Scheduling of Software Test to Minimize the Total Completion Time

This paper investigates a single-machine scheduling problem of a software test with shared common setup operations. Each job has a corresponding set of setup operations, and the job cannot be executed unless its setups are completed. If two jobs have the same supporting setups, the common setups are performed only once. No preemption of any processing is allowed. This problem is known to be computationally intractable. In this study, we propose sequence-based and position-based integer programming models and a branch-and-bound algorithm for finding optimal solutions. We also propose an ant colony optimization algorithm for finding approximate solutions, which will be used as the initial upper bound of the branch-and-bound algorithm. The computational experiments are designed and conducted to numerically appraise all of the proposed methods.