On scheduling an unbounded batch machine

Authors:
Zhaohui Liu;Jinjiang Yuan;T. C. Edwin Cheng
Affiliations:
Department of Management, The Hong Kong Polytechnic University, Hong Kong SAR, Kowloon, People's Republic of China and Department of Mathematics, East China University of Science and Technology, S ...;Department of Management, The Hong Kong Polytechnic University, Hong Kong SAR, Kowloon, People's Republic of China and Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, Peo ...;Department of Management, The Hong Kong Polytechnic University, Hong Kong SAR, Kowloon, People's Republic of China
Venue:
Operations Research Letters
Year:
2003

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Abstract

A batch machine is a machine that can process up to c jobs simultaneously as a batch, and the processing time of the batch is equal to the longest processing time of the jobs assigned to it. In this paper, we deal with the complexity of scheduling an unbounded batch machine, i.e., c=+~. We prove that minimizing total tardiness is binary NP-hard, which has been an open problem in the literature. Also, we establish the pseudopolynomial solvability of the unbounded batch machine scheduling problem with job release dates and any regular objective. This is distinct from the bounded batch machine and the classical single machine scheduling problems, most of which with different release dates are unary NP-hard. Combined with the existing results, this paper provides a nearly complete mapping of the complexity of scheduling an unbounded batch machine.