This paper proposes a novel, bi-objective mixed-integer mathematical programming for an open shop scheduling problem (OSSP) that minimizes the mean tardiness and the mean completion time. To obtain the efficient (Pareto-optimal) solutions, a fuzzy multi-objective decision making (fuzzy MODM) approach is applied. By the use of this approach, the related auxiliary single objective formulation can be achieved. Since the OSSP are known as a class of NP-hard problems, a tabu search (TS) method is thus used to solve several medium to large-sized instances in reasonable runtime. The efficiency of the results obtained by the proposed TS for small, medium and large-sized instances is evaluated by considering the corresponding overall satisfactory level of all objectives. Also the adaptability of the yielded solutions of the proposed TS for the small-sized instances is evaluated by comparing the results reported by the Lingo software. Several experiments on differentsized test problems are considered and the related results are indicated the ability of the proposed TS algorithm to converge to the efficient solutions.