*Article* **Transportation and Batching Scheduling for Minimizing Total Weighted Completion Time**

### **Hongjun Wei \* , Jinjiang Yuan and Yuan Gao**

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China **\*** Correspondence: weihongjun@zzu.edu.cn

Received: 20 August 2019; Accepted: 3 September 2019; Published: 5 September 2019

**Abstract:** We consider the coordination of transportation and batching scheduling with one single vehicle for minimizing total weighted completion time. The computational complexity of the problem with batch capacity of at least 2 was posed as open in the literature. For this problem, we show the unary NP-hardness for every batch capacity at least 3 and present a polynomial-time 3-approximation algorithm when the batch capacity is at least 2.

**Keywords:** Transportation; batching scheduling; total weighted completion time; unary NP-hard; approximation algorithm
