Page 175 - DMGT206_PRODUCTION_AND_OPERATIONS_MANAGEMENT

Production and Operations Management

Notes  The unit time will decrease at a decreasing rate, and
 The reduction in time will follow a predictable pattern.
Each of these assumptions has been found to hold true in the aircraft industry. Though this
technique was started by the aviation industry, it has been found applicable in most production
applications. The learning percent is usually determined by statistical analysis of actual cost
data for similar products.
Examples are:

1. Aerospace 85%
2. Shipbuilding 80-85%
3. Complex machine tools for new models 75-85%

4. Repetitive electronics manufacturing 90-95%
5. Repetitive machining or punch-press operations 90-95%
6. Repetitive electrical operations 75-85%

7. Repetitive welding operations 90%
8. Raw materials 93-96%
9. Purchased parts 85-88%

There are several models of learning curves in use in business and industry; the most common
form of the relationship between inputs per product is a log-linear model in the form of the
function:
y = ax -b
Where: y = input cost for the xth unit

x = cumulative number of units produced
a = input cost for the first unit
b = progress rate

The log-linear model states that the improvement in productivity is constant (i.e., it has a
constant slope) as output increases. There are two basic forms of the log-linear model—the
average cost function and the unit cost function.

Average Cost Model

The average cost model is used more than the unit cost model. It specifies the relationship
between the cumulative average cost per unit and cumulative production. The relationship
indicates that cumulative cost per unit will decrease by a constant percentage as the cumulative
production volume doubles.

Unit Cost Model

The unit cost model is expressed in terms of the specific cost of producing the ‘x’th unit. The unit
cost formula specifies that the individual cost per unit will decrease by a constant percentage as
cumulative production doubles. A typical graph is shown in Figure 8.6.

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