Question

Race One Motors is an Indonesian car manufacturer. At its largest manufacturing? facility, in? Jakarta, the company produces subcomponents at a rate of 295 per? day, and it uses these subcomponents at a rate of 12,100 per year? (of 250 working? days). Holding costs are ?$3 per item per? year, and ordering costs are ?$31 per order.

a. what is the economic production quantity? (round to two decimal places)

b. how many production runs per year will be made? (round to two decimal places)

c. what will be the maximum inventory level? (round 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 to two decimal places)

Answer 1

Given information:

Daily production rate (p) = 295 per day

Annual demand (D) = 12,100 units

Number of working days = 250

Daily demand = Annual demand / Number of days = 12100 / 250

Daily demand (d) = 48.4 units

Holding cost (H) = $3 per item per year

Ordering cost (Co) = $31 per order

Solution:

(a) Economic Production Quantity (EPQ) is calculated as;

EPQ = SQRT (2 x D x Co) / [H x (1 - d/p)]

where,

D = Annual demand

Co = Ordering cost

H = Holding cost

EPQ = SQRT (2 x 12100 x 31) / [3 x (1 - 48.4/295)]

EPQ = 546.92 units

(b) Number of production runs per year is calculated as;

Number of production runs = D/EPQ

Number of production runs = 12100 / 546.92

Number of production runs = 22.12 runs per year

(c) Maximum inventory level is calculated as;

Maximum inventory level = EPQ/p x (p - d)

Maximum inventory level = 546.92/295 x (295 - 48.4)

Maximum inventory level = 457.19 units

(d) Percentage of time will the facility be producing components is calculated as;

Percentage of production time = [(EPQ/p x Number of productions per year) / Total working days] x 100

Percentage of production time = [(546.92 / 295 x 22.12) / 250] x 100

Percentage of production time = 16.40%

(e) Annual cost of ordering is calculated as;

Annual cost of ordering = D/EPQ x Co

Annual cost of ordering = 12100/546.92 x 31

Annual cost of ordering = $685.84

Annual cost of holding inventory is calculated as;

Annual cost of holding inventory = EPQ/2 x H x (1 - d/p)

Annual cost of holding inventory = 546.92/2 x 3 x (1 - 48.4/295)

Annual cost of holding inventory = $685.84