Tooling choices and product performance

One of the dilemmas that manufacturers face involves the tradeoff between the cost of maintaining a variety of production processes, and the cost of not having the ideal process for every product that they produce. This issue is continuing to become more of a problem as manufacturers are forced by market conditions to offer a wider selection of products. We study an instance of this problem in the manufacture of sheet metal parts. We model the problem of selecting and/or designing tools to punch holes in these parts. The cost of not having an `ideal process' is the cost of not having a tool that precisely matches a hole's design diameter. We consider both general `process deviation' costs as well as the Taguchi loss function. Solution procedures are provided for several versions of the problem.