9
958,181.9 958,210.9 958,240.9
958,158.9 958,185.9 958,298.9
1,958,165.9 1,958,140.9 1,958,365.9
958,184.9 958,120.9 958,308.9 Total F&B revenue (?)
Total room revenue (?) Occupancya(%)
978,500.9 328,600.9 958,550.9
1,053,800.9 1,712,300.9 1,958,163.1
826,300.9 369,300.9 958,162.4
306,500.9 213,400.9 958,166.8
1,126,800.9 1,151,700.9 1,958,135.8
978,900.9 347,600.9 958,150.9 Total expenditures (?)
Payroll and related (?) Material-type exp. (?) Energycosts (?) Cleaning costs (?) Maintenance costs (?) Communication costs (?) Marketing costs (?) Administration costs (?)
958,500.9 475,200.9 212,700.9 66,100.9 13,600.9 82,900.9 16,900.9 58,700.9 32,300.9
1,222,200.9 1,624,000.9 1,249,100.9 1,973,000.9 1,922,100.9 1,118,500.9 1,918,000.9 1,946,600.9 1,970,900.9
492,600.9 194,900.9 105,500.9 40,800.9 12,900.9 30,500.9 9,200.9 45,800.9 53,100.9
296,200.9 126,800.9 82,900.9 24,900.9 4,700.9 21,200.9 7,800.9 7,800.9 19,900.9
1,881,500.9 1,475,600.9 1,236,000.9 1,952,300.9 1,922,700.9 1,943,200.9 1,957,800.9 1,952,800.9 1,941,100.9
843,700.9 428,900.9 200,400.9 53,100.9 19,000.9 58,600.9 10,700.9 23,400.9 49,600.9 Gross profit (?) 348,700.9 1,543,900.9703,000.9 223,700.9 1,396,900.9482,900.9
aPer opening days;bbenchmark (composite group) based on LP solution withλ20*= 0.262, λ27*= 0.202,λ40*= 0.083 andλ48*= 0.453;e35*= 0.880.
Table 7.5. DEA benchmarks for hotel no. 2223.