Race One Motors is an Indonesian car manufacturer. At its largest manufacturing facility, in Jakarta, the company produces subcomponents at a rate of 305 per day, and it uses these subcomponents at a rate of 12,700 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? 561.21 units (round your response to two decimal places).
b) How many production runs per year will be made? 22.63 production runs (round your response to two decimal places)
c) What will be the maximum inventory level? 467.71 units (round your response to two decimal places).
d) What percentage of time will the facility be producing components? 16.66 % enter your response as a percentage rounded o two decimal laces
e) What is the annual cost of ordering and holding inventory? $ 701.57 (round your response to two decimal places)
Ans ) We are given:
Annual demand= 12700 units
Production (P) per day = 305 units
Daily consumption (d)= Annual demand / no. of working days = 12700 / 250 = 50.8 units
ordering cost = $ 31
Holding cost = $ 3
a) EOQ = Sq rt [ (2 * annual demand * ordering cost) / holding cost {1- (d/p)} ]
Sq rt [(2*12700*31) / 3 {1- (50.8/305)} ]
Sq rt [ 787400 /2.50]
= 561.21 units
b) Production runs per year = Annual demand / EOQ
= 12700 / 561.21
= 22.63 production runs
c) Maximum Inventory level= EOQ [ 1- (d/p) ]
= 561.21 [ 1- ( 50.8 /305) ]
= 467. 74 units
d) time (t)= EOQ / p = 561.21 / 305 = 1.84 hour
percenatge of production time = (t * no. of optimum orders) / no. of days in a year
= (1.84 * 22.63) / 250= 16.66 %
e) Annual cost = Ordering cost + Holding cost
= (ordering cost * annual demand) / EOQ + (Carrying cost per unit * EOQ) /2 * [ 1- (d/p)]
= (31*12700) / 561.21 + (3 * 561.21) /2 * [1-0.17]
= 701.52 + (841.815 * 0.833)
= $1402.75