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16DEA (DATA ENVELOPMENT ANALYSIS) APPROACH TO MEASURING EFFICIENCY OF BANKING SECTOR Khamdamov M.M.1, Rakhimova M.S.2, Alimova S.R.3
1Khamdamov Mirzoumid Mirzaevich - PhD, Senior Lecturer, INTERNATIONAL ECONOMICS DEPARTMENT;
2Rakhimova Margarita Sergeevna - Lecturer;
3Alimova Sofiya Rozumbaevna - Lecturer, SYSTEM ANALYSIS AND MANAGEMENT DEPARTMENT, UNIVERSITY OF WORLD ECONOMY AND DIPLOMACY, TASHKENT, REPUBLIC OF UZBEKISTAN
Abstract: this article provides a history and usages of DEA. The research extends DEA approach to measuring efficiency of banking sector. Data envelopment analysis (DEA) is a linear-programming-based method for assessing the performance of homogeneous organizational units and is increasingly being used in banking.
Keywords: DEA, input, output, efficiency, technical efficiency, ratios, banking sector, efficient frontier, possibility set, inefficiency.
Data envelopment analysis (DEA), occasionally called frontier analysis, was first put forward by Charnes, Cooper and Rhodes in 1978.
It is a performance measurement technique which, as we shall see, can be used for evaluating the relative efficiency of decision-making units (DMU's) in organizations. Here a DMU is a distinct unit within an organization that has flexibility with respect to some of the decisions it makes, but not necessarily completes freedom with respect to these decisions. Examples of such units to which DEA has been applied are: banks, police stations, hospitals, tax offices, prisons, defense bases (army, navy, and air force), schools and university departments. Note here that one advantage of DEA is that it can be applied to non-profit making organizations. Since the technique was first proposed much theoretical and empirical work has been done. Many studies have been published dealing with applying DEA in real-world situations. Obviously there are many more unpublished studies, e.g. done internally by companies or by external consultants. We will initially illustrate DEA by means of a small example. Note here that much of what you will see below is a graphical approach to DEA. For each branch we have a single output measure (number of personal transactions completed) and a single input measure (number of staff).
The data we have is as follows
№ Branches Personal transactions (000's) Number of staff
(output) (input)
1 Bank 1 100 15
2 Bank 2 56 18
3 Bank 3 49 12
4 Bank 4 78 10
5 Bank 5 69 13
6 Bank 6 44 11
7 Bank 7 125 16
8 Bank 8 120 14
9 Bank 9 102 17
10 Bank 10 95 16
For example, for the Bank 4 branch in one year, there were 78,000 transactions relating to personal accounts and 10 staff was employed.
Ratios. A commonly used method is ratios. Typically we take some output measure and divide it by some input measure. Note the terminology here; we view branches as taking inputs and converting them (with varying degrees of efficiency, as we shall see below) into outputs. For our
bank branch example we have a single input measure, the number of staff, and a single output measure, the number of personal transactions. Hence we have:
№ Branches Personal transactions (000's)
1 Bank 1 100\15 6.67
2 Bank 2 56\18 3.11
3 Bank 3 49\12 4.08
4 Bank 4 78\10 7.8
5 Bank 5 69\13 5.30
6 Bank 6 44\11 4
7 Bank 7 125\16 7.81
8 Bank 8 120\14 8.57
9 Bank 9 102\17 6
10 Bank 10 95\16 5.93
Here we can see that Bank 8 has the highest ratio of personal transactions per staff member, whereas Bank 2 has the lowest ratio of personal transactions per staff member. As Bank 8 has the highest ratio of 8.57 we can compare all other branches to it and calculate their relative efficiency with respect to Bank 8. To do this we divide the ratio for any branch by 8.57 (the value for Bank 8) and multiply by 100 to convert to a percentage. This gives:
№ Branches Relative efficiency
1 Bank 1 100(6.67\8.57) 77.8%
2 Bank 2 100(3.11\8.57) 36.2%
3 Bank 3 100(4.08\8.57) 47.6%
4 Bank 4 100(7.8\8.57) 91%
5 Bank 5 100(5.30\8.57) 61.8%
6 Bank 6 100(4\8.57) 46.7%
7 Bank 7 100(7.81\8.57) 91.1%
8 Bank 8 100(8.57\8.57) 100%
9 Bank 9 100(6\8.57) 70%
10 Bank 10 100(5.93\8.57) 69.1%
The other branches do not compare well with Bank 8, so are presumably performing less well. That is, they are relatively less efficient at using their given input resource (staff members) to produce output (number of personal transactions). We could, if we wish, use this comparison with Bank 8 to set targets for the other branches. For example we could set a target for Bank 2 of continuing to process the same level of output but with one less member of staff. This is an example of an input target as it deals with an input measure. An example of an output target would be for Bank 2 to increase the number of personal transactions by 10%. Plainly, in practice, we might well set a branch a mix of input and output targets which we want it to achieve.
