*2.4. Manufacturing Processes Implemented in SLS and SLM Technologies, Determining the Necessary Number of Machines*

For computational purposes, a hypothetical production plan was assumed; the production processes of two types of products will be carried out on 3D machines: product X manufactured in the SLS technique and product Y manufactured in the SLM technique. The production plan assumes the production of 20,000 pieces of product X and 23,000 pieces of product Y per year. Additional assumptions:

• number of products simultaneously printed on the working plate: Eight (for the SLS method) and 10 (for the SLM method);


To calculate the number of necessary devices in order to be able to implement the assumed production plan within the prescribed time, a formula was used that considered the ratio of the time necessary for technological operations to the available number of man-hours per year:

$$i\_0 = \frac{t\_{pz} + n \cdot t\_j}{\psi\_{d'} D \cdot I \cdot \\$} \tag{6}$$

where *tpz* is the unit time of a technological operation; *tj* is the preparation and completion time of a technological operation; *n* is the number of manufactured items; ψ*<sup>d</sup>* is the working day utilization factor; *D* is the number of working days per year; and *I* is the number of shifts.

The form of the technological process for product X and Y is recorded in Tables 1 and 2, these tables present the designated number of machines according to Equation (6):


**Table 1.** Sequence of technological operations for product X with the calculated i0 number of machines and devices necessary to implement the production plan.

<sup>1</sup> Devices shared for the manufacturing process of products X and Y, *i*<sup>0</sup> values are then added up before rounding up.

**Table 2.** Sequence of technological operations for product Y along with the calculated i0 number of machines and devices necessary to implement the production plan.


<sup>1</sup> Devices shared for the manufacturing process of products X and Y, *i*<sup>0</sup> values are then added up before rounding up.

The calculated number of 3D printing machines and devices, along with their dimensions, will be the key information at the next stage of developing layout plans.

#### **3. Results—The E**ff**ects of the Arrangement Optimization of 3D Printing Stations**

To optimize the arrangement of workstations, it was decided to use the MST method, based on the adjacency weight matrix, built on the basis of material flows. With this algorithm of procedure, auxiliary stations, characteristic for 3D printing machines and devices, are not taken into account. Thanks to this, it will be possible to collect information on whether this limitation is a significant disadvantage of this type of optimization method in the case of 3D printing devices.

#### *3.1. Results of Optimization of the Arrangement of Workstations*

For the purposes of the calculations, the MST method assumed that the size of the transport batch would correspond to the number of parts on the platforms of SLS and SLM devices. Machines will be located in a way providing, apart from the minimum recommended distances between them, access to the transport road for each of them. It was assumed that a hand truck would be used to transport a batch of elements. It will also be necessary to provide additional space for buffers (intermediate storage areas). The minimum recommended distances depend on the requirements of the manufacturers or on the size of the machines, the type of adjacency (side of the device, rear of the device, side of the machine where the operator works in relation to the sides of another machine, wall or transport road, etc.), and the dimensions of the machines.

Table 3 contains the information matrix of the part flow for the assumed technological process of products X and Y. The sequence of technological operations to be implemented is recorded in this matrix. It also includes the calculated number of transport activities, based on the number of manufactured products and the number of pieces in the transport batch.

The next step in the MST method is the development of the flow matrix (Table 4), containing information on the number of transport activities connecting workstations into subsequent pairs. Certainly, these calculations are based on the part flow information matrix. The numbering of workstations from Table 3 was also retained in the following tables (Tables 4–8).

Table 5 contains the selected distances between the stations connected by transport activities, depending on the method of the assumed adjacency (in this case "side to side") or the requirements taken from the technical and commissioning documentation provided by the manufacturer of the device.

The selected distances between the devices in Table 5 also depended on the dimensions of the machines (Table 6), where the larger the dimensions of the machines, the greater the recommended distances between them.

The values in the adjacency weight matrix f ij, presented in Table 7, were calculated on the basis of the previously presented Equation (5) from Section 2.2.

The result of the MST method is the sequence of workstations, read from the adjacency weight matrix f ij, written in the characteristic form of a single-line matrix. For the analyzed case, the results are presented in Table 8.

The pair of Output Warehouse (14) and Packing (13) stations showed the greatest weight of adjacency, therefore the pair from which the reading of the sequence of the arrangement of workstations began. The Output Warehouse (14) was the last station in the chain, therefore subsequent stations were selected from the adjacency weight matrix preceding the Packing (13) station, guided by the calculated weight for transport activities.



**Table 4.** Flow matrix fij.


1 All selected distances between devices are expressed in meters.

**Table 6.** Machine lengths *l* for the analyzed case.


**Table 7.** Adjacency weight matrix f ij.

**Table 8.** Designated sequence of workstations for the analyzed case.


#### *3.2. Developed Layout Plan*

When developing the layout plan, the information collected thus far regarding workstations, the required and recommended distances between them, their number and dimensions, and the location determined according to the MST method were used. In addition, it was assumed that the shape of the plot on which the production hall is located enables the delivery of the necessary raw materials and other consumables on one side of the production hall and the receipt of finished products on the other. With this location of the Input and Output Warehouses, it was easier to ensure non-intersecting material flows. Access to the transport road was ensured via inter-operational buffers for batch-based transport operations. The developed layout plan, taking into account the above requirements, is shown in Figure 3.

A certain difficulty in the design process was the transfer of the designated layout of workstations from the MST method to a specific layout plan, due to the need to consider technological limitations related to:


The social part for employees was not included in the designed production hall in order to limit the size and detail of the drawing and thus increase its readability. For the same reason, the dimensions of machines and devices or the assumed distances between them are not shown.

**Figure 3.** Sample layout plan design for 3D printing machines and devices.
