Scheduling semi-malleable jobs to minimize mean flow time

Abstract

This paper deals with the problem of scheduling $$n_\mathrm{A}$$nA malleable and $$n_\mathrm{B}$$nB non-malleable jobs to be executed together on two parallel identical machines to minimize mean flow time. We propose a set of dominant schedules for this problem, and a dynamic programming algorithm that finds an optimal schedule in this dominant set in time $$O(n_\mathrm{A}^2n_\mathrm{B})$$O(nA2nB).