Assessing the efficiency of bread shops by means of DEA-CCR comparative analysis

July 2021 | Przegląd Piekarski i Cukierniczy (Baking and Confectionery Review)

Data scientist in the bakery

The Data Envelopment Analysis (DEA) method is a popular tool for measuring the efficiency of independent, but procedurally constrained, economic or social entities.

Every such entity shows inputs and results in its activity. The inputs may be energy costs, the level of employment, the depreciation of machines or cleaning costs. As results we may take: revenues, profits, or for example the quantity of bread sold.

The exact way of creating a CCR ranking has already been discussed by me in the March issue of „Przegląd”. Today, without using formulas, I would like to show how to make use of the ranking results. The CCR model is a very useful tool for managing networks of similar economic entities. It is obvious that a shop’s efficiency is decided above all by its location, in second place by the quality of the products and by the decor and customer service.

Nevertheless it is very important to determine the optimal level of inputs for running a bread shop. What is the point of a shop having great sales if excessive inputs consume all the profit generated? Though the mill grinds – there is little flour.

W-MOSZCZYNSKI ppic 7-21

Assessing the efficiency of shops

One of the most important elements of effectively managing a bakery’s sales network is an appropriately designed method of comparing shops. It should be objective, fair and transparent. It should also teach something, give valuable indications for the future.

Efficiency is the result of an entity’s activity described by the relation of the effects obtained to the inputs incurred. Assessing the results alone, such as a shop’s sales volume or its profit, while at the same time omitting the inputs, does not give a proper picture. After all, we want the bakery’s shops to make good use of the resources entrusted to them.

The CCR comparative analysis indicates the places in which the inputs are too high in relation to the results achieved. In order to assess the efficiency of a sales network, one must first separate out the inputs incurred by the individual shops and the effects obtained by them.

Results and inputs may be described directly as time, costs, distances or other measurable values. One may also apply percentage indicators or certain kinds of categorical values, such as the number of cash registers or the number of employees.

The CCR DEA algorithm

The CCR algorithm came into being as an alternative to comparative analyses based on weighted averages. It was published in 1978 as an algorithm based on the marginal efficiency of inputs. The name CCR comes from the initials of its creators: Charnes, Cooper and Rhodes.

The aim of this article is to show how to interpret and how to use this model effectively. As I have already mentioned, the way of calculating this algorithm was described in detail in the March issue of „Przegląd”. Writing out its formulas would take up too much space, and that is why I have decided to concentrate on the ways of using the results.

As I mentioned, the main application of the DEA (Data Envelopment Analysis) method is to autonomous economic units which, within a certain defined scope, have freedom in taking decisions.

Such units are shops selling bread and confectionery products. Most large bakeries have their own retail sales network. Each such shop bears its own inputs, among which we can distinguish:

• Cost of renting the premises (thousands/month)
• Employment in full-time posts
• Depreciation and servicing (thousands/month)
• Number of cash registers
• Labour costs (thousands/month)
• Cost of deliveries (thousands/month)
• Cost of energy and cleaning (thousands/month)
• Percentage share of returns

and its own effects:

• Monthly revenues (thousands/month)
• Daily sales of bread (items)
• Daily sales of cakes (items)

Let us note that every increase in the inputs specified is negative in character for the bakery’s economic account. The configuration of the inputs listed for each shop we will call that shop’s sales technology.

Table 1: Inputs and effects of the bread shops

	SK1	SK2	SK3	SK4	SK5	SK6	SK7	SK8	SK9
Cost of renting the premises (thousands/month)	3.4	3.2	3.5	3	2.2	1.8	3	2.2	3
Employment in full-time posts	3.2	2.32	3.2	2.5	3	4.5	2.3	3.5	4.2
Depreciation and servicing (thousands/month)	2.1	2.4	1	1.6	1.8	2.7	1.9	1.8	1.5
Number of cash registers	3	3	4	2	3	2	3	4	3
Labour costs (thousands/month)	17	16	7.7	12.4	11	18	15	15.2	10.5
Cost of deliveries (thousands/month)	0.79	0.79	0.7	1.2	1.1	0.8	0.5	1.5	0.5
Cost of energy and cleaning (thousands/month)	1.4	1.8	1.1	1.2	1.3	1.8	0.6	0.43	1.5
Percentage share of returns	0.14	0.3	0.2	0.2	0.13	0.11	0.1	0.14	0.15
Monthly revenues (thousands/month)	9.71	18.59	7.66	10.4	8.09	11.8	9.5	6.6	5.7
Daily sales of bread (items)	85	160	52	90	72	84	96	54	47
Daily sales of cakes (items)	15	36	12	15	12	24	29	11	17

In the above table the columns denote the individual shops. To each retail outlet an individual set of inputs and effects is assigned.

