Question

PLEASE INCLUDE DETAILED CALCULATION AS WELL!

Problem 6

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?

Answer 1

Given are following data :

Annual demand = D = 9000 monitor

Set up cost = Cs =$7500

Annual unit holding cost = Ch = $120

Monthly demand = d = 9000/12 = 750 monitors

Monthly production = p =2000 monitors

Economic Production lot size ( EPQ )

= Square root ( 2 x Cs x D / Ch x ( 1 – d/p))

= square root ( 2 x 7500 x 9000 / 120 x ( 1 – 750/2000))

= Square root ( 2 x 7500 x 9000/ 120 x 0.625)

= 1341.64 ( 1342 rounded to nearest whole number )

ECONOMIC PRODUCTION LOT SIZE = 1342

Annual set up cost

= Set up cost x Number of set ups

= Cs x Annual demand / EPQ

= $ 50298 ( rounded to nearest whole number )

= Annual unit holding cost x Average inventory

= Ch x EPQ( 1 – d/p)/2

= $120 x 1342 x ( 1 – 750/2000)/2

=$120 x 1342 x 0.625/2

Therefore , Total variable inventory cost per year

= Annual set up cost + Annual holding cost

= $50298 + $50325

= $100623

ANNUAL SET UP COST = $50298

ANNUAL HOLDING COST = $50325

TOTAL VARIABLE INVENTORY COST = $100623

Duration of each production run ( in months)

= EPQ/ Monthly production quantity

= 0.671 months

Frequency of production run ( i..e number of production runs in a year )

= Annual demand / EPQ

= 9000/ 1342

DURATION OF EACH PRODUCTION RUN = 0.671 MONTHS

FREQUENCY OF PRODUCTION RUN = 6.70 TIMES IN A YEAR

Maximum inventory level = EPQ x ( 1 – d/p) = 1342 x ( 1 – 750/2000) =1342 x 0.625 = 838.75 monitors

While the manufacturer will produce p units in a month , d number of units will be consumed in a month. This will result in a generation ( p – d) units of inventory for every unit of p produced .

Therefore , quantity of inventory produced for every unit of monitor produced = ( p – d) / p = ( 1 – d/p)

Therefore , quantity of inventory produced ( which will be the maximum inventory which can be produced ) for EPQ quantity of monitors produced = EPQx( 1 – d/p)

Since ( 1 – d/p) < 1 , EPQ ( 1 – d/p) < EPQ

Therefore Maximum inventory level i.e. EPQ x ( 1 – d/p) <ProductionLot size EPQ