BMO2181 Operations Management Percentages of Categorizin
Questions:
(i) A printing company estimates that it will require 1,000 reams of a certain type of paper in a given period. The cost of carrying one unit in inventory for that period is 50 cents. The company buys the paper from a wholesaler in the same town, sending its own truck to pick up the orders at a cost of $20.00 per trip. Treating this cost as the order cost,
(a) what is the optimum number of reams to buy at one time?
(b) How many times should lots of this size be bought during this period?
(c) What is the total minimum cost (holding and ordering) of maintaining inventory on this item for the period?
|
Item |
Annual Demand |
Unit Cost |
|
A211 |
1200 |
$9 |
|
B390 |
100 |
$90 |
|
C003 |
4500 |
$6 |
|
D100 |
400 |
$150 |
|
E707 |
35 |
$2000 |
|
F660 |
250 |
$120 |
|
G473 |
1000 |
$90 |
|
H921 |
100 |
$75 |
Answers:
(i) A printing company estimates that it will require 1,000 reams of a certain type of paper in a given period. The cost of carrying one unit in inventory for that period is 50 cents. The company buys the paper from a wholesaler in the same town, sending its own truck to pick up the orders at a cost of $20.00 per trip. Treating this cost as the order cost,
(a) What is the optimum number of reams to buy at one time?
The company is demand for the reams of certain type of paper is 1000 reams. The carrying cost of one unit is 50 cent or $0.5 and the ordering cost is $20.00.
Thus, the EOQ formula will be used to get the optimum number of reams per order.
The EOQ formula is –
Where,
Q is the Economic Ordering quantity,
D is the demand of the company
O is the ordering cost for each order
C is the carrying cost for each unit in the inventory
Q = (2*1000*20/0.5)^0.5
Q = 282.8427 or, 283 (approx)
The calculation in the excel is given in the below table –
Table 1
|
Terms |
Cost |
|
D |
1000 |
|
O |
20 |
|
C |
0.5 |
|
Q (EOQ) |
282.8427 |
(b) How many times should lots of this size be bought during this period?
The times that the lot of size 283 will be bought by the company is –
T = (D / EOQ)
Where,
T is the no. of times,
D is the demand of the reams of paper for the company,
EOQ is the economic ordering quantity as derived in the above question
T = (1000/283)
T = 3.533569 or, 4 (approx)
(c) What is the total minimum cost (holding and ordering) of maintaining inventory on this item for the period?
The total cost of holding and ordering of maintaining the inventory for the purpose mentioned above is as follows –
The formula required for the total cost derivation is –
Where,
TC is the total cost
D is the demand for the certain period
O is the ordering cost
Q is the Economic Ordering quantity
C is the carrying cost
TC = {(1000*20)/283} + {(0.5*283)/2}
TC = $141.4214 or, $141
The calculation in the excel is given in the below table –
Table 2
|
Terms |
Cost |
|
D |
1000 |
|
O |
20 |
|
C |
0.5 |
|
Q (EOQ) |
283 |
|
Total Cost |
141.4214 |
- ii) Perform an ABC analysis on the following set of products.
|
Item |
Annual Demand |
Unit Cost |
|
A211 |
1200 |
$9 |
|
B390 |
100 |
$90 |
|
C003 |
4500 |
$6 |
|
D100 |
400 |
$150 |
|
E707 |
35 |
$2000 |
|
F660 |
250 |
$120 |
|
G473 |
1000 |
$90 |
|
H921 |
100 |
$75 |
The ABC analysis of the given database of the inventory can be explained by the Excel calculation provided here.
Table 3
|
Item Name |
Usage per year |
Cost/Unit |
Usage Cost |
Usage/Total |
Cumulative consumption |
% of total cumulative consumption |
|
G473 |
1000 |
90 |
90000 |
0.30 |
0.30 |
29.57608 |
|
E707 |
35 |
2000 |
70000 |
0.23 |
0.53 |
52.57969 |
|
D100 |
400 |
150 |
60000 |
0.20 |
0.72 |
72.29708 |
|
F660 |
250 |
120 |
30000 |
0.10 |
0.82 |
82.15577 |
|
C003 |
4500 |
6 |
27000 |
0.09 |
0.91 |
91.02859 |
|
A211 |
1200 |
9 |
10800 |
0.04 |
0.95 |
94.57772 |
|
B390 |
100 |
90 |
9000 |
0.03 |
0.98 |
97.53533 |
|
H921 |
100 |
75 |
7500 |
0.02 |
1.00 |
100 |
|
|
|
Total |
$304,300 |
|
|
|
The items which will be considered here as in the A category are the G473, E707 and the D100. The items which can be considered here as in the B category are the F660, C003 and A211. The items which can be considered here as in the C category are the B390 and H921.
The percentages of categorizing is as follows –
A – ≤72%, 72%<B≤95% and 95%
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