Inventory Control Guide Page 14
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403.6 EOQ with Discount on all units
In the previous models, the cost of the items did not play any role since your order policy did
not affect these costs. Here we will consider two models where discounts are made according
to the volume which is ordered. That is, ordering larger quantities Q lead to lower prices.
≤
100
if
Q 30
All-items Discount:
Q =
≤
≤
I
( )
99
if
31 Q 80
≤
98
if
81
Q
In this model, if you buy 100 units, you will pay them at 98 BEF each.
All-units discount
10000
9000
at 100
8000
at 99
7000
at 98
6000
5000
4000
3000
2000
1000
0
10
20
30
40
50
60
70
80
90
100
Q
When dealing with different cost models that are valid in different ranges, the methodology is
quite systematic. You forget about the constraint, then you solve the problem and, finally, you
re-consider the constraints again.
Methodology:
1. Take one cost function (and forget the constraint);
2. Solve the problem with this cost function;
3. Consider the constraint again and conclude.
Let us try to apply this methodology to our example.
1.
Get the cost model
Because the price is different according to the quantity we order, we must introduce the cost
of the items in the model. This is a term of the form I×D. Furthermore, the holding cost also
changes since the stored value is different.
Express C(Q) using I(Q) and H=I(Q) × × × × rate
The cost functions have thus the form:
Prod 2100-2110
Inventory Control
13
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