We study the design and production process of manufacturers who provide customers with personalized products. Each customer’s order needs to go through two stages: design and production. For this problem, we consider the two scheduling problems with the objective of minimizing the total weighted completion time. Then we consider two models of manufacturing at a personalized level. In the first model, personalized products have the same personalization level, which is proved to have an optimal solution. In the second model, we propose an approximate algorithm with an absolute worst-case ratio of no more than two for personalized products with arbitrary personalization levels, which is proved to be NP-hard in the strong sense.

我们研究为客户提供个性化产品的制造商的设计和生产过程。每个客户的订单都需要经过两个阶段：设计和生产。对于这个问题，我们考虑两个调度问题，目标是最小化总加权完成时间。然后我们考虑个性化层面的两种制造模型。在第一个模型中，个性化产品具有相同的个性化水平，这被证明具有最优解。在第二个模型中，我们提出了一种对于任意个性化级别的个性化产品绝对最坏情况比率不超过2的近似算法，该算法被证明是强意义上的NP-hard。