Question

Race One Motors is an Indonesian car manufacturer. At its largest manufacturing​ facility, in​ Jakarta, the company produces subcomponents at a rate of 290 per​ day, and it uses these subcomponents at a rate of 12,800 per year ( of 250 working days).  Holding costs are $2 per item per year, and ordering costs are $31 per order.

a, What is the economic production quantity? (ROUND YOUR RESPONSE TO TWO DECIMAL PLACES)

b, How many production runs per year will be made? (ROUND YOUR RESPONSE TO TWO DECIMAL PLACES)

c, What will be the maximum inventory level?(ROUND YOUR RESPONSE TO TWO DECIMAL PLACES)

d, What percentage of time will the facility be producing components? (ENTER YOUR RESPONSE AS A PERCENTAGE ROUNDED TO TWO DECIMAL PLACES)

e, What is the annual cost of ordering and holding inventory? (ROUND YOUR RESPONSE TO TWO DECIMAL PLACES)

Answer 1

Answer to question a :

Annual demand = D = 12800 units

Daily demand = d = 12800/250 = 51.2

Daily production rate = p = 290

Ordering cost = S = $31

Holding cost = H = $2 per unit per year

Economic production quantity ( EPQ)

= Square root ( 2 x D x S/H x p/(p -d))

= square root ( 2 x 12800 x 31/2 x 290 / ( 290 – 51.2))

= 694.17

Answer to question b :

Number of production runs in a year

= Annual demand / Economic production quantity

= 12800/694.17

= 18.44

Answer to question C :

Maximum inventory level

= EPQ/p x ( p-d)

= 694.17/290 x ( 290 – 51.2)

= 571.61

Answer to question d :

Number of production days to meet the demand

= Annual demand/ Production per day

= 12800 / 290

= 44.137

Number of days in a year = 250

Percentage of time facility will be producing components

= 44.137/250   x 100

= 17.658%

Answer to question e :

Annual cost of ordering

= Ordering cost x Number of production run in a year

=31 x 18.44

= $571.64

Annual cost of holding inventory

= Annual unit holding cost x Average inventory

= Annual unit holding cost x Maximum inventory / 2

= $2 x 571.61/2

= $571.61

Annual cost of ordering and holding inventory = $571.61 + $571.61 = $1143.22

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