After running the CCR algorithm we obtain a ranking matrix, presented in Table 2 (Ranking of the efficiency of the bread shops).

The column k denotes the efficiency k of each o-th shop. In the column „Shop” we can read the ordinal symbols assigned to the shops.

Every shop which received the value 1 in the column k is an optimal shop. The algorithm found the three best shops: SK2, SK6 and SK7.

The group of the best shops is designated as the peloton. The shops rated worst were: SK1, SK4 and SK9. Let us note that shop SK4 has very good economic results. Unfortunately the inputs into its activity seem too high. The values assigned to these shops in the column k show the efficiency of those shops in relation to the efficient shops belonging to the peloton.

For example, shop SK9 achieved 76% of the efficiency of the optimal shops. This means that this shop achieves barely 76% of the results which it should achieve given the inputs incurred. That is, its level of inefficiency amounts to as much as 24%.

Restructuring

The CCR algorithm not only creates a ranking of the efficiency of a set of objects. It also indicates the directions in which the restructuring of the non-optimal shops should go, so that their performance becomes optimal. This is a very significant advantage, because every analysis should carry with it a solution to the problem.

Shop SK5 achieved a similar place in the ranking to shops SK4 and SK1. Its performance constitutes barely 85% of the performance of the objects qualified to the peloton.

In Table 2, in the row describing shop SK5, there are optimisation indicators. One should choose those indicators which are located in the columns of the optimal shops: SK2, SK6 and SK7.

Table 3. Optimisation indicators λ for shop SK5

Shop	SK2	SK6	SK7
SK5	0.253	0.077	0.261

The indicators from Table 3 should be multiplied by the parameters of the shops belonging to the peloton from Table 1. This operation is written down in Table 4 (The optimal technology for shop SK5).

In the columns SK2, SK6 and SK7 of Table 4 there are the same values as those contained in Table 1. The following columns contain the product of the values from the first three columns with the optimisation coefficients λ from Table 3. The last column contains the sum of the products of the inputs and effects. This column represents the optimal technology for the non-optimal shop SK5.

In the table we find the theoretical levels of inputs for shop SK5, necessary to achieve optimal performance in at least one of the three current results.

In Table 5 two vectors of effects (Monthly revenues and Daily sales of bread) are almost identical, which indicates the high credibility of the optimal technology worked out for shop SK5. The input Daily sales of cakes does not agree, which means that the algorithm did not find an ideal common technology for all three results.

The CCR algorithm indicates that in order for shop SK5 to become optimal it should reduce its monthly rental costs by 500 zł. This means that in relation to the optimal shops the rental cost of shop SK5 is too high. The other indicators can be interpreted similarly. Employment is half as large again as it should be, and the costs of depreciation and servicing are too high. Labour costs in the shop are too high by 1700 zł a month. The optimal shops achieve their level of sales while engaging considerably fewer costs, human resources and infrastructure. The high inputs of shop SK5 are not accompanied by corresponding economic benefits.

The above advice is fairly clear; however, in order for the bakery’s management to be able to make use of it, specific indications should appear as to how to lower the level of costs and other inputs. The management should make use of the specific solutions applied in the optimal shops SK2, SK6 and SK7.

Wojciech Moszczyński

Wojciech Moszczyński — graduate of the Department of Econometrics and Statistics of Nicolaus Copernicus University in Toruń; specialist in econometrics, finance, data science, and management accounting. He specializes in the optimization of production and logistics processes. He conducts research in the area of the development and application of artificial intelligence. For years he has been engaged in the popularization of machine learning and data science in business environments.