Question

JL.53 Bob's Bumpers has a repetitive manufacturing facility in Kentucky that makes automobile bumpers and other auto body parts. The facility operates 290 days per year and has annual demand of 75,000 bumpers. They can produce up to 330 bumpers each day. It costs $59 to set up the production line to produce bumpers. The cost of each bumper is $131 and annual holding costs are $37 per unit. Setup labor cost is $28 per hour.

What is the optimal size of the production run for bumpers? (Display your answer to the nearest wholenumber.)
   

Based on your answer to the previous question, and assuming the manufacturer holds no safety stock, what would be the average inventory for these bumpers? (Display your answer to the nearest wholenumber.)
   

Based on your answer two questions back, how many production runs will be required each year to satisfy demand? HINT: As a general rule, whenever calculating a value that is based on previous calculations in Excel, always be sure to use cell references rather than a rounded value as a calculation input. (Display your answer to the nearest whole number.)
   

Suppose the customer (an auto manufacturer) wants to purchase in lots of 620 and that Bob's Bumpers is able to reduce setup costs to the point where 620 is now the optimal production run quantity. How much will they save in annual holding costs with this new lower production quantity? (Display your answer to two decimal places.)
  

How much will they save in annual setup costs with this new lower production quantity? (Display your answer to two decimal places.)

Answer 1

Annual demand (D) = 75000

Daily demand (d) = 75000/290 = 258.62

Daily production capacity (p) = 330

Setup cost (S) = 59

Product cost (P) = 131

Holding cost (H) = 37

Optimal size

Q = sqrt( 2DS/ (H*(1-(d/p))))

Q = sqrt (2*75000*59/(37*(1-(258.62/330)))) = 1051.57 units or 1052 units

Average inventory

I = (Q/2)*(1 – d/p)

I = (1052/2)*(1-(258.62/330)) = 113.775 units

Number of production run

R = D/Q = 75000/1052 = 71.29 or 72 runs

Annual holding cost

C = (HQ/2)*(1-(d/p))

The setup cost has no role in the annual holding cost of the inventory.

At the current situation, C1 = (37*1052/2)*(1-(258.62/330)) = 4209.68

With the new quantity, C2 = (37*620/2)*(1-(258.62/330)) = 2480.99

The saving is 1728.69

Annual setup cost

O = DS/Q

However, we need to determine the new value of S.

620 = sqrt(2*75000*X/(37*(1-(258.62/330))))

X = 20.50

Old annual setup cost = 75000*59/1052 = 4206.27

New annual setup cost = 75000*20.5/620 = 2479.83

The saving is 1726.43