Quantity Curve Theory
Quantity Curve Theory is based upon the observation that larger quantities of a given manufactured or processed item can be produced more economically than smaller quantities. Quantity Curve Theory assumes manufacturing and processing techniques become more efficient as the quantity increases. The rate of efficiency improvement is assumed to be relatively constant if no major changes are made in the production method. In fact, the amount of decrease in cost to produce an item has been observed to follow a logarithmic relationship with the quantity being produced. The amount of cost decrease is less for each successive unit produced and tends to flatten out at large quantities. The quantity curve formula is expressed as:
y = axb where y = unit price
a = coefficient
x = quantity
b = logarithmic slope expression
The logarithmic slope is closely related to the Quantity Curve Percent. The Quantity Curve Percent can be defined as the amount of the cost of the first unit the second unit will cost to produce. In fact, the percent is the amount to multiply a prior quantity by whenever the quantity doubles to arrive at the cost of the new quantity. For example, a 90% Quantity Curve Percent indicates that the cost of each of 2 units will be 90% of the cost of 1 unit, the cost of each of 4 units will be 90% of the cost of each of 2 units, and the cost of each of 4 units will be 90% of the cost of each of 2 units. To illustrate, a 90% Quantity Curve and an 80% Quantity Curve have the following data points.
|
Quantity |
Price 90% Curve |
Price 80% Curve |
|
|
|
|
|
1 |
$100.00 |
$100.00 |
|
2 |
$90.00 |
$80.00 |
|
4 |
$81.00 |
$64.00 |
|
8 |
$72.90 |
$51.20 |
|
16 |
$66.61 |
$40.96 |
|
32 |
$59.05 |
$32.77 |
|
64 |
$53.14 |
$26.22 |
Since we are constantly multiplying the price by a fraction (the Quantity Curve Percent) every time we double the quantity the quantity curve tends to flatten out. This reflects the nature of the manufacture or processing of an item. Larger Iot sizes decrease the number of costly set-ups, decrease the amount of material handling, encourage the use of mass production techniques, decrease shipping and packaging costs, decrease administrative cost, and improve efficiency due to learning through repetition. Once capacity limitations are reached on an increasing number of work stations the decrease in cost gradually declines until it tapers off to the point where it goes unnoticed.
Various factors influence the Quantity Curve Percent. They include the length of the production run, the initial manufacturability of the item, the quality and automation of the initial tooling, the training of the manpower, and the nature of the item itself. For example, an item requiring a great deal of assembly will tend to have a lower Quantity Curve Percent than an item that is totally processed complete. The following table suggests some of the effects of these factors on the Quantity Curve Percent.
| Factor | Effect |
| Manufacturability High | Increase |
| Tooling Well Planned | Increase |
| Tooling Poorly Planned | Decrease |
| Trained Manpower | Increase |
| Untrained Manpower | Decrease |
| Efficient Plant Layout | Increase |
| Long Production Run | Increase |
| Modern Equipment | Increase |
| Tight Tolerances | Decrease |
| High Hand Labor Content | Decrease |
| Extensive Pre-production Phase | Increase |
| High Design Complexity | Decrease |
| Shop Well Organized | Increase |
| Excessive Handling and Move Time | Decrease |
| High Stability of Personnel | Decrease |
| High Employee Morale | Decrease |
| Good Production Control Policies | Decrease |
Other factors have an unpredictable effect on the Quantity Curve Percent such as management policy, amount of supervision, purchasing efficiency, quality of subcontracted materials and supplies, type of manufacturing or processing, rate of production, and the extent of subcontracting.
As a general guideline, percents of 90 are applicable to most procurements. A percent of 70 would be applicable during the pre-production phase of a major system or assembly. A percent of 98 would be applicable to an item that has been mass produced for a great Iength of time. The most rapid improvement, thus a low Quantity Curve Percent, would be associated with items requiring a large proportion of assembly and fabrication. The greater the labor content, the lower the percent.