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Problem 11

# Define learning curve. Outline two models that can be used when incorporating learning into the estimation of cost functions.

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A learning curve is a graphical representation of the relationship between the cumulative output of a process and the time or effort required for each additional unit, showing how the unit cost decreases as cumulative production quantity increases due to increased experience and efficiency. Two models that can be used when incorporating learning into the estimation of cost functions are Wright's Law and DeJong's Progressive Learning Model. Wright's Law states that the cost of producing the Nth unit decreases by a constant percentage known as the learning rate when cumulative production doubles, and is represented by the equation: C(N) = C1 * N**(-b) DeJong's Progressive Learning Model suggests that learning follows a gradual approach, where productivity improves as the learning rate increases over time, and is represented by the equation: C(N) = C1 * N**(a - bn) Both these models offer different approaches to incorporating learning effects in cost estimation depending on the specific circumstances and the nature of learning in a given organization or workforce.
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## Step 1: Define Learning Curve

A learning curve is a graphical representation that shows how the unit cost of producing a product or service decreases as the cumulative production quantity increases due to increased experience and efficiency gained over time. It represents the relationship between the cumulative output of a process and the time or effort required for each additional unit. The learning curve theory implies that as workers, teams, or organizations gain experience in performing a task, they become faster and more efficient, resulting in reduced production costs.

## Step 2: Model 1: The Wright's Law

Wright's Law, also known as the Experience Curve or the Cumulative Average Model, is a widely used model to estimate the learning effect on production costs. Formulated by Theodore Wright in 1936, it states that the cost of producing the Nth unit of a product decreases by a constant percentage known as the learning rate when the cumulative production doubles. In mathematical terms, the cost per unit (C) can be represented as: C(N) = C1 * N**(-b) Here, C(N) is the cost per unit of the Nth unit produced, C1 is the cost of producing the first unit, N is the cumulative quantity, and b is the learning rate coefficient, usually expressed as a constant percentage. The learning rate typically ranges between 10% - 30%. The key assumption of Wright's Law is that the percentage reduction in cost remains constant as production doubles.

## Step 3: Model 2: The DeJong's Progressive Learning Model

The DeJong's Progressive Learning Model, introduced by Adrian DeJong in 1967, is another model that can be used to incorporate learning effects into the estimation of cost functions. The model suggests that learning in an organization or workforce can follow a gradual or progressive approach, where productivity improves as the learning rate increases over time. The Progressive Learning Model is represented by a power function with linearly increasing exponents. The equation can be expressed as: C(N) = C1 * N**(a - bn) In this equation, C(N) is the cost per unit of the Nth unit produced, C1 is the cost of producing the first unit, N is the cumulative quantity, a is a constant, and b is the rate at which the learning rate increases as a function of the cumulative production. Rather than assuming a constant percentage reduction in cost like Wright's Law, DeJong's Progressive Learning Model captures situations where the learning rate may gradually increase over time. In conclusion, understanding the learning curve is essential for organizations to estimate the costs associated with the production of goods and services as their experience and efficiency improve over time. Both the Wright's Law and DeJong's Progressive Learning Model offer different approaches to incorporating learning effects in cost estimation and can be utilized based on the specific circumstances and the nature of learning in a given organization or workforce.

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