I need help with answering Chapter 7 questions for Matching

I need help with answering Chapter 7 questions for Matching Supply with Demand. In specific, questions 7.2 (PTests).

Solution

(a). What is the capacity of the stamping unit?

One Batch of Part A = 360 units

One Batch of Part B = 720 units

Each window box has 3 pieces = a base (one Part A) + two sides (two Part B)

Therefore,

One Batch of window box (B)= 360 units

Set-up time of stamping machine (S) = 120 minutes

Switching time between Part A and Part B = S = 120 minutes

Time to process each Part A = 1 min

Time to process each Part B = .5 min

Time to process the entire batch (Tb) = Time to process 3 pieces

                                                                        = Time to process batch of Part A

+ Switching time

+ Time to process batch of Part A

                                                                        = 360 unit * 1 min

+ 120 min

+ 720 unit * .5 min

                                                                        = 840 minutes

Formula for process capacity with Batching

            = B/ (S+Tb) where B = Batch Size,

S = Set-up time of stamping machine

Tb = Time to process the entire batch

Process capacity at stamping unit

            = 360 / (120+840) units per minute

            = 360 * 60 / 960 units per hour

            = 22.5 units per hour

b) What batch size would you recommend for the process?

At assembly:

Labor time for each product to assemble (T) = 27 minutes

Number of workers at assembly (W) = 12

The capacity at Assemble unit    = (1/T) * W units per minute

                                                            = (1/27)*12 units per minutes

                                                            = (1/27)*12*60 units per hour

                                                            = 26.67 units per hour

Let recommended batch size be B, we need to match the process capacity of stamping unit with the assembly capacity.

(B * 60) / (120 + B *1 + 120 +2*B *.5) = 26.67

(B * 60) / (240 + 2B) = 26.67

60 B = 26.67 (240+2B)

60 B = 6400.8 + 53.34 B

(60-53.34) B   = 6400.8

6.66 B = 6400.8

B = 6400.8 /6.66

= 961.08

So, the recommended batch size is 961 units.

CHECK:

Process capacity at stamping unit

            = 961 / (120+ 961 + 120 + 1922*.5) units per minute

            = 961 * 60 / 2162 units per hour

            = 26.67 units per hour