In this research we address a sequence-dependent group scheduling problem on a set of unrelated-parallel machines where the run time of each job differs on different machines. To benefit both producer and customers we attempt tominimize a linear combination of totalweighted completion time and totalweighted tardiness. Since the problem is shown to be NP-hard, meta-heuristic algorithms based on tabu search are developed to find the optimal/near optimal solution. For some small size yet complex problems, the results fromthese algorithms are comparedto the optimal solutions foundbyCPLEX. The resultobtained inall of theseproblems is that the tabu search algorithms could find solutions at least as good as CPLEX but in drastically shorter computational time, thus signifying the high degree of efficiency and efficacy attained by the former