• Three-Dimensional Nesting

Sometimes the primary value of materials and sometimes side expenses in three-dimensional Nesting result in considering Nesting. In jewelry industries, military industries with special materials or sculpture industries which require costly primary materials, for instance, including three-dimensional Nesting is of high significance. Three-dimensional Nesting also matters in packaging and transporting industries, where the value of the pieces themselves is not taken into account and the objective is to reduce the cost of shipment through considering the best layout and thus using the most space available.

We return back to the table at the outset of the discussion. What is the best layout according to Nesting principles? There is no doubt that we cannot reach the best layout relying merely on ordinary calculations, considering the number and variety of pieces; rather, we definitely require a software. History of Nesting as a scientific issue dates back to late 18th century B.C. In line with computer development, various soft wares have been created in that respect through the course of recent years. Searching online, you will get access to a considerable list of these software. The answer to the first problem will be provided by one of these soft wares as shown below:


As you can see, the precise answer to even this simple and one-dimensional problem will be different from what we have estimated theoretically, and we will surely encounter lack of materials if applying the theoretically estimated amounts. This issue will gain more significance when it comes to two-dimensional problems. The answer to the question whose data was presented at the beginning of the discussion is as follows:

In this table, pay attention to the amounts in off column which indicate the remaining and usable extra materials from each standard length. Prior to anything else, these numbers imply that the combination of pieces to be aligned is selected by the software in such a way that by the end of the process no extra material would remain from a twelve-meter standard length! This is the most important priority of Nesting software. A subject whose unperformability in absence of the software might be unquestionably confirmed.

Two-dimensional Nesting problems are even more intriguing! Keep in mind that in addition to the pieces’ material and thicknesses, the direction of their alignment plays a role as a serious restriction in the problem, as well. Take the following pieces into consideration to enter two-dimensional Nesting discourse:

These pieces are classified as below with regard to their material and thickness:

These pieces are all rectangular in shape. Suppose that we have other pieces as the figure below, as well:

These pieces, too, are placed in that group regarding their material and thickness but are shaped like a ring. Consider other pieces which are disk-shaped and whose data is given in the table below:

Some of these pieces must be only placed on the length of the main plate (before which the word “No” is written in Rotation column in the first table. This means that we are not allowed to rotate them while setting the layout and applying Nesting principles). Imagine that the dimensions of existing and available raw materials for setting the layout and specifying the number of raw plates are 6,000 x 1,500 millimeters. The length of none of the pieces including the word “No” in the Rotation column in the first table is smaller than the present width (1,500 millimeters). As a result, excluding the word “No,” even, does have no effect in the problem solution. However:

Row 9 which is distinguished as green has a piece length of 1,200 millimeters. Therefore, there is the possibility of placing its length on the raw plates’ width; this task, nevertheless, is forbidden by the problem. This issue (no rotation allowed) is the most critical restriction in solving two-dimensional Nesting problems. Overlooking these topics, unraveling two-dimensional problems will not differ qualitatively from one-dimensional Nesting problems. To simulate a two-dimensional Nesting problem, the question will be as follows:


There are 190 pieces shaped as rectangle, ring, and disk comprised of three materials with each material comprising three thicknesses. The net weight of these pieces is approximately 38 tons. Adhering to Nesting principles, under what combination of existing materials in tables 1 to 3 can we reach the least raw materials required? Reminding the fact that:

The weight for primary materials must be minimized.

This layout must be achieved through the least cuts.

The least waste must be generated.

The fact of the matter is that even if the number of pieces is less than 190, setting such a layout without the aid of the software is a dire and to some extent personalized task. By utilizing Nesting soft wares, however, not only can you increase the speed of the project and thus disregard the number of pieces, but you can also calculate with high accuracy. Unraveling this problem through the software bears the following results:

55 sheets of raw plates with features inserted in the previous table are required to organize all the pieces defined in the three tables above. You can see the layout of several sheets in the following figures to gain mastery over this accomplishment.

Fig. 134 – (Graphic Results of a Two-Dimensional Nesting)


Nesting tool serves as one of the most powerful assets and the strength point of PVManage software. By the use of this tool, the following phrase can be brought up as the motto and statement claimed by creators of PVManage software:


From Data Sheet to Cutting Plan with Just a Few Clicks!

Fig. 135 – (Nesting Menu)


As mentioned earlier, Nesting can be run as one- or two-dimensional. These two capabilities are designed as independent from one another.

In estimating materials for pressured vessels (which is the focal point of PVManage software), one-dimensional Nesting is employed to organize Spacer, Standard Profile, Pipe, and Tie Rod, while two-dimensional Nesting is employed to organize different sorts of project plates in various shapes.



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