Optimal production size with partially inspected batches

Abstract

While it is desirable to manufacture and ship perfect products, in many cases it is possible to ship products even though they do not stand up to all aspects of inspections. In this study a single machine is considered, that produces m products per day and there are n parameters that each product should pass. The number of passes (b) is a decision vector. A mathematical programming approach is used in order to model and optimize the number of products to be shipped under the constraints of failures. The results can be used for predetermined manufacturing, i.e. to set a series of tests less than m for each batch of production. In addition, aspects of calculation and computation are considered since the problem involves integer variables. Numerical examples and simulation runs of the suggested model are provided along with sensitivity runs.