Production Rate Effects and Breaks in Production
It is reasonable to expect that unit costs decrease not only as more units are produced but also as the production rate increases. This theory accounts for cost reductions that are achieved through economies of scale. Some examples are quantity discounts and reduced ordering, processing, shipping, receiving, and inspection costs. Conversely, if the number of quantities to be produced decreases, then unit costs can be expected to increase, because certain fixed costs have to be spread over fewer items. At times, an increase in production rate does not result in reduced costs, as when a manufacturer’s nominal capacity is exceeded. In such cases, unit costs increase because of factors such as overtime, capital purchases, hiring actions, and training costs.
These effects can be modeled by adding a rate variable to the unit learning formula. The equation becomes:
Y = AXbQr, where
Y = the cost of the Xth unit
A = the first unit (T1) cost,
X = the unit number
b = the constant slope coefficient of the learning curve, defined as ln slope / ln 2
Q = production rate (that is, quantity per time period or lot)
r = rate coefficient, defined as ln rate slope / ln 2, where rate slope = 2r
The rate at which items can be produced can also be affected by the continuity of production. Production breaks may occur because of program delays (budget or technical), time lapses between initial and follow-on orders, or labor disputes. Production breaks can last anywhere from a few weeks to several years, depending on the situation. Depending upon the length of the break, cost analysts need to account for learning that is lost due to workers forgetting how to efficiently produce items. Examining a production break can be divided into two questions:
How much learning achieved to date has been lost (or forgotten) because of the break in production?
How will the learning loss affect the costs of future production items?
An analyst can answer the first question by using the Anderlohr method for estimating the loss of learning. An analyst can then answer the second question by using the “Retrograde Method,” which determines which unit on the original learning curve is the appropriate unit from where to start again from a cost perspective.
Anderlohr Method
When assessing the effect of a production break on costs, it is necessary first to quantify how much learning was achieved before the break and then to quantify how much was lost due to the break. The Anderlohr method divides learning loss into five categories: personnel learning, supervisory learning, continuity of production, methods, and tooling. Personnel learning loss occurs because of layoffs or removal of staff from the production line. Supervisory learning loss occurs when the number of supervisors is reduced because the number of production line staff has been reduced, so that supervisors who may no longer be familiar with the job are unable to provide optimal guidance.
Learning can also be lost when production continuity changes because the physical configuration of the production line has moved or optimization for new workers is necessary. Methods are usually affected least by production breaks, as long as they are documented. However, revisions to the methods may be required if the tooling has to change once the production line restarts. Finally, tools may break or be lost during the production halt or may not be replaced when they are worn, causing productivity loss.
Each category must have a weight assigned to capture its effect on learning. The weights can vary by production situation but must always total 100 percent. To find the percentage of lost learning—known as the learning lost factor—the estimator must determine the learning lost factor in each category and then calculate the weighted average (see table 46).
Table 46: The Anderlohr Method for the Learning Lost Factor
| Category | Weight | Learning lost | Weighted loss |
|---|---|---|---|
| Personnel learning | 30% | 51% | 0.153 |
| Supervisory learning | 20 | 19 | 0.038 |
| Production continuity | 20 | 50 | 0.1 |
| Tooling | 15 | 5 | 0.0075 |
| Methods | 15 | 7 | 0.0105 |
| Total learning lost | 100 | 0.3090 or 30.9% | |
Source: GAO. | GAO-20-195G
In the table, if the production break is 6 months, the effect on learning would be almost a 31 percent reduction in efficiency since the production line shut down.
Retrograde Method
Assume that 10 units were produced before the production break. The true cost of the first unit produced after the production break would then equal the cost of the 11th unit—assuming no production break—plus the 30.9 percent penalty from the lost learning. The retrograde method simply goes back up the learning curve to the unit (X) where that cost occurred. The number of units up the curve is the number of retrograde or lost units of learning. Production restarts at unit X rather than at unit 11.
As illustrated by the Anderlohr and retrograde methods, costs may increase as a result of production breaks. Cost estimators and auditors should question how the costs were estimated to account for learning that is lost, taking into account all factors that can be affected by learning.