\nAverage speed of performing one taking operation (for a volume of goods of 4 dm\u00b3)<\/td>\n 2.4 seconds<\/td>\n<\/tr>\n<\/table>\nTable 2. Average Time for Warehouse Operations<\/i><\/p>\n
We have established the method for calculating movement costs. Now, it is necessary to determine how to calculate costs for selecting the container cell<\/b>Here, things are much more complicated than the costs of movement because: <\/p>\n\nfirstly, the costs must be directly proportional to the volume of the cell \u2013 the same volume of stock being moved from donor cells should preferably be placed in a smaller container rather than a large one, provided that the volume fully fits into both containers. By minimizing the overall costs of container selection, we aim to save 'scarce' available warehouse capacity in the picking area in order to perform subsequent product placement operations in cells. Figure 4 illustrates the options for moving stocks into large and small containers and the consequences of such moving options during subsequent warehouse operations.<\/li>\n secondly, since we need to minimize overall costs in the initial task solution, which is the sum of both the movement costs and the container selection costs, the volumes of the cells in cubic meters must be somehow correlated with seconds, which is far from trivial.<\/li>\n<\/ul>\n\nFig. 4. Options for moving stocks into containers of different capacities.<\/i><\/p>\n
In Figure 4, the red color represents the volume of stocks that no longer fit into the container at the second stage of placing subsequent goods. <\/p>\n
The following requirements for the computed solutions of the problem will help correlate cubic meters of container selection costs with seconds of movement costs:<\/p>\n
\nIt is necessary that the stocks from the donor cell be moved to the container cell in any case if it reduces the total number of container cells in which the goods are located.<\/li>\n It is necessary to maintain a balance between the volumes of containers and the time costs of movement: for example, if in the new solution variant compared to the previous solution variant, the gain in volume is significant, while the loss in time costs is small, then the new variant should be chosen.<\/li>\n<\/ul>\n\nLet's start with the last requirement. To specify the ambiguous word 'balance', we conducted a survey of warehouse employees to find out the following. Suppose there is a container cell with a volume
The question arises: what is the minimum volume gain
Fig. 5. Chart of the relationship between the minimum allowable volume savings and the increase in time difference for the operation.<\/i><\/p>\n
That is, if the additional time costs amount to 40 seconds, we are only willing to incur them if the volume gain is at least 500 dm3. Despite the slight non-linearity observed in the relationship, for simplicity in further calculations, we will assume that the relationship between the quantities is linear and described by an inequality.<\/p>\n
In the figure below, we will consider the following methods of placing goods in containers.<\/p>\n
Fig. 6. Option (a): 2 containers, total volume 400 dm3, total time 150 sec.<\/i>Fig. 6. Option (b): 2 containers, total volume 600 dm3, total time 190 sec.<\/i>Fig. 6. Option (c): 1 container, total volume 400 dm3, total time 200 sec.<\/i><\/p>\n
Option (a) for choosing containers is more preferred than the initial option, as the inequality is satisfied: (800-400)\/10 >= 150-120, which leads to 40 >= 30. Option (b) is less preferred than the initial option since the inequality is not satisfied: (800-600)\/10 >= 190-150, which leads to 20 >= 40. But option (c) does not fit into such logic! Let's examine this option in more detail. On one hand, the inequality (800-400)\/10 >= 200-120 holds, which means the inequality 40 >= 80 is not satisfied, indicating that the volume gain does not justify such a significant time loss. <\/p>\n
On the other hand, in such option (c), we are not only reducing the total occupied volume but also decreasing the number of occupied cells, which is the first of two important requirements for computed solutions to the problems listed above. Clearly, for this requirement to start being fulfilled, we need to add a certain positive constant to the left side of the inequality.
Transforming the inequality above, we obtain <\/p>\n
Based on this, we have a formula for calculating the total cost
But now the question arises<\/b>: what value should such a constant have
Let
The first method of calculating the magnitude<\/b>
from which it follows<\/p>\n
Substituting the average execution time of elementary operations into the formula above, we get<\/p>\n
The second method of calculating the magnitude<\/b>
Transforming the inequality, we get<\/p>\n
To 'enhance' the value of the magnitude
Taking the largest value computed for each variant, this will be the value of the magnitude
Now, after all the titanic efforts<\/b> to transform the input data, we can say that all input data has been transformed into the required format and is ready for use in the optimization algorithm.<\/p>\nConclusion<\/h4>\n
\nAs practice shows, the labor intensity and importance of the data preparation and transformation stage for the algorithm is often underestimated. In this article, we specifically paid a lot of attention to this stage to show that only well-prepared input data can make the solutions computed by the algorithm truly valuable for the client. Yes, there were many formula outputs, but we warned you about this earlier \ud83d\ude42<\/p>\n
In the next article, we will finally get to the purpose of the previous two publications \u2013 the discrete optimization algorithm.<\/p>\n
The article was prepared byhabr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"\u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043a\u0430\u0436\u0435\u043c, \u043a\u0430\u043a \u0440\u0435\u0448\u0430\u043b\u0438 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0443 \u043d\u0435\u0445\u0432\u0430\u0442\u043a\u0438 \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0445 \u044f\u0447\u0435\u0435\u043a \u043d\u0430 \u0441\u043a\u043b\u0430\u0434\u0435 \u0438 \u043e \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0435 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0442\u0430\u043a\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438. \u0420\u0430\u0441\u0441\u043a\u0430\u0436\u0435\u043c \u043e \u0442\u043e\u043c, \u043a\u0430\u043a \u043c\u044b \u00ab\u0441\u0442\u0440\u043e\u0438\u043b\u0438\u00bb \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438, \u0438 \u043e \u0442\u043e\u043c \u0441 \u043a\u0430\u043a\u0438\u043c\u0438 \u0442\u0440\u0443\u0434\u043d\u043e\u0441\u0442\u044f\u043c\u0438 \u043c\u044b \u043d\u0435\u043e\u0436\u0438\u0434\u0430\u043d\u043d\u043e \u0441\u0442\u043e\u043b\u043a\u043d\u0443\u043b\u0438\u0441\u044c \u043f\u0440\u0438 \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0435 \u0432\u0445\u043e\u0434\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 \u0434\u043b\u044f \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430. \u0415\u0441\u043b\u0438 \u0432\u0430\u043c \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u044b \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0432 \u0431\u0438\u0437\u043d\u0435\u0441\u0435 \u0438 […]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":27819,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[702],"tags":[],"class_list":["post-37108","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t
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