Tabu search algorithms for minimizing total completion time on a single machine with an actual time-dependent learning effect

Abstract

In this paper, we investigate a single machine problem with actual time-dependent learning effect considering unequal release times, where the objective is to minimize the total completion time. At first, a mathematical model of the problem was formulated, which was verified to be effective by ILOG CP (a constraint programming tool provided by ILOG). Then a branch-and-bound algorithm incorporating with two dominance properties and two lower bounds was developed to obtain solutions for small size problems. However, since this problem is NP-hard, two tabu search algorithms combined with dominance rules, called TSDR, were proposed for solving problems with large number of jobs. The experimental results demonstrated that the proposed branch-and-bound algorithm had a better performance than CP in small size problems. The TSDR algorithms can also obtain optimal solutions for some situations in small problems. In addition, the proposed TSDR algorithms outperformed the benchmark algorithms in the literature and the advantage became more obvious with the number of jobs increasing.