Inventory Control Guide Page 17
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403.7 EOQ with incremental discount
Here we assume incremental discount. In this model, if you buy 100 units, you will pay the first
30 items at 100 BEF, the next 50 units at 98 and the last 20 units at 95.
Incremental Discount:
≤
100
Q
if
Q 30
×
=
+
−
≤
≤
I
( )
Q
Q
3000 98
(
Q
30
)
if
31 Q 80
+
−
≤
7900 95
(
Q
80
)
if
81
Q
Incremental discount
10000
9000
part 1
8000
part 2
7000
part 3
6000
5000
4000
3000
2000
1000
0
10
20
30
40
50
60
70
80
90
100
Q
1.
Get the cost model
The procedure is again the same. First, the total cost function must be expressed as a
function of the variable Q. This means we first need to determine the item cost I(Q).
≤
100
if
Q 30
=
+
≤
≤
I
( )
Q
60
/
Q
98
if
31 Q 80
+
≤
300
/
Q
95
if
81
Q
Next we can define the holding cost as a function of the item cost.
=
+
+ [
C( ) O (D / ) D I( )
Q
Q
Q
rate I
( )]
Q Q
/ 2
Three different cost functions are then obtained. Here there are assuming a holding rate of 20
percent of the stored value.
[
]
[
]
=
+
+
C
( ) O (D / ) D 100
Q
Q
0.20 100
Q
/ 2
100
[
]
[
]
=
+
+
+
+
C ( ) O (D / ) D
Q
Q
60
/
Q
98
0.20 60 98
Q
/ 2
98
[
]
[
]
=
+
+
+
+
C ( ) O (D / ) D
Q
Q
300
/
Q
95
0.20 300 95
Q
/ 2
95
Prod 2100-2110
Inventory Control
16
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