Mail centers, the essential postal facilities that sort and dispatch postal items, should be operated efficiently to provide customers with high quality postal services. The efficiency analysis for mail centers should be conducted in order to induce them to good performance. But current performance evaluation system has ninety-five percent predetermined and weighted non-quantitative indices, so this study raises doubts about objectivity and propriety of evaluation. But, until now, only few attempts have so far been made at measuring the efficiency for mail centers.
The main objective of this study is to analyze the efficiency for twenty-four mail centers empirically using data envelopment analysis(DEA) methods and to suggest the desirable methods for measuring the efficiency.
The data on inputs and outputs were gathered from the Korea Post. The initial list of factors or variables to be considered for assessing the decision making units(DMUs) includes eleven input factors and two output factors. Five input factors were eliminated from the list by judgemental screening and three input factors and one output factor were dropped from the list through backwards stepwise selection approach. At last, the input factors list includes building area, small size letter post items sorting machine and temporary employees, and the output factor list contains the quantity of handled postal items .
Charnes, Cooper and Rhodes described DEA as a mathematical programming model applied to observational data which provides a new way of obtaining empirical estimates of extremal relations - such as the production functions and/or efficient production possibility surfaces that are a cornerstone of modern economics. Adler, Friedman and Sinuany-Stern explained that DEA is an mathematical model that measures the relative efficiency of DMUs with multiple inputs and outputs but with no obvious production functions to aggregate the data in its entry. Relative efficiency is defined as the ratio of total weighted output to total weighted input. Thompson, Langemeier, Lee, Lee and Thrall said that DEA does not require any a priori weights in a frontier analysis of the inputs and outputs.
The CCR model, suggested by Charnes, Cooper and Rhodes in 1978, is based on the assumption that constant returns to scale prevails at the efficient frontiers, whereas BCC model, suggested by Banker, Charnes and Cooper in 1984, assumes variable returns to scale frontiers.
The results of empirical analyses of twenty-four mail centers by CCR and BCC model show that average scores are 0.58302 and 0.87713 respectively, and efficient mail centers are three and sixteen respectively. These analyses imply that CCR and BCC model don't have sharp ranking discrimination for the efficient DMUs.
The assurance region(AR) method, developed by Thompson, Singleton, Thrall and Smith in 1986, is a special case of cone-ratio method. The AR is a subset of W such that vectors w excluded from AR are not reasonable input and output virtual multipliers.
This study set up AR using analytic hierarchy process(AHP). The results of analyses by CCR-AR model and BCC-AR model show that average scores are 0.43762 and 0.70177 respectively, and one and three mail centers are efficient respectively. The results indicate that CCR-AR and BCC-AR model has sharper ranking discrimination than CCR and BCC model. But the subjective response to the AHP survey can bring about an inappropriate result of fixing AR.
The cone-ratio method, developed by Sun in 1988, Charnes, Cooper, Wei and Huang in 1989 and Charnes, Cooper, Huang and Sun in 1990, is more general than AR method and impose a set of linear restrictions that define a convex cone to provide for more realistic multipliers.
The result of cone-ratio DEA by transformed data using the weights for the preferable efficient DMUs shows that average score is 0.56631 and three mail centers are efficient. The result of cone-ratio DEA using prioritization of factors shows that average score is 0.51686 and only one mail center is efficient, and this method has better discrimination than the former. But the more a model has factors, the heavier a worker needs computational work.
The cross-efficiency technique, first developed by Sexton, Silkman and Hogan in 1986, is one of useful ranking methods in the DEA context. Sexton et al.(1986) defined the cross-efficiency of DMU j as measured by DMU k as the ratio of weighted output to weighted input obtained when using the input and output levels of DMU j and the input and output weights derived for DMU k.
The cross-efficiency analysis calculated the efficiency score of twenty-four mail centers using optimal weights calculated by CCR model. The result of analysis shows that this method can rank the DMUs explicitly. But this method needs a heavy workload of calculation when a model has many DMUs.
The super-efficiency technique, developed by Andersen and Petersen in 1993, is a procedure for ranking efficient DMUs. This method enables an extreme efficient DMU k to achieve an efficiency score greater than one by excluding the kth constraint in the primal formulation, and ranks inefficient DMUs in the same manner as the standard DEA model.
The result of analysis by CCR super-efficiency model shows that average score is 0.60199 and ranks the three CCR efficient mail centers discriminately. The BCC super-efficiency analysis ranks fifteen from sixteen BCC efficient mail centers explicitly, but one BCC efficient DMU has a problem of infeasibility.
The window analysis, developed by Klopp in 1985, is a method for time varying efficiency analysis. The basic idea of window analysis is to choose a window of k observations for each DMU, and treat these as if they represented k different DMUs. Row views of window analysis results make it possible to determine trends and/or observed behavior with the same data set, and column views to examine the stability of results across different data sets.
In the result of window analysis, row views, average through window, show that eight mail centers exhibit improving efficiency over time and sixteen DMUs exhibit irregular trends. Column views, average by term, show that six DMUs exhibit stable improvement in efficiency over time and eighteen DMUs exhibit unstability.
The Malmquist productivity index(MPI), first suggested by Malmquist in 1953, is an index representing total factor productivity growth of a DMU. DEA based MPI was developed by Färe, Grosskopf, Norris and Zhang in 1994. The index can be decomposed into two components: changes in technical efficiency (catching up to the frontier) over time and shifts in technology (innovation) over time. And the changes in technical efficiency can be decomposed into pure efficiency change and scale efficiency change. The indexes greater than unity translate into improvements in productivity, while unity and less than unity respectively indicate the status quo and deterioration in performance over time.
In the results of MPI analysis, the average productivity index by time series indicates that the total factor productivity of twenty-four mail centers progressed by 0.6 percent. It is due to progress in technical efficiency change, pure efficiency change and scale efficiency change rather than deterioration in technical change. The geometric mean of MPI shows that the average productivity per quarter progressed by 0.6 percent. The cumulated MPI indicates that the productivity from first quarter to fourth quarter of 2008 progressed by 1.82 percent. The lowest average productivity index of mail center '03210' is due to low technical efficiency change, technical change, scale efficiency change, and status quo of pure efficiency change. Indicating the catching up potential and innovation potential, this mail center needs to reduce costs and to improve the rate of operation of facilities in order to progress its productivity.
Consequently, this study suggest that, under static conditions, it is desirable to use cone-ratio DEA to analyze the efficiency or evaluate the performance for mail centers when a DEA model has not a great number of factors, and to use cross-efficient analysis when a DEA model has not a large number of DMUs. Under dynamic situations, MPI analysis is useful to analyze the productivity change over time and to provide ways to improve their productivity. And this study implies that the efficiency analysis using DEA methods can be applied in measuring the efficiency or evaluating the performance for logistics centers, public institutions, companies, etc. as well as mail centers.