Reference no: EM13500601
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
|
$ 200
|
|
K2
|
$ 100
|
|
H
|
$ 1
|
|
Q1
|
10000
|
|
Q2
|
20000
|
|
K
|
Q1
|
Q2
|
TC1
|
TC2
|
TC
|
|
1
|
10,000
|
20,000
|
$ 5,200
|
$ 10,100
|
$ 15,300
|
|
2
|
5,000
|
10,000
|
$ 2,900
|
$ 5,200
|
$ 8,100
|
|
3
|
3,333
|
6,667
|
$ 2,267
|
$ 3,633
|
$ 5,900
|
|
4
|
2,500
|
5,000
|
$ 2,050
|
$ 2,900
|
$ 4,950
|
|
5
|
2,000
|
4,000
|
$ 2,000
|
$ 2,500
|
$ 4,500
|
|
6
|
1,667
|
3,333
|
$ 2,033
|
$ 2,267
|
$ 4,300
|
|
7
|
1,429
|
2,857
|
$ 2,114
|
$ 2,129
|
$ 4,243
|
|
8
|
1,250
|
2,500
|
$ 2,225
|
$ 2,050
|
$ 4,275
|
|
9
|
1,111
|
2,222
|
$ 2,356
|
$ 2,011
|
$ 4,367
|
|
10
|
1,000
|
2,000
|
$ 2,500
|
$ 2,000
|
$ 4,500
|
|
11
|
909
|
1,818
|
$ 2,655
|
$ 2,009
|
$ 4,664
|
|
12
|
833
|
1,667
|
$ 2,817
|
$ 2,033
|
$ 4,850
|
|
13
|
769
|
1,538
|
$ 2,985
|
$ 2,069
|
$ 5,054
|
|
14
|
714
|
1,429
|
$ 3,157
|
$ 2,114
|
$ 5,271
|
|
15
|
667
|
1,333
|
$ 3,333
|
$ 2,167
|
$ 5,500
|