A machine makes two components; call them types A and B. It takes 250 seconds to switch production between the component types. During that time, no production occurs. When in production, each unit of A or B requires 0.5 second to be completed. The two components, A and B, are combined in an assembly process to make a final product; call it C. The assembly step can combine the two components into 1 unit every 2 seconds, or 30 units per minute.

"A machine makes two components, call them type A and B. It takes 250 seconds to switch production between the component types. During that time no production occurs. When in production, each unit of A or B requires 0.5 seconds to be completed. The two components, A and B are combined in an assembly process to make a final product, call it C. The assembly step can combine the two components into 1 unit every 2 seconds. What is the average inventory of B components?"

We have two steps in this process: the manufacturing of A and B and the assembly process.

We are not told about the batch size, so we will treat that as a variable called n. This represents the amount of units (of A or B) that are manufactured per cycle.

Time (seconds) to manufacture n units of A and n units of B:

[tex]T_m=n*0.5+n*0.5+250=n+250[/tex]

Time (seconds)to assemble n units of C

[tex]T_a=n*2=2n[/tex]

Then the total time of the cycle is:

[tex]T_m+T_a=n+250+2n=3n+250[/tex]

The average inventory of B is n units per cycle, which lasts (3n+250) seconds.

[tex]Inventory=\frac{n}{3n+250}[/tex]

For a batch size of 100 units, the average inventory is:

[tex]I_{100}=\frac{100}{3*100+250}=\frac{100}{550}= 0.182\, units/second[/tex]

For a batch size of 1,000 units, the average inventory is:

[tex]I_{1000}=\frac{1000}{3*1000+250}=\frac{1000}{3250}= 0.308\, units/second[/tex]