Question

Race One Motors is an Indonesian car manufacturer. At its largest manufacturing facility, in Jakarta, the company produces subcomponents at a rate of 300 per day, and it uses these subcom-ponents at a rate of 12 500 per year (of 250 working days). Holding costs are $2 per item per year, and ordering costs are $30 per order. a) What is the economic production quantity? b) How many production runs per year will be made? c) What will be the maximum inventory level? d) What percentage of time will the facility be producing components? e) What is the annual cost of ordering and holding inventory?

Answer 1

a)

Economic production quantity means determining that level of quantity which should be ordered by a company to minimize the total inventory costs by maintaining adequate balance betwen the inventory holding cost and average fixed ordering cost. This concept is designed to help inventory managers to better understand the benefits of maintaining the right level of inventory to ensure smooth level of production without any kind of hindrances related to shortage of inventory. So, EPQ can be calculated as:

Production Per day (P) = 300

Usage rate of sub-components (D) = 12,500 per year (250 working​ days)

Holding cost (H) = $2 per item

Ordering costs (S) = ​$30 per order

So, first we will calculate d and d = D/ total working days

d = 12500 / 250 = $50

now, (1-d/P) = (1- 50/300)

= (1-.17)

= .83

Now, calculating EPQ by putting values

  

= 672.17 units

b)

Production runs per year = Annual demand (D) / EPQ

= 12500 / 672.17

= 18.59 production runs

c)

Maximum Inventory level = EPQ * [ 1- (d/p) ]

= 672.17 * [ 1- ( 50 /300) ]

= 672.17 * .83

= 557.90

d)

time (t) = EOQ / P

= 672.17 / 300

= 2.24 hour

production time in percenatge = ( t * no. of optimum orders) / no. of days in a year

= (2.24 * 18.59) / 250

= 16.66 %

e)

Annual cost of ordering and holding inventory = Ordering cost + Holding cost

= (ordering cost * annual demand) / EPQ + (Carrying cost per unit * EPQ) /2 * [ 1- (d/p)]

= (30*12500) / 672.17 + (2 * 672.17) /2 * [1-0.17]

= 557.89 + (672.17 * 0.833)

= $ 557.89 + $ 559.91

= $1,117.81