A particular operation may be performed by two kinds of process. Process A requires a setup time of 40 minutes, whereas Process B requires a setup time of 180 minutes. On the other hand, the per unit run times are: 0.015 minutes on A and 0.0023 minutes on B. Which batch sizes would you route to A and which ones to B?

If batch size is more than 11,024 we will prefer  B process otherwise we will prefer Process A.

Explanation:

Given,

Setup time of Process A = 40 minutes.

Setup time of Process B= 180 minutes.

The production time for the x batch size in the process A is given by Ta(x)=40+0.015×x

The production time for the x batch size in the process B is given by

Tb(x)=180+0.0023×x

Equating the both equations to the find the balancing point Ta(x) =Tb(x)

                                 40+0.015×x = 180+0.0023×x

Rearranging the terms in the equations and bringing the similar terms on same side of the equation.

                                x×(0.015-0.0023) = 180-40

                                         ⇒0.0127×x  = 140

                                                         x   = 11,023.6

Round off x we get x= 11,024

Therefore if batch size is more than 11,024 we will prefer  B process otherwise we will prefer Process A.