May 2021 | Przegląd Piekarski i Cukierniczy (Baking and Confectionery Review)
Data scientist in the bakery
A bakery’s and confectioner’s own retail sales network is an important element of competitive advantage. Bread shops must meet appropriate standards and be well managed. Above all, one must respond to customers’ needs and requirements.
Three levels of needs can be identified, among which the most important seem to be the basic needs, colloquially called „must be”. This is the level of services without which the customer will not even enter the shop. Among them one may count cleanliness, smell and the quality of service. The customer assumes that they will not be cheated when given their change, and that the bread will be fresh, clean and fragrant. Departing from customers’ basic expectations leads to a loss of trust. A bakery is usually an important element of the local community and tradition.
The needs of customers in rural communities differ somewhat from the requirements of the inhabitants of towns and cities. For the latter, the time of service – that is, the time they devote to buying bread – is of enormous importance. If it is too long, customers will give up their purchases. If the situation repeats itself, they may give up visiting that shop.
W-MOSZCZYNSKI ppic 5-21Mathematics
The scientific theory colloquially called the queueing problem developed during the Second World War. The point was to optimise the process of landing great squadrons of strategic bombers returning from over the Third Reich at English airfields. At that time very many aircraft were landing simultaneously at a limited number of airfields. The formations numbered as many as several hundred bombers. Some of the aircraft were damaged, and on board others there were wounded crew members. Aircraft returning from combat usually had little fuel. Practically all the aircraft required immediate landing.
This was a great organisational problem, which led to the creation of this mathematical theory.
The queueing problem serves to assess systems in which theoretically queues should not arise. The basis of the theory is the assumption that the number of objects arriving in the queue λ (e.g. the number of aircraft arriving within a minute) is smaller than the number of elements served, denoted as μ (e.g. the number of aircraft received by the airfield within a minute).
Despite the fulfilment of this basic condition, that λ < (μ × r), there is nevertheless a probability of a jam appearing. The queueing problem aims to determine the theoretical probability of its arising.
In combat conditions, when aircraft were returning from the front, every jam could end in an air disaster. The methodology described below served for the early identification of the probability of a jam arising and for the rapid elimination of the threat even before it arose.
The situation in the shops
A frequent development strategy of large suburban bakeries is locating retail sales outlets in the vicinity of the main transport hubs. The ideal place for a bread shop is the vicinity of railway stations and bus stations. There, from where the inhabitants of villages and small towns commute to work in large urban agglomerations.
Customers on their way to work usually drop into food shops. For these people it is important that service should be fast, because otherwise they will miss their train or bus.
A certain local bakery located four shops in the vicinity of railway stations. The shop assistants of some of the shops reported to the management that queues were forming in the shops. It was noticed that when people wait in the queue longer than 3 minutes, they give up their purchase and leave.
Giving up is often permanent in character. Customers who usually appeared in the bakery, after several such situations went over permanently to competing bread shops. The very sight of a queue discouraged a large part of them. The management decided that the situation should be looked into.
In the four bread shops the number of customers was counted, and it was calculated how many customers were on average served by one till position within an hour. The measurements were taken over many days during the morning peak, that is, at the time when consumers’ patience was at its lowest.
In the shop in Pruszków on Sienkiewicza Street (designated in the exercise as Pruszków PKP), during two hours of morning sales an average of 182 people came. This means that the average frequency of arrivals amounted to 182/2 = 91 people/h, that is λ = 91. During the morning peak, each of the three POS terminals in this shop served on average μ = 33 people within an hour.
In this way data was collected from four shops located in the immediate vicinity of railway stations. The numbers were substituted into the traffic intensity indicator ϱ, where r denotes the number of actively working retail tills.
ϱ = λ / (μ · r) (1)
The table below presents the analysis of average traffic in the shops during one hour of the morning peak.
| Pruszków PKP | Sulejówek SKM | Milanówek PKP | Pruszków WKD | |
|---|---|---|---|---|
| Number of tills (r) | 3 | 2 | 2 | 2 |
| Number of people arriving (λ) | 91 | 65 | 45 | 70 |
| Number of people served (μ) | 33 | 34 | 32 | 36 |
| Traffic intensity indicator ϱ = λ/(μ·r) | 0.92 | 0.96 | 0.7 | 0.97 |
As can be seen, at the outlets Sulejówek SKM and Pruszków WKD there is a high level of traffic intensity. It is calmest in the shop in Milanówek. For the customer the most important thing is whether there is a queue in the shop and whether they will catch their train if they decide to enter the shop.
In order to calculate the probability that there is no queue in the shop, one has to make use of the formula (2), which determines the probability that there will be no queue in the shop, that is n = 0, where n denotes the number of people in the queue.
The formula is simple; it is enough to substitute the values which have already been collected.
All these formulas are simple; it is enough to enter them into a spreadsheet and calculate the values.
The table below contains the assessment of the probability of a queue at the four retail sales outlets mentioned.
| Pruszków PKP | Sulejówek SKM | Milanówek PKP | Pruszków WKD | |
|---|---|---|---|---|
| Number of tills (r) | 3 | 2 | 2 | 2 |
| Number of people arriving (λ) | 91 | 65 | 45 | 70 |
| Number of people served (μ) | 33 | 34 | 32 | 36 |
| Traffic intensity indicator ϱ = λ/(μ·r) | 0.92 | 0.96 | 0.7 | 0.97 |
| Probability of no queue | 0.4 | 0.35 | 0.48 | 0.35 |
| Probability of 1 person in the queue | 0.36 | 0.34 | 0.34 | 0.34 |
| Probability of 2 people in the queue | 0.17 | 0.16 | 0.12 | 0.16 |
| Probability of 3 people in the queue | 0.05 | 0.08 | 0.04 | 0.08 |
| Probability of 4 people in the queue | 0.02 | 0.04 | 0.01 | 0.04 |
| Probability of 5 people in the queue | 0.0 | 0.02 | 0.01 | 0.02 |
| Probability of 6 people in the queue | 0.0 | 0.01 | 0.0 | 0.01 |
| Probability of 7 people in the queue | 0.0 | 0.0 | 0.0 | 0.0 |
| Probability of 8 people in the queue | 0.0 | 0.0 | 0.0 | 0.0 |
| Sum of probabilities | 1.0 | 1.0 | 1.0 | 1.0 |
| Waiting longer than 3 minutes | 0.01 | 0.05 | 0.02 | 0.05 |
| Average number of people in the queue | 0.03 | 0.28 | 0.1 | 0.3 |
The most difficult situation prevails in the shops Sulejówek SKM and Pruszków WKD. The traffic intensity indicator ϱ described by formula (1) amounts there to 0.96 and 0.97.
At both these stations the percentage of customers waiting to be served in queues for longer than 3 minutes is 5%. One may say that in each of these shops about 3–4 customers are irritated. The probability that, on entering the shop, the customer will find a queue amounts in these shops to 65%. Fortunately, with a probability of 34% this queue will consist of one customer. Let us remember that customers may flow in in waves. The analytical technology shown here allows the process to be assessed only in an averaged way.
The management must consider opening additional tills in the shops Sulejówek SKM and Pruszków WKD, because, as the analysis shows, there is a problem there with the continuity of sales.
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.
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