batch size

1. The Effect of Economic Order Quantity
How much should we optimize the
batch size?
By Amir Weisenstern
Based on Theory of Constraints, Dr. Eli Goldratt

2. What should be the batch size?
Our objective – Earn more money to the company
Naturally, we think we must reduce the cost per unit
The batch size controls both inventory levels and their
cost derivatives as well as the amount of setups and
efficiency
How should we calculate the “optimal” batch size?
o Should we enlarge batch size to save setup time
o Should we reduce the batch size in order to save carrying
costs?

3. Two cost-per-unit graphs
Cost per unit
Carrying cost curve: a
larger batch means a
longer time to hold
inventory.
Batch size
The curve is linear
Setup cost curve: a larger
batch means that setup is
divided to more units.
The curve is a/x

4. The unified cost-per-unit graph
Cost per unit
Cost-per-unit curve:
Summation of carrying cost
and setup cost curves
Optimal point Batch size

5. From cost world to profit world – a
different view on the subject
Our real goal is: make more money. The meanings are:
1. Better profit per unit
2. Better ROI per unit
Assuming the sales price per unit is fixed: Cost per unit
and profit per unit have a reverse (mirror) relationships
o When cost increases profit decreases
o When cost decreases profit increases
Therefore the profit-per-unit graph is a mirror of the cost
per unit graph

6. The Profit-per-unit graph
Profit per unit
Optimal point Batch size

7. The optimal profit per unit is not that
sensitive
The optimal point of profit per unit is in a “flat” area of the
graph
Therefore we can choose a non optimal point to the left
or to the right of the optimal point and still have a very
good profit per unit
Batch size
Profit per unit
Optimal
point
Non Optimal
point: almost
as good as
the optimal
Non Optimal
point: almost
as good as
the optimal

8. Return of Investment (ROI)
Investment is in correlation to batch size:
o Because when batch size increases we need to invest more money
to keep inventory (raw material, work in process and finished goods) in
the system
Therefore, we can replace “X” axis from “batch
size” to “inventory”
o The scale may change but the graph remains the same due to the linear
correlation between batch size and inventory

9. ROI and profit-per-unit
Better ROI is achieved in the left “non optimal point” in the
flat area than to the right of it
The right “non optimal” point may need to invest twice the
money from the left “non optimal” point. Therefore
achieving ½ the ROI
Investment
Profit per unit
Optimal
point
Good profit
per unit point,
worse ROI
Good profit
per unit ,
better ROI

10. Survival vs. bankruptcy scenario
Suppose we have cash available for investment somewhere in a
point between the left “non optimal” and the right “non optimal”
(could be to the left of the optimal point!)
If we chose our batch size to the right of our cash point we will go
bankrupt at the end of the day
If we chose our batch size to the left of the cash point we survive
and even flourish
Investment
Profit per unit
Available
cash
Good profit
per unit point,
worse ROI,
bankruptcy
Good profit
per unit point,
better ROI,
survival

11. Summary
Many people tend to maximize cost-per-unit as a local objective.
For that they use mathematic formulas to calculate “optimal” batch
size.
Cost-per-unit is not that sensitive around the optimal point
Profit-per-unit is therefore not that sensitive around the optimal point
Profit-per-unit can be close to optimum. Many times, even when
cutting the current batch drastically
A much better ROI is achieved with a much smaller batch
A much smaller batch size means much less investment. There are
cases that this is the difference between bankruptcy and survival
People forget their real global objective which is: make more
money