# Inspection location in capacity-constrained lines

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## Abstract

We consider the effects of inspection and repair stations on the production capacity and product quality in a serial garments production line with possible inspection and repair following each operation. We construct a profit function that takes into account inspection, repair, scrap, and goodwill costs, as well as the capacity of each station. Then we discuss how the profit function can be maximized and provide properties of the optimal inspection plan. Our analysis captures the possibility of increasing production capacity by scrapping or repairing defective items before a bottleneck operation station, and hence reducing the waste of operation capacity on defective products. Our numerical results show that incorporating such capacity considerations can have substantial impact on the optimal inspection policy and that optimal inspection allocations can be identified quickly even for large problem instances.

## Keywords

Production Quality control Bottleneck stations Throughput Profit maximization## Notes

### Acknowledgements

This research was supported by the National Science Foundation under Grants CMMI-0856600 and CMMI-1536990. We would like to thank two anonymous referees for their insightful comments that led to substantial improvements to this paper.

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