The Effect of Economic Order QuantityThe Effect of Economic Order Quantity

How much should we optimize the

batch size?

By Amir Weisenstern

Based on Theory of Constraints, Dr. Eli Goldratt

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 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?

Two cost-per-unit graphs

Cost per unitCarrying cost curve: a larger batch means a longer time to hold inventory.

Batch size

Setup cost curve: a larger batch means that setup is divided to more units.

The curve is a/x

The curve is linear

The unified cost-per-unit graph

Cost per unitCost-per-unit curve: Summation of carrying cost and setup cost curves

Batch sizeOptimal point

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) relationshipsand profit per unit have a reverse (mirror) relationshipso 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

The Profit-per-unit graph

Profit per unit

Batch sizeOptimal point

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

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

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 ROIachieving ½ the ROI

Investment

Profit per unit

Optimal

point

Good profit

per unit point,

worse ROI

Good profit

per unit ,

better ROI

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 flourishand even flourish

Investment

Profit per unit

Available

cash

Good profit

per unit point,

worse ROI,

bankruptcy

Good profit

per unit point,

better ROI,

survival

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 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