Safety is paramount in the construction industry and the fixed sprinkler and water spray systems used in firefighting involve networks of pipes of various lengths. Manufacturers of such fixed firefighting systems need to either cut the existing stocks to length—a (one-dimensional) cutting-stock problem—or lengthen the existing stocks or leftover segments through welding, a (one-dimensional) cutting-stock problem with welding. Best industry practice safety requirements allow only one weld per length of pipe. The case of a Hungarian manufacturer of fixed firefighting systems motivates this article, which argues that the cutting-stock problem with welding (with single- or multiple-size stocks) may be converted to an equivalent cutting-stock problem (with multiple-size stocks). Readily available algorithms and software may then be used to generate an optimal cutting plan for the equivalent cutting-stock problem. Subject to certain restrictions, the optimal cutting plan for the equivalent cutting-stock problem may then be converted to cutting patterns for the original cutting-stock problem with welding.

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焊接对一维切割问题的影响：以建筑行业的固定消防系统为例

安全是建筑业的重中之重，用于消防的固定式洒水系统和喷水系统涉及各种长度的管网。这种固定式消防系统的制造商需要将现有的库存削减到一定的长度（一个（一维）切割材料问题），或者通过焊接来加长现有的库存或剩余部分，而一个焊接的（一维的）切割材料问题则需要。最佳的行业实践安全性要求每条管道长度只能进行一次焊接。匈牙利固定式消防系统制造商的案例激发了这篇文章的观点，该文章认为，焊接的切割问题（使用单尺寸或多尺寸库存）可以转换为等效的切割问题（使用多尺寸库存） ）。然后可以使用现成的算法和软件来为等效的切割问题生成最佳的切割计划。在一定的限制下，等效的切削问题的最佳切削计划可随后转换为焊接时原始切削问题的切削方式。