Color View is a manufacturer of monitors for personal computers. Color View’s ne
ID: 349294 • Letter: C
Question
Color View is a manufacturer of monitors for personal computers. Color View’s newest monitor is X-435 model. The company expects sales of this model to run at the rate of 9,000 per year for a while. The facilities for producing this model are shared with several other models. While these production facilities are devoted to the X-435 model, the production rate is 2,000 monitors per month. The cost each time the facilities are set up for production run for this model is $7,500. The annual cost of holding each of these monitors in inventory is estimated to be $120.
(a) Determine the economic production lot size.
(b) Find the corresponding annual setup cost, annual holding cost and total variable inventory cost per year.
(c) How long each production run last and how frequently should they occur? (Give your answer in month).
(d) What is the maximum inventory level? Why is this less than the production lot size?
Explanation / Answer
Setup cost (Co)=7500
Holding Cost (Ch)=120/unit
Demand (D)=9000/yr
Production (P)=2000/month=2000*12=24000 per yr
a) Production Lot Size (Q) =((2CoD)/(Ch(1-D/P)))^0.5
=((2*7500*9000)/(120(1-(9000/24000))))^0.5
= 1341.64 = 1342
b) Total variable cost TV(Q) = Co(D/Q) + Ch((1-D/P)/2)Q
=7500(9000/1342) + 120((1-9000/24000)/2)*1342
=50298.06 + 50325 = 100623.06
c) No of set-ups per yr = D/Q = 9000/1342= 6.76 = 7
Length of production run = Q/P = 1342/24000= 0.0559 yr = 0.0559*365 =20.41 days
Length of production cycle = Q/D = 1342/9000 = 0.149 yr = 0.149*365 = 54.42 days
d) Maximum Inventory = Imax = (1-D/P)Q
=(1-9000/24000) * 1342
= 838.75 = 839
Average Inventory = Imax/2= 419.375 =420
Inventory does not jump to the production lot size. It actually builds up to maximum inventory value. This point of maximum inventory value is reached when the production is ceased. Hence, maximum inventory is less than production lot size.