Minimizing the sum of maximum earliness and maximum tardiness in the single-machine scheduling problem with sequence-dependent setup time

Abstract

This paper considers the problem of scheduling a given number of jobs on a single machine to minimize the sum of maximum earliness and maximum tardiness when sequence-dependent setup times exist (1∣ST_sd∣ET_max). In this paper, an optimal branch-and-bound algorithm is developed that involves the implementation of lower and upper bounding procedures as well as three dominance rules. For solving problems containing large numbers of jobs, a polynomial time-bounded heuristic algorithm is also proposed. Computational experiments demonstrate the effectiveness of the bounding and dominance rules in achieving optimal solutions in more than 97% of the instances.

Keywords:

• scheduling
• single machine
• maximum earliness
• maximum tardiness
• setup time