You are in charge of the replenishment of component A. The annual demand is 20,0
ID: 2472915 • Letter: Y
Question
You are in charge of the replenishment of component A. The annual demand is 20,000 units. The purchasing cost is $50 dollars per component. Placing an order has a fixed cost of $500 and a fixed leadtime of 2 weeks. The cost of capital is 10% per year. Determine the optimal ordering level for component A. What is the total annual holding + ordering + purchasing cost? What is the optimal Reorder Point? Suppose that you decide to order component A only 4 times per year. What is the total annual holding + ordering + purchasing cost in this case? Effect of pooling: Disregarding b., suppose that the manager of another location has contacted you to consolidate your inventory orders and storage with hers. The characteristics of the second location are identical to yours. If you decide to order jointly, what would be the optimal ordering quantity? What is the effect of this consolidation on the total cost associated with ordering and holding inventory? Disregarding c., consider a second component, B, whose annual demand is 30,000 and purchasing cost is $40/unit. To save on ordering cost, you have decided to coordinate the orders of the two components, so that every order will be placed for both components at the same time. The ordering cost in this case is $720. How many orders you will place per year? What are the optimal ordering levels for components A and B?Explanation / Answer
Solution:
Annual Demand (A) = 20,000 Units
Purchasing Cost per component = $50
Ordering Cost per order (O) = $500
Carrying / Holding Cost per unit per annum = $50 x 10% = $5
a)
Optimal Ordering Level for Component = (2 x Annual Demand x Ordering Cost per order / Carrying / Holding Cost per unit per annum)1/2
= (2 x 20,000 x 500 / 5)1/2
= 2,000 Units
Calculation of Total Cost
Total Annual Holding Cost
1/2 x Optimal order level x Carrying cost per unit per annum
(1/2 x 2,000 x $5)
$5,000
Total Annual Order Cost
No. of Orders x Order Cost per order
(20,000 / 2,000 x $500)
$5,000
Total Purchasing Cost
Annual Demand x Purchase Price per unit
(20,000 x 50)
$1,000,000
Total Cost
$1,010,000
Optimal Re-order point
Re-Order Point = Average weekly Usage x Lead time = 20,000 / 52 x 2 = 769.23 Units
b)
If component A is ordered 4 times per year..
No. of Orders in a year = 4
Ordering quantity per order = 20,000 / 4 = 5,000 Units
Total Annual Holding Cost
1/2 x Order quantity x Carrying cost per unit per annum
(1/2 x 5,000 x $5)
$12,500
Total Annual Order Cost
No. of Orders x Order Cost per order
(4 x $500)
$2,000
Total Purchasing Cost
Annual Demand x Purchase Price per unit
(20,000 x 50)
$1,000,000
Total Cost
$1,014,500
Please ask separate question for rest requirement....as part a) has already 3 requirements and part b one
Total Annual Holding Cost
1/2 x Optimal order level x Carrying cost per unit per annum
(1/2 x 2,000 x $5)
$5,000
Total Annual Order Cost
No. of Orders x Order Cost per order
(20,000 / 2,000 x $500)
$5,000
Total Purchasing Cost
Annual Demand x Purchase Price per unit
(20,000 x 50)
$1,000,000
Total Cost
$1,010,000
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