Order-preserving allocation of jobs to two machines

In this paper, we consider the problem of minimizing the mean flow time of jobs to be processed on two machines. The jobs have a predetermined order, perhaps reflecting the order of arrival, and each job has a known processing time. We wish to assign the jobs to machines so as to minimize the mean flow time, with the constraint that the original order must be preserved within the subset of jobs assigned to each machine. An efficient algorithm based on dynamic programming is developed.     

One machine sequencing to minimize mean flow time with minimum number tardy

The problem of sequencing n jobs on one machine is considered, under the multiple objective of minimizing mean flow time with the minimum number of tardy jobs. A simple procedure is first proposed to schedule for minimum flow time with a specified subset of jobs on time. This is used in conjunction with Moore's Algorithm in a simple heuristic producing good and often optimal schedules. A branch-bound algorithm is presented to produce the optimal schedule efficiently with the help of several theorems which eliminate much branching.