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.
Highlights
Tang and Gong [1] first raised and studied the problem of transportation and batching scheduling (TBS)
Tang and Gong [1] studied the TBS problem which aims to minimize the sum of the total completion time of the jobs and the processing cost of the batching machine
We studied the coordination of transportation and batching scheduling with one single vehicle for minimizing the total weighted completion time of the jobs without considering the processing cost of the batching machine
Summary
Tang and Gong [1] first raised and studied the problem of transportation and batching scheduling (TBS). Tang and Gong [1] studied the TBS problem which aims to minimize the sum of the total completion time of the jobs and the processing cost of the batching machine. For this problem, the authors proved the binary NP-hardness and further established a pseudo-polynomial-time algorithm and an FPTAS for any fixed m. We consider the TBS problem (1, c)|τ | ∑ w j Cj , in which we have one single vehicle in the transportation stage, the scheduling criterion is to minimize the total weighted completion time of the jobs, and the processing cost is given by 0. The complexity of problem (1, 2)|τ | ∑ w j Cj is still open
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