A branch-and-bound parallel algorithm for single-machine total weighted tardiness problem

Abstract

This paper presents the branch-and-bound algorithm for the single-machine total weighted tardiness problem. Among exact solution approaches, the branch-and-bound algorithm from Potts and Van Wassenhove solves problems of up to 40 jobs and the algorithm from Babu et al. for 50 jobs (not for all instances). We have taken advantage of the properties of permutation broken into blocks. These properties are much stronger than elimination criteria (Potts CN, Van Wassenhove LN, 1991. IIE Trans 23:346–354; Rinnoy Kan AGH, Lageweg BJ, Lenstra JK 1975 Minimizing total cost one-machine scheduling. Oper Res 26:908–972) applied so far and they allow us to eliminate many branches of the solution tree. Parallel implementation of the algorithm enables us to reduce computational time significantly and to solve larger problems. We have tested the algorithms on randomly generated instances (of up to 80 jobs) and benchmark instances taken from the OR-Library [4]. The solutions obtained have been compared with the results yielded by the best algorithms discussed in the literature. The results show that the proposed algorithm solves the problem instances with high accuracy in a very short time.