Question

Assignment 4.6: Inventory Controls Assignment A

1. A game controller manufacturer uses approximately 31,000 computer chips annually. The chips are used at a steady rate during the 230 days a year that the plan operates. Annual holding cost is $3 per chip, and ordering cost is $120. Determine:

a) the optimal order quantity

b) the number of workdays in an order cycle

2. The Garble Corporation produces brass rings for its assembly of Fancy Garbles. The firm operates 220 days a year and uses the rings at a steady rate of 50 per day. Rings can be produced at a rate of 200 per day. Annual storage cost is $2 per ring, and the machine setup cost is $70 per run.

a) determine the economic run quantity

b) how many runs per year will there be?

c) what is the average inventory on hand?

3. The Happy Baker can produce a box of cookies at a rate of 5,000 per day. Happy supplies cookies to local stores at a steady rate of 260 boxes per day. The cost to prepare the ovens and machinery for producing and boxing cookies is $65. Annual holding costs are 45 cents per box. The company operates 300 days a year. Find

a) the optimal run size

b) the number of runs per year

c) how many days does it take to produce the optimal run quantity?

Answer 1

1.

a. Optimal order quantity EOQ = √2AO/C

where A is annual demand, O is ordering cost, C is carrying/ holding cost

EOQ= √2 * 31000* 120 / 3

EOQ = √2,480,000

EOQ = ~1575

b.

Total number of orders =Demand/ EOQ = 31000/ 1575 = 54 approximately

Chips are used at steady rate during 230 work days in a year.

Number of workdays in an order cycle = Total workdays in a year/ Total number of orders = 230/ 54 = 4.25 days

2.

a.

Economic run quantity= √2AS/C √p / (p-u)

where p is production rate and u is usage rate, S is set up cost, A is annual demand

p = 200 per day, u = 50 per day

A = u * number of working days = 50 * 220 = 11,000

ERQ= √(2 * 11000* 70 / 2) √200 / (200-50)

ERQ = 1013 approximately

Economic run quantity = ~1013

b.

Number of runs per year = A/ Q = 11000/ 1013 = 10.8 or 11 approximately

c.

Average inventory on hand = (Q/ p) * (p-u)* (1/2)

Average inventory on hand = (1013/200) * (200 - 50) * (1/2) = 380 approximately

3.

a.

Economic run quantity= √2AS/C √p / (p-u)

where p is production rate and u is usage rate, S is set up cost, A is annual demand

p = 5000 per day, u = 260 per day

A = u * number of working days = 260 * 300 = 78,000

ERQ= √(2 * 78000* 65 / 0.45) √5000 / (5000 -260) =4747

ERQ = 4,875 approximately

Economic run quantity = ~4,875

b.

Number of runs per year = A/ Q = 78000/ 4875 = 16

c.

Number of days to produce optimal run quantity = Q/ p

Run time = 4,875 / 5000 = 0.98 or 1 day approximately

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