Based on historical data, the forecasted annual demand for the disposable earpho
ID: 370210 • Letter: B
Question
Based on historical data, the forecasted annual demand for the disposable earphones is 22500 units. The SWG’s manufacturing plant will operate 50 weeks per year.
SWG's financial analysts have established a cost of capital of 17% on the use of funds for investments within the company. In addition, accounting information shows that a total of 4% of costs were spent on taxes and insurance related to the company's inventory. It has been estimated that another 2.5% was lost due to inventory shrinkage, which included damaged goods as well as pilferage. Finally, 4.5% was spent on warehouse overhead, including utility expenses for heating and lighting.
An analysis of the purchasing operation shows that approximately two hours are required to process and coordinate an order for Southwest Airlines regardless of the quantity ordered. Purchasing salaries average $28 per hour, including employee benefits. In addition, a detailed analysis of 135 orders showed that $2375 was spent on telephone calls, e-mails, paper, and postage directly related to the ordering process.
Currently the company has a contract to purchase the disposable earphones from a supplier at a cost of $0.44 per unit. However, with the opening of the Southwest Goods manufacturing facility, Southwest Airlines will now have the capacity to produce support items themselves. As a result, Southwest Goods is considering the alternative of producing the disposable earphones itself.
Forecasted utilization of equipment shows that production capacity will be available for the earphones being considered. The production capacity is available at the rate of 1000 sets of earphones per week. It is felt that with a short lead-time, schedules can be arranged so that the disposable earphones can be produced whenever needed. Production costs are expected to be $0.41 per pair of earphones.
A concern of management is that setup costs will be significant. The total cost of labor and lost production time is estimated to be $100 per hour, and it will take a full 7-hour shift to set up the equipment for producing the earphones.
Problem: Develop an inventory policy (how many earphones to order and how frequently) for the following two alternatives (a) ordering a fixed quantity Q from the supplier or (b) ordering a fixed quantity Q from in-plant production. Be sure to include the (1) Optimal quantity Q* and (2) the total annual cost for each option.
GIVEN:
Annual demand (D) = 22500
Number of weeks per year = 50
Weekly demand rate (d) = 22500/50 = 450
Option 1: Buy
Holding cost rate, (i) = 17%+4%+2.5%+4.5% = 28%
Ordering cost (S) = 28*2 + 2375/135 = $ 73.6
Cost of earphones, C = $ 0.44
Holding cost (h) = C*i = 0.44*28% = 0.1232
Optimal order quantity = (2DS/h) = (2*22500*73.6/0.1232) = 5185
Total annual cost = Ordering cost + Holding cost + cost to purchase = (D/Q)*S + (Q/2)*h + D*C = (22500/5185)*73.6+(5185/2)*0.1232+22500*0.44 = $ 10,539
Option 2: Make
Production rate, (p) = 1000 per week
Production cost (C) = $ 0.41
Holding cost (h) = C*i = 0.41*28% = 0.1148
Setup cost (S) = 100*7 = $ 700
Optimal production run size = (2DS/(h*(1-d/p))) = (2*22500*700/(0.1148*(-450/1000))) = 22336
Total annual cost = Ordering cost + Holding cost + cost to purchase = (D/Q)*S + (Q/2)*(1-d/p)*h + D*C = (22500/22336)*700+(22336/2)*(1-450/1000)*0.1148+22500*0.41 = $ 10,635
Total cost of Buy option is lesser. Therefore, management should purchase the earphones from the supplier instead of manufacturing inhouse.
Explanation / Answer
The decision to buy instead of making the items is based on the calculations of economic order quantity and optimal production quantities. Since the annual cost calculated for both options reveals that the cost to buy is lower than cost to make, the decision to buy is being adopted.
With the company deciding to buy, the economic order quantity being 5185 units, the number orders needed to meet the annual demand will be 22500/ / 5185 = 4.339 or rounded off to 5 orders. In a 50 week year, if there are 5 orders, then on an average there will be one order every 10 weeks.
The nventory policy will be to place 5 orders in a year at a frequency of 10 weeks. To meet a weekly demand of 450 earphones, the company will have to maintain inventory of 450 x 10 = 4500 earphones.
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