An agent purchases silicon wafers from a supplier then later resells them to man
ID: 333690 • Letter: A
Question
An agent purchases silicon wafers from a supplier then later resells them to manufacturers of electronic chips The supplier sells the agent the wafers for $2.50 each. The quarterly requirement of silicon wafers is equal to x5,000, The costs associated with placing an order is S100, and holding cost is computed based on a interest rate. (a) (5 points) How many silicon wafers should the agent purchase each time an order is placed? (b) (5 points) What is the time between subsequent orders? (c) (15 points) Suppose that a new supplier offers the agent to provide the wafers at a cost of $2.40, but can only accept orders of 3,000 wafers. Should the agent make use of this offer or not? (d) (5 points) The agent is considering to produce the wafers in house via acquiring a manufacturing system that can produce the wafers at the rate of 30,000 wafers per year. The cost associated with initiating a production run is $150, What is the optimal size of a production run in this case?Explanation / Answer
Answer to question a:
Annual demand of wafers = D = 5000 / quarter x 4 quarters = 20,000
Ordering cost = Co = $100
Annual unit holding cost = Ch = 20% of $2.50 = $0.50
Optimum order quantity = Square root ( 2 x Co x D / Ch ) = Square root ( 2 x 100 x 20,000/0.50) =2828.42 ( 2828 rounded to nearest whole number )
AGENT SHOULD PURCHASE 2828 SILICON WAFERS EACH TIME AN ORDER IS PLACED
Answer to question b:
Daily demand = annual demand / 365 days = 20,000/365 = 54.79
Time between subsequent orders = Optimum order quantity . Daily demand = 2828/54.79 = 51.61 days
Answer to question c :
Data corresponding to optimum order quantity :
Annual purchase cost of wafers = $2.50 / wafer x 20000 wafers = $50,000
Annual ordering cost = Co x Number of orders = Co x D/Optimum order qty = $100 x 20000/2828 = $707.21
Annual holding cost = Ch x average inventory = Ch x Optimum order quantity/2 = 0.50 x 2828/2 = $ 707
Therefore , total cost = annual purchase cost + annual ordering cost + annual holding cost= $50,000 + $707.21 + $707=$51414.21
Data corresponding to order quantity of 3000:
Annual purchase cost of wafers = $2.4 / wafer x 20000 = $48000
Annual ordering cost = Co x Annual demand / 3000 = $100 x 20,000 /3000 = $666.66
Annual unit inventory cost = Ch = 20% of $2.4 = $0.48
Annual holding cost = Ch x average inventory = $0.48 x Order quantity/2 = $0.48 x 3000/2 = $720
Therefore , total cost = annual purchasing cost + annual ordering cost + annual holding cost= $48000 +$666.66 + $720 =$49386.66
Since total cost for order quantity of 3000 is less , agent must make use of this order
Answer to question d :
Following are the relevant data required for calculation :
Annual Demand = D = 20,000
Annual production capacity = P =30,000
Production set up cost = Cs = $150
Annual unit inventory holding cost = Ch = 20% of $2.5 = $0.50
Optimal size of the production run ( EPQ)
= Square root ( 2 x Cs x D / Chx ( 1 – D/P) )
= Square root ( 2 x 150 x 20,000 / 0.50 x ( 1 – 20000/30000))
= square root ( 2 x 150 x 20,000/ 0.50 x 0.333)
= 6003
OPTIMAL SIZE OF PRODUCTION RUN = 6003
AGENT SHOULD PURCHASE 2828 SILICON WAFERS EACH TIME AN ORDER IS PLACED
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