摘要
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.