Extending the example. Typically we have more than one input and one output. For the bank branch example suppose now that we have two output measures and the same single input measure as before [1, p. 1262]. The data we have is as follows:
№ Branches Personal transactions Business Number of staff
(000's) transactions (input)
(output) (000's) (output)
1 Bank 1 100 26 15
2 Bank 2 56 20 18
3 Bank 3 49 30 12
4 Bank 4 78 32 10
5 Bank 5 69 55 13
6 Bank 6 44 41 11
7 Bank 7 125 38 16
8 Bank 8 120 25 14
9 Bank 9 102 35 17
10 Bank 10 95 19 16
For the Bank 2 branch in one year, there were 56,000 transactions relating to personal accounts, 20,000 transactions relating to business accounts and 18 staff was employed. How now can we compare these branches and measure their performance using this data? As before, a commonly used method is ratios, just as in the case considered before of a single output and a single input. Typically we take one of the output measures and divide it by one of the input measures. For our bank branch example the input measure is plainly the number of staff (as before) and the two output measures are number of personal transactions and number of business transactions. Hence we have the two ratios:
№ Branches Personal transactions Business transactions
(000's)\per staff (000's)\per staff
1 Bank 1 6.67 1.73
2 Bank 2 3.11 1.11
3 Bank 3 4.08 2.5
4 Bank 4 7.8 3.2
5 Bank 5 5.30 4.23
6 Bank 6 4 3.72
7 Bank 7 7.81 2.38
8 Bank 8 8.57 1.79
9 Bank 9 6 2.06
10 Bank 10 5.93 1.19
Here we can see that Bank 8 has the highest ratio of personal transactions per staff member, whereas Bank 5 has the highest ratio of business transactions per staff member. Other banks do not compare so well with Bank 8 and Bank 5, so are presumably performing less well. That is, they are relatively less efficient at using their given input resource (staff members) to produce outputs (personal and business transactions). One problem with comparison via ratios is that different ratios can give a different picture and it is difficult to combine the entire set of ratios into a single numeric judgment. This problem of different ratios giving different pictures would be especially true if we were to increase the number of branches (and/or increase the number of input/output measures).
Graphical analysis. One way around the problem of interpreting different ratios, at least for problems involving just two outputs and a single input, is a simple graphical analysis. Suppose we plot the two ratios for each branch as shown below.
Fig. 1. Efficient frontier of the set1
The positions on the graph represented by Bank 4, Bank 5 and Bank 8 demonstrate a level of performance which is superior to all other branches. A horizontal line can be drawn, from the y-axis to bank 5, from Bank 5 to Bank 4 and Bank 8, and a vertical line from Bank 8 to the x-axis. This line is called the efficient frontier (sometimes also referred to as the efficiency frontier).
