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 360 days per year and has annual demand of 77,000 bumpers. They can produce up to 350 bumpers each day. It costs $88 to set up the production line to produce bumpers. The cost of each bumper is $129 and annual holding costs are $39 per unit. Setup labor cost is $20 per hour.
(a) Based on the above information, what is the optimal size of the production run for bumpers? display answer to two decimal places
(b) 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?
(c) Based on your answer two questions back, how many production runs would be required each year to satisfy demand?
(d) Suppose the customer (an auto manufacturer) wants to purchase these bumpers in lots of 500 and that bob's bumper is able to reduce setup cost to the poi t where 500 is now the optimal production run quantity. how much will they save in annual holding cost with this new lower production quantity?
(e) How much will they save in annual set up costs with this new lower production quantity?

Answer 1

Answer:

a)

Annual demand = 75000 = D

S = ordering cost/set up cost = $53

d = daily demand = 75000/250 = 300

h = holding cost per unit per year = $25

p = Daily production rate = 320

optimal size of the production run =EPQ = sqrt((2*D*S)/(h*(1-(d/p))))

= sqrt((2*75000*53)/(25*(1-(300/320))))

= 2255.659549 = 2255.66 (Rounded to 2 decimal places)

b)

maximum inventory = EPQ*(1 - (d/p))

= 2255.66*(1 - (300/320))

= 140.97875

Avergae inventory = 140.97875/2 = 70.49

c)

Number of production runs = Annual demand/EPQ = 75000/2255.66 = 33.25

d)

Holding cost with EPQ = 2255.66 = 70.49*25 = 1762.25

With EPQ = 500, maximum inventory = 500*(1 - (300/320)) = 31.25

Holding cost with EPQ = 500, holding cost (31.25/2)*25 = 390.625

Savings = 1762.25 - 390.625 = 1371.625