August 2021 | Przegląd Piekarski i Cukierniczy (Baking and Confectionery Review)
Data scientist in the bakery
Management is a process of never-ending decisions. Each of them changes the process to a greater or lesser degree, influences its efficiency, profitability, the quality of the products or safety at work. Every day we have to decide, to face never-ending dilemmas and variants of procedure. We have to manage, because such is the role of the owner of a bakery or confectioner’s shop.
Some problems are easy to resolve; others consist of so many variables and so many unknowns that we are not able to take a decision rationally. Unfortunately, with the development of technology everything becomes more and more intricate, subtle and evidently more and more complicated. In times of low margins and high competition, taking decisions on the basis of intuition and one’s own experience may bring a bakery to the brink of bankruptcy.
What is to be done when we have a dozen or so variants at our disposal, and the level of complexity of each of them exceeds the level of perception of the average person?
Fortunately econometrics comes to our aid. Of course for most entrepreneurs who shun mathematics, the appearance of econometrics in the decision-making process may mean even greater trouble. However, with a little determination it may turn out that modern decision-making tools will bring an enormous facilitation in everyday struggles and will incidentally improve profitability.
W-MOSZCZYNSKI ppic 8-21Today we will present a tool which helps to take decisions about the allocation of the means of production.
Every manager has many times had to decide whether and where to begin a particular production or particular services. This is often accompanied by a process of calculating and comparing various variants. Unfortunately, this type of decision-making process is very burdensome. Non-optimally located production means lost opportunities and unnecessary costs.
A person by nature tries to work as well as possible. Most of us want to have a clear conscience and the awareness that we cannot reproach ourselves with anything, that we have taken the best decision that could be taken, that we have achieved the lowest possible level of costs or the highest safety at work, the best achievable production time or the highest quality of products.
What is optimisation?
The tools of operational programming aim at optimisation. Optimisation is the choice of the variant which maximises or minimises particular effects – that is, that which the owner of the process cares about most.
Let us assume that someone wants to have the lowest achievable technical cost of manufacture. The optimisation algorithm will indicate such a setting of the process as will allow this to be achieved. Then we can easily convince ourselves that every other solution, every other choice of the means of production, will have significantly higher costs.
An example of choosing the place of production
A confectionery plant consists of five independent production departments called confectionery workshops. The management of the confectionery plant intends to produce three kinds of biscuits on a mass scale. Because of technical conditions and the organisation of work, one confectionery workshop can produce only one kind of biscuit. The management of the confectionery plant has to allocate production to the individual workshops in such a way that the plant produces the maximum achievable number of tonnes of biscuits. The goal is therefore such a location of production that the production time of one tonne of each kind of biscuit is as short as possible.
The production manager measured the average time which each of the confectionery workshops needs to produce one tonne of each kind of biscuit.
The result of these measurements is presented in Table 1. Workshop 2 produces biscuits considerably faster, because it is equipped with the most modern production machines. The remaining workshops have similar manufacturing technologies.
Table 1. Average production time of biscuits in the production workshops
| Biscuits_A | Biscuits_B | Biscuits_C | |
|---|---|---|---|
| Workshop 1 | 214 min. | 162 min. | 180 min. |
| Workshop 2 | 96 min. | 56 min. | 66 min. |
| Workshop 3 | 105 min. | 180 min. | 124 min. |
| Workshop 4 | 146 min. | 173 min. | 127 min. |
| Workshop 5 | 116 min. | 183 min. | 167 min. |
As we remember, there are five confectionery workshops. The management plans the production of only three kinds of biscuits. This means that two workshops will be excluded from production.
The solution of this task’s algorithm consists of 25 answers – in other words, unknowns or variants. The distribution of the unknowns can be presented in Table 2 (Unknowns in the choice of the means of production).
Let us assume that biscuits A will be produced in workshop number 4. Such a variant will have the designation x₄₁ = 1. For the remaining workshops in the column Biscuits_A the unknowns will be equal to zero.
At the end of the table two columns have appeared: No work 1 and No work 2. These are columns which locate non-existent production. Quite simply, this type of algorithm requires the calculation matrix to have an equal number of rows and columns. If one of the workshops is located in these columns, it will mean that it has dropped out of the production process.
Formulating the limiting conditions
If, for example, workshop number 4 is to produce biscuits A, then no other workshop may produce them any longer. One kind of biscuit may be produced by only one workshop. This condition can be written as:
x₁₁ + x₂₁ + x₃₁ + x₄₁ + x₅₁ ≤ 1 (Workshop 1)
The objective of the algorithm is the minimum common production time of one tonne of each of the kinds of biscuits. Each of the 25 unknowns has assigned to it a particular production time recorded in Table 1.
The values are entered into the special windows of the calculator. The solution of the problem is presented in the table below.
Table 3. Optimal allocation of biscuit production
| Biscuits_A | Biscuits_B | Biscuits_C | No work 1 | No work 2 | |
|---|---|---|---|---|---|
| Workshop 1 | 0 | 0 | 0 | 0 | 1 |
| Workshop 2 | 0 | 1 | 0 | 0 | 0 |
| Workshop 3 | 1 | 0 | 0 | 0 | 0 |
| Workshop 4 | 0 | 0 | 0 | 1 | 0 |
| Workshop 5 | 0 | 0 | 1 | 0 | 0 |
The algorithm indicated that biscuits A should be produced in workshop number 3, biscuits B in workshop number 2, and biscuits C in workshop number 5. Workshops 1 and 4 should be excluded from the production of biscuits.
The application of the algorithm described here seems complicated, but in reality it is really easy. In algorithms of this type the most difficult thing is always to formulate the mathematical conditions. This time they are relatively simple and can be adapted to various situations.
The algorithm for allocating the means of production works excellently when we have to decide who is to do what. For example, we have four confectioners. Each of them is to make one product. Knowing each of them, we can very easily divide the work between them. If the situation is somewhat more complicated, if too many variables appear, or for too many employees, we can use the algorithm described here.
Wojciech Moszczyński
(In collaboration with Ewa Moszczyńska)
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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