This research proposes computational models for concurrent design process of large complicated systems toward the development of agent-based distributed design support systems. In this second report, we mathematically formulate the partial design problem of each divided task in the distributed design process under the concepts introduced in the first report. Following them, the backward-chaining operation for refining a tentative design solution is modeled as an optimization problem. Its form belongs to a style of goal programming, since the goals, each of which is the play of an intermediate variable among divided tasks, are defined with a set of regions and domains. The associated mathematical programming method is configured by combining linear approximation, monotonicity analysis and active set strategy to support designer's decision making. The issues on design process management over such optimization-based support are further discussed. Finally, the coordinative design process among divided tasks is briefly demonstrated in an application to preliminary aircraft design.