摘要
Two-agent single-machine scheduling problem is considered in this paper.Agent A’s goal is to minimize the sum of the total weighted delivery time and the total delivery cost,and agent B has the delivery time window.First,the NP-hardness of the general problem is proved,and then two special cases are considered.One case is that A’s jobs have agreeable ratio and this problem is still NP-hard.A pseudo-polynomial dynamic programming algorithm and a 32-approximation algorithm are designed.In the other case,A’s jobs have agreeable ratio and B’s jobs have deadline at the same time.This problem is polynomial solvable.
基金
the National Natural Science Foundation of China(No.11371137)。