You order two products from the same supplier. The annual demand for Product 1 is 10,000 units and the annual demand for Product 2 is 20,000 units. Note that demand for both products is constant throughout the year. The holding cost is the same for both products, $1 per unit per year. However, you incur a fixed cost of $200 each time you order Product 1, and a fixed cost of $100 each time you order Product 2. These fixed order costs are independent of the size of the order.
a. How many units of Product 1 and Product 2 should be ordered at a time in order to minimize total holding + order cost?
Product 1 :
EOQ = Sqrt (2*K*R/H) where
R = Annual demand = 10,000
K = Order cost = $200
H = Holding cost factor = $1
EOQ (P1) = Sqrt (2*K*R/H) = SQRT(2*200*10000/1) = 2,000 Nos
Number of Units of Product 1 to Order 2000 Nos
EOQ (P2) = Sqrt (2*K*R/H) = SQRT(2*100*20000/1) = 2,000 Nos
Number of Units of Product 2 to Order 2000 Nos
b. Suppose that the supplier insists that orders for Product 1 and Product 2 be coordinated so that they can be shipped at the same time (still incurring the fixed cost of $200 and $100, respectively). Given this requirement, how many units of Product 1 and Product 2 (to the nearest integer) should be ordered at a time in order to minimize total holding + order cost? (Hint: the products must be ordered the same number of times per year)
We use Different values of K to calculate TC1 + TC2 = TC as shown below.
We observe that for No of Order = 7, Q1 = 1429 & Q2 = 2857 giving us lowest total cost of $4243.
|
K1
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$ 200
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|
K2
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$ 100
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|
H
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$ 1
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|
Q1
|
10000
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|
Q2
|
20000
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|
K
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Q1
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Q2
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TC1
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TC2
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TC
|
|
1
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10,000
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20,000
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$ 5,200
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$ 10,100
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$ 15,300
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|
2
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5,000
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10,000
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$ 2,900
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$ 5,200
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$ 8,100
|
|
3
|
3,333
|
6,667
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$ 2,267
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$ 3,633
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$ 5,900
|
|
4
|
2,500
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5,000
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$ 2,050
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$ 2,900
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$ 4,950
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|
5
|
2,000
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4,000
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$ 2,000
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$ 2,500
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$ 4,500
|
|
6
|
1,667
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3,333
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$ 2,033
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$ 2,267
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$ 4,300
|
|
7
|
1,429
|
2,857
|
$ 2,114
|
$ 2,129
|
$ 4,243
|
|
8
|
1,250
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2,500
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$ 2,225
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$ 2,050
|
$ 4,275
|
|
9
|
1,111
|
2,222
|
$ 2,356
|
$ 2,011
|
$ 4,367
|
|
10
|
1,000
|
2,000
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$ 2,500
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$ 2,000
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$ 4,500
|
|
11
|
909
|
1,818
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$ 2,655
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$ 2,009
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$ 4,664
|
|
12
|
833
|
1,667
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$ 2,817
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$ 2,033
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$ 4,850
|
|
13
|
769
|
1,538
|
$ 2,985
|
$ 2,069
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$ 5,054
|
|
14
|
714
|
1,429
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$ 3,157
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$ 2,114
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$ 5,271
|
|
15
|
667
|
1,333
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$ 3,333
|
$ 2,167
|
$ 5,500
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