A branch-and-bound algorithm for identical parallel machine total tardiness scheduling problem with preemption

Abstract

This article examines the problem of scheduling preemptive jobs on identical parallel machines to minimize total tardiness. The problem is known to be NP-hard. An efficient heuristic is developed for solving large-sized problems. A lower bound scheme is also presented. Both of the proposed heuristic and lower bound are incorporated into a branch-and-bound algorithm to optimally solve small-sized problems. Computational results are reported. The branch-and-bound algorithm can handle problems of up to 16 jobs and 5 machines in size within a reasonable amount of time. The solution obtained by the heuristic has an average percentage deviation of 4.01% from the optimal value, while the initial lower bound has an average percentage deviation of 41.55% from the optimal value. Moreover, the heuristic finds approved optimal solutions for more than 45% of the problem instances tested.

Keywords:

• scheduling
• parallel machine
• branch-and-bound
• preemption