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:
10:00 casting-mold $(a)$ preparation
10:05 casting-mold $(a)$ sending for production and start processing the next casting-mold $(b)$
10:10 casting-mold $(b)$ sending for production and start processing the next casting-mold $(c)$
10:15 casting-mold $(c)$ sending for production and start processing the next casting-mold $(d)$
10:20 casting-mold $(d)$ sending for production
10:20 - 10:30 Wait until the first casting-mold $(a)$ gets available again
10:30 casting-mold $(a)$ preparation (since 10:05 + 00:25 = 10:30)
10:35 casting-mold sending $(a)$ for production and start processing the next casting-mold $(b)$
10:40 casting-mold $(b)$ sending for production and start processing the next casting-mold $(c)$
10:45 casting-mold $(c)$ sending for production and start processing the next casting-mold $(d)$
10:50 casting-mold $(d)$ sending for production
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: