Homework 6 Project Learning Curve

Hw 6 Project Learning Curve 1docxhw 6 Project Learning Curv

Assume the network and data that follow: You have just completed a pilot run of 10 units of a major product and found the processing time for each unit was as follows: Lambda Computer Products competed for and won a contract to produce two prototype units of a new type of computer with learning effects occurring on both labor and materials. If Lambda was asked to present a bid for an additional 10 units after a 3-month delay, during which personnel and equipment were reassigned, what would be the total production costs for these additional 10 units? When considering the forgetting effects, the production unit count should be an integer; any fractional results must be rounded to the nearest integer. Use method 2 for calculating the forgetting effect.

Paper For Above instruction

The concept of the learning curve is fundamental in operations management, especially when estimating production costs and times for large-scale manufacturing. It posits that as workers and processes gain experience, efficiency improves, and the time and cost per unit decrease. However, after a certain period, if no ongoing learning occurs—such as during a reversion or reassignment phase—the effects of learning may 'forget,' potentially increasing the time and costs in subsequent production runs. This paper explores the application of learning curves, specifically focusing on forgetting effects, in estimating costs for a new product, considering a delay in production.

In the case of Lambda Computer Products, the initial production of two prototypes allowed the company to analyze the learning effect on both labor and materials. Typically, the learning curve is modeled mathematically assuming that each unit takes less time or resources as cumulative output increases. For the initial two units, the company observed certain processing times, which then serve as a basis to estimate the costs for additional units. When the company is asked to produce ten more units after a three-month delay, the personnel and equipment have been partially reassigned, which may result in a loss of the accumulated learning effects—a phenomenon known as the forgetting effect.

Method 2 for calculating the forgetting effect considers that the rate of learning diminishes over time, especially when the production process is interrupted or deliberately halted. In this context, the production unit count must be rounded to the nearest integer because fractional units are impractical. The mathematical model involves applying the learning curve percentage, which represents the percentage of the previous unit time or cost that the new unit will take, adjusted for the delay and reallocation of resources.

Specifically, the model computes the expected processing time per unit after the delay, considering the degree of forgetting, which is a function of the elapsed time since the last production. The total cost for the additional ten units then follows from multiplying the adjusted unit cost by the number of units, considering the revised learning or forgetting parameters. This approach allows companies like Lambda to accurately bid on contracts and plan budgets when production schedules are disrupted or when keeping personnel and equipment constant is not feasible.

Calculating these costs requires understanding the initial learning curve, the percentage reduction per unit, and the pace at which learning is forgotten over time. The process involves deriving the adjusted unit processing time, applying the rounded integer constraints, and summing the costs for all units in the subsequent batch. The practical application of such models ensures more accurate cost estimation, resource allocation, and strategic planning, which are critical for competitiveness in high-technology manufacturing sectors.

References

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