Based on historical data, the forecasted annual demand for the disposable earpho
ID: 368342 • 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: Clearly define the holding cost (h), ordering cost (S) (when ordering from supplier), and set-up cost (S) (when producing the part) for each scenario (ie. Make and Buy).
Explanation / Answer
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.
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