TECHNICAL NOTE Scheduling jobs with release dates and deadlines on a batch processing machine T.C. EDWIN CHENG 1, *, ZHAOHUI LIU 1;2 and WENCI YU 2 1 Department of Management, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China E-mail: mscheng@polyu.edu.hk 2 Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China Accepted October 2000 In this paper, we investigate the unbounded version of scheduling jobs with release dates and deadlines on a batch processing machine. NP-completeness is established for the case where all jobs have agreeable processing times and deadlines. Polynomial time algorithms are presented for the following cases: agreeable release dates and deadlines; agreeable release dates and processing times; a ®xed number of distinct release dates, distinct processing times or distinct deadlines. 1. Introduction A batch processing machine is a machine that can process several jobs simultaneously as a batch. Speci®cally, this research is concerned with the so-called burn-in model (Lee et al., 1992). That is, once processing of a batch is initiated, it cannot be interrupted, nor can other jobs be introduced into the batch, and the processing time of a batch is equal to the largest processing time of the jobs assigned to the batch. Then all the jobs processed in a batch have the same start time and the same completion time. See also Webster and Baker (1995) and Potts and Kovalyov (2000) for other models that combine sched- uling with batching. The problems that we consider in this paper are all special cases of the following batch processing machine scheduling problem. There are n independent jobs J 1 ; J 2 ; ... ; J n to be processed on a batch processing ma- chine that can process up to c jobs simultaneously. Each job J j (j  1; 2; ... ; n) is associated with a release date r j , a processing time p j and a deadline d j . The objective is to ®nd a feasible schedule for the n jobs, i.e., to partition them into batches and schedule the batches so that 1. Each batch contains at most c jobs. 2. Each job is started no earlier than its release date and is completed no later than its deadline. The problem has two variants: (i) the bounded version, in which c is a constant smaller than n; and (ii) the unbounded version, in which c  n so that all available jobs can be processed in a batch whenever the machine is free. Note that the unbounded version is the same as setting c  1. For the bounded version, Brucker et al. (1998) proved that the problem is unary NP-complete even if all jobs have a common release date or a common deadline. Liu and Yu (2000) proved the binary NP-completeness for the case where all jobs have two distinct release dates and a common deadline. Li and Lee (1997) showed that the problem is polynomially solvable under the assumption that release dates, deadlines and processing times are agreeable, i.e., the jobs can be re-indexed in such a way that r 1  r 2  r n , d 1  d 2  d n and p 1  p 2  p n . Liu (1998) presented a polynomial time algorithm for the case where all jobs have the same processing time. As to the unbounded version, Brucker et al. (1998) provide an extensive discussion on minimizing various regular cost functions when all jobs have the same release date. In this paper, we address the unbounded version of scheduling n jobs with unequal release dates and unequal deadlines on a batch processing machine. In the next section, we show that this problem is NP-complete even if the processing times and deadlines are agreeable. This result also answers several open questions listed in Brucker and Knust (2000). In Sections 3 and 4, we pre- sent polynomial time algorithms for the case of agreeable release dates and deadlines and the case of agreeable release dates and processing times, respectively. In Sec- tion 5, a polynomial time algorithm is designed for the 0740-817X Ó 2001 ``IIE'' *Corresponding author IIE Transactions (2001) 33, 685±690