Robust optimization design essentially has multiple objectives. The compromise Decision Support Problem (DSP) is a multi-objective mathematical programming formulation that is used to model engineering decisions involving multiple tradeoffs. In this paper, the compromise DSP is introduced to robust optimization design, and mathematic model of a compromise DSP for robust optimization design is presented. In this framework, the tradeoff between the mean and deviation of performance is made by solving the bi-objective robust design problem. To demonstrate the feasibility of this approach, a case study involving the design of the compensative pulley block of luffing mechanism is considered.