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 350 days per year and has annual demand of 55,000 bumpers. They can produce up to 395 bumpers each day. It costs $85 to set up the production line to produce bumpers. The cost of each bumper is $106 and annual holding costs are $23 per unit. Setup labor cost is $25 per hour.

1) What is the optimal size of the production run for bumpers? (Display your answer to the nearest whole number.) Incorrect

2) 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 whole number.)

3) 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.)

4) Suppose the customer (an auto manufacturer) wants to purchase in lots of 510 and that Bob's Bumpers is able to reduce setup costs to the point where 510 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.)

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

Answer 1

1) Optimal size of the production run for bumpers, Q= √[2DS/H(1-d/p)]

Given annual demand, D = 55,000 bumpers for 350 days

Hence daily demand rate, d= 55000/350= 157.14

Daily production rate, p = 395 bumpers

Set up cost= $85

Annual holding cost= $23 per unit

Q= √[2*55000*85/23(1-157.14/395)]= 821.64≈822 bumpers

2) Average inventory for the bumpers = Maximum inventory level/2

Maximum inventory level = Q(1-d/p)= 821.64(1-157.14/395)= 494.77

Hence average inventory= 494.77/2 = 247.39≈247 bumpers

3. Production runs that will be required each year to satisfy demand = D/Q = 55000/821.64= 66.94≈67 production runs

4. Annual holding cost= average inventory level*holding cost per unit per year

Annual holding cost when (Q=821.64)= 247.39*23= $5689.89

New optimum order quantity= 510 units

Annual holding cost= average inventory level*holding cost per unit per year= Q/2(1-d/p)H= 510/2(1-157.14/395)23= $3531.77

Hence savings in annual holding cost= 5689.89-3531.77= $2158.12

5. Annual setup cost with Q= 510

S= [Q²H(1-d/p)]/2D= [510²x23(1-(157.14/395))]/(2*55000)

= $32.749

Annual setup cost = (D/Q)S= (55000/510)32.749= $3531.77

When (Q= 821.64 and S=85);

Annual setup cost = (55000/821.64)85 = $5689.84

Savings in annual setup cost with the new lower production order quantity = 5689.83- 3531.76 = $2158.07