An algorithm for minimizing flow time and maximum earliness on a single machine

This study presents an algorithm for efficient scheduling in terms of total flow time and maximum earliness. All the algorithms in the literature for solving this problem are based on heuristic procedures, and cannot necessarily generate all efficient schedules. This study shows that this problem can actually be solved in pseudo-polynomial time, and develops an algorithm for so doing. The complexity of the algorithm is O (n²&pmacr; log n). Its computational performance in solving problems of various sizes is determined.