In this paper, we investigate a single machine scheduling problem with a proportional job deterioration. Under release times (dates) of jobs, the objective is to minimize the total weighted completion time. For the general condition, some dominance properties, a lower bound and an upper bound are given, then a branch-and-bound algorithm is proposed. In addition, some meta-heuristic algorithms (including the tabu search (TS), simulated annealing (SA) and heuristic (NEH) algorithms) are proposed. Finally, experimental results are provided to compare the branch-and-bound algorithm and another three algorithms, which indicate that the branch-and-bound algorithm can solve instances of 40 jobs within a reasonable time and that the NEH and SA are more accurate than the TS.
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