Abstract

In the production process, some jobs can only be done sequentially, while others can be done synchronously. Given the time needed to complete each job, an oriented graph with a source vertex and a sink vertex can be generated. Each route starting from the source vertex and ending at the sink vertex represents a way of completing the project. It is possible to find the minimum production time and the optimal production path when time for each job is given by a rational number. However, this paper proves that there does not exist a computer program that can always generate the minimum time and optimal path when the time needed for each job is a constructive real number.

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