Abstract: For the coordinated optimization problem of product family design and postponement decisions in crowdsourced manufacturing,a mixed integer nonlinear bi-level programming model with product family design as a leader and postponement decisions as the followers was established,in which the upper-level model maximized the expected profit of the manufacturer by determining the design of product family,the lower-level model maximized the expected profits of the distributors by optimizing the types of postponed product modules,and the decisions among the distributors were mutually independent.A novel virtual postponement structure was introduced to concretize this research and to justify which product modules should be postponed.A nested genetic algorithm was developed to solve the proposed model.A case study of smart refrigerator design for postponement was reported to illustrate the feasibility of the proposed approach,and the sensitivity analysis on the proposed postponement preference parameter was carried out.

Key words: crowdsourced manufacturing, product family design, postponement decisions, hierarchical joint optimization, nested genetic algorithm

摘要： 针对众包制造环境下产品族设计与延迟决策之间的协同优化问题,建立了以产品族设计为主、延迟决策为从的混合整数非线性双层规划模型。模型上层由制造商设计产品族架构以最大化自身的期望利润,下层由多个分销商优化延迟产品模块的类型以最大化各自的期望利润,且各分销商之间的决策具有相互独立性。考虑到延迟产品模块事先不确定,提出虚拟延迟结构将该优化问题具体化,并证明需要被延迟的产品模块。开发了一个双层嵌套遗传算法对模型进行求解。用智能冰箱产品族延迟案例验证了所提模型和算法的有效性,并对所提延迟偏好参数进行了灵敏度分析。

关键词: 众包制造, 产品族设计, 延迟决策, 主从关联优化, 嵌套遗传算法