Mathematically the efficient frontier is the convex hull of the data. The efficient frontier, derived from the examples of best practice contained in the data we have considered, represents a standard of performance that the branches not on the efficient frontier could try to achieve. You can see therefore how the name data envelopment analysis arises - the efficient frontier envelopes (encloses) all the data we have. Whilst a picture is all very well a number is often easier to interpret. We say that any branches on the efficient frontier are 100% efficient. Hence, for our example, Bank 4, Bank 5 and Bank 8 have efficiencies of 100%. This is not to say that the performance of Bank 4, Bank 5 and/or Bank 8 could not be improved. It may, or may not, be possible to do that. We can say that, on the evidence available, we have no idea of the extent to which their performance can be improved. Thus, this article introduces Data Envelopment Analysis, a performance measurement technique, in such a way as to be appropriate to decision makers with little or no background in economics and operational research. The use of mathematics is kept to a minimum. This article therefore adopts a strong practical approach in order to allow decision makers to conduct their own efficiency analysis and to easily interpret results.
DEA helps decision makers for the following reasons: by calculating an efficiency score, it indicates if a firm is efficient or has capacity for improvement; by setting target values for input and output, it calculates how much input must be decreased or output increased in order to become efficient; by identifying the nature of returns to scale, it indicates if a firm has to decrease or increase its scale in order to minimize the average cost; by identifying a set of benchmarks, it specifies which other firms' processes need to be analyzed in order to improve its own practices [2, p. 235]. The article also presents the essentials about DEA, alongside a case study to intuitively understand its application and introduces packages that conduct efficiency analysis based on DEA methodology.
References
1. Andersen P., Petersen N.C. (1993), "A procedure for ranking efficient units in data envelopment analysis", Management Science. 39. 1261-1264.
1 Done by the authors in the Frontier Analyst Software.
63
2. Banker R.D., Chang H., Cooper W.W. (1996), "Simulation studies of efficiency, returns to scale, and misspecification with nonlinear functions in DEA". Annals of Operations Research. 66. 233-253.
ЛОГИСТИЧЕСКАЯ СПЕЦИФИКА ДОСТАВКИ ГРУЗОВ НА ТРАНСГРАНИЧНЫХ ТЕРРИТОРИЯХ Литвинова И.В.
Литвинова Ирина Владимировна - член-корреспондент, старший преподаватель,
кафедра гуманитарных и социально-экономических дисциплин, Владивостокский государственный университет экономики и сервиса, г. Находка
Аннотация: в статье анализируется оптимальный способ доставки груза к заказчику на трансграничных территориях. Проведён анализ вариантов относительно доставки морем или по суше.
Ключевые слова: анализ, логистика, вариант доставки, таможенная ставка.
DOI 10.24411/2414-5718-2022-10102
Перед современными логистами на сегодня стоит острый вопрос - как оптимально быстро и выгодно отправить груз заказчику, тем более, если речь идёт о трансграничной территории.
Стоимость доставляемого товара высокая. Для быстрой окупаемости данного груза необходима быстрая доставка. Поэтому примем за наилучший вариант - вариант с минимальным временем доставки. Выяснив, что самым быстрым вариантом является морской, в данном разделе нам необходимо рассчитать стоимость доставки и выяснить, насколько он выгодный [1. С. 56].
На первый взгляд перевозить груз очень просто, но это только на первый взгляд. Встречается груз, который относится к категории «хрупкий», поэтому необходимо соблюдать определенные правила перевозки. Если это новый товар, то он идет в заводской упаковке. Главное правильно эти коробки расставить в ящике. Так как груз хрупкий, то при погрузке паллетов в контейнер нужно учитывать то, что нельзя ставить эти паллеты друг на друга, поэтому груз придется укладывать в один ярус [2. С. 70].
Пространства в коробке заполняют кусками пенопласта или плотным картоном, а еще лучше - пузырчатой пленкой, которая надежно защитит все комплектующие. Важно хорошо закрепить коробки в контейнере, чтобы исключить их тряску и повреждение.
Для оценки предложенных и существующего варианта, проведём SWOT анализ доставки груза автоперевозкой и морем.
