Optimal parallel machine scheduling in consideration of total actual flow time and total processing time

Total actual flow time is known as an effective evaluation measure under Just-In-Time environments. In such case, minimization of the total actual flow time has been previously studied, but an algorithm which minimizes total processing time after minimization of total actual flow time has never been proposed. This paper proposes an optimal scheduling algorithm in a parallel machine scheduling problem to minimize total processing time on the assumption that total actual flow time has been minimized beforehand under a Just-In-Time environment. The optimal algorithm is developed on the basis of an active new node search procedure utilizing the Branch and Bound method. Some computational experience shows the usefulness of the algorithm, which is coded in C-language.