Optimum Batch Sizes for Circuit Board Assembly Lines
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Solution Overview
Problem
Current methods for determining batch sizes in electronics production, such as the Economic Order Quantity (EOQ) formula, fail to account for the production of assemblies in set-up families, leading to inefficiencies in set-up and warehousing costs in pick and place lines.
Innovation Solution
A method and device for determining optimum batch sizes by recording set-up and warehousing costs, calculating time intervals between production orders, and optimizing batch sizes to minimize the sum of total set-up and warehousing costs, considering the formation of set-up families and the probability of production orders within a planning time period.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If batch size is increased to reduce set-up frequency, then set-up costs decrease, but warehousing costs increase due to larger buffer requirements
Solution Approach 1:
The patent dynamically adjusts batch sizes by changing the parameter of production quantity based on probability-weighted set-up costs and warehousing costs. The optimization formula q_r = sqrt((2 * D_r * K_cl) / (h_r + H_cl)) explicitly calculates optimal batch size as a parameter that balances set-up frequency reduction against buffer size increase, resolving the contradiction between these two factors.
2Quantity of substance
If batch size is decreased to reduce buffer size, then warehousing costs decrease, but set-up frequency increases leading to higher set-up costs
Solution Approach 1:
The patent employs parameter optimization by calculating the derivative of total cost function with respect to batch size and setting it to zero. This mathematical approach determines the optimal batch size parameter that minimizes the sum of set-up costs and warehousing costs, effectively balancing the trade-off between reduced buffer requirements and acceptable set-up frequency.
3Device complexity
If static set-up families are used for medium-term planning, then set-up organization is simplified, but actual set-up frequency may increase due to random order receipt not matching planned intervals
Solution Approach 1:
The patent introduces dynamic adjustment to static set-up families by incorporating probability distributions for order arrival and calculating expected set-up costs. The model allows set-up frequencies to adapt dynamically based on actual order patterns while maintaining the organizational structure of set-up families, resolving the contradiction between simplified organization and actual productivity.
4Productivity
If set-up families are formed to group producible components, then set-up efficiency improves, but batch size optimization becomes more complex due to multiple interdependent variables
Solution Approach 1:
The patent segments the optimization problem by treating each set-up family as an independent decision unit with its own cost parameters (K_cl, h_r, H_cl). This segmentation allows the complex multi-variable optimization to be decomposed into manageable family-specific calculations, maintaining set-up efficiency while reducing optimization complexity through modular problem structure.
Data Source
AI summary
Provided is a method for determining optimum batch sizes for the placing of components on circuit boards within an assembly line, wherein a set of circuit board types to be produced on the assembly line within a specified planning period is specified; a number of circuit boards to be produced is specified for each circuit board type; the number of circuit boards per circuit board type forms a set that is to be divided into equal-sized subsets, also referred to as batches, which are production orders that are produced at regular intervals during the planning period; the batch size of a circuit board type is equal to the number of circuit boards in a subset; the specified circuit board types are divided into a set of clusters, wherein a cluster and its associated set-up includes a set of circuit board types which can be produced with the associated set-up.