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Problem Clustering and Suggestions for Solving it (Job-Shop?)

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I am trying to find the amount that an item may get produced.

To produce this item I need casting-molds. A casting-mold can be used multiple times after it becomes available again.

For the production I have to take into consideration the following parameters:

  • The production period
  • The duration a casting-mold needs to get prepared before it gets sent to production
  • The number of casting-molds
  • The time it gets for a casting-mold to be available again.

In this case, the quantity of this item to produce is infinite.

Here is a simple example:

  • Production period: 10:00 - 11:00 (60 Minutes)
  • Casting-mold preperation time: 5 Minutes
  • Number of casting-molds: $|\{a,b,c,d\}| = 4$
  • Re-use time: 25 Minutes

Production Process:

  1. 10:00 casting-mold $(a)$ preparation

  2. 10:05 casting-mold $(a)$ sending for production and start processing the next casting-mold $(b)$

  3. 10:10 casting-mold $(b)$ sending for production and start processing the next casting-mold $(c)$

  4. 10:15 casting-mold $(c)$ sending for production and start processing the next casting-mold $(d)$

  5. 10:20 casting-mold $(d)$ sending for production

  6. 10:20 - 10:30 Wait until the first casting-mold $(a)$ gets available again

  7. 10:30 casting-mold $(a)$ preparation (since 10:05 + 00:25 = 10:30)

  8. 10:35 casting-mold sending $(a)$ for production and start processing the next casting-mold $(b)$

  9. 10:40 casting-mold $(b)$ sending for production and start processing the next casting-mold $(c)$

  10. 10:45 casting-mold $(c)$ sending for production and start processing the next casting-mold $(d)$

  11. 10:50 casting-mold $(d)$ sending for production

  12. End (The casting-mold $(a)$ can be used at 11:00 again which is out of the production window)

In this case, the item gets produced 8 times.

It is irrelevant which mold gets processed first.

Added for clarification:

The production happens to one machine.

The products may get finished after the production time frame (10:00 - 11:00), e.g., the items produced at 10:40 $(b)$, 10:45 $(c)$ and 10:50 $(d)$ end respectively at 11:05 $(b)$, 11:10 $(c)$ and 11:15 $(d)$

How would you tackle such a problem?

Thanks to @A.Omidi for the idea of a Gantt-chart:

enter image description here


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