Park Sung Inc. is a fictional South Korean manufacturer of refrigerators. The company produces at its manufacturing plant in Busan subcomponents for its refrigerators at the rate 275 units per day. The annual usage rate of this subcomponents is 30,000 units. The holding cost is US$3 per unit per year, and the setup cost of producing these subcomponents is US$50 per setup. The company operates its manufacturing facility for 300 days during a year: What is the economic production quantity (EPQ) ? a. What is the average inventory level for this optimum production quantity? b. How many production setups would there be in a year? C. What is the optimal length of production run in days d. e. What would be the savings in annual inventory Cost if setup costs can be reduced to US$40 per setup?

The answer for each requirement is given separately below.

Explanation:

What is the economic production quantity (EPQ) ?

EPQ = ((Annual Requirement * setup cost * 2) / Carrying cost per unit) ^ (1/2)

= ((30,000 * 50 * 2) / 3^ (1/2)

= 1000 Units

a. What is the average inventory level for this optimum production quantity?

Average Inventory level = EPQ/2 = 500 units

b. How many production setups would there be in a year?

Production setups = Annual Usage / EPQ = 30 set ups

C. What is the optimal length of production run in days

length of production = Total Requirement/production per day

= 30,000/275

=110 days approx

d. What would be the savings in annual inventory Cost if setup costs can be reduced to US$40 per setup?

If set up cost reduce to $40 than EPQ = 895

So Set up cost = 30,000 / 895 * 40 = 1,360

Carrying cost = 883/2 * 3 = 1,325

Total Cost = $ 2,685 - A

If set up cost $50 than EPQ = 1000

So Set up cost = 30,000 / 1000 * 50 = 1,500

Carrying cost = 1000/2 * 3 = 1,500

Total Cost = $ 3,000 - B

Saving = B-A = 315 Dollars