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Title: Batch delivery scheduling with batch delivery cost on a single machine
Authors: Ji, M
He, Y
Cheng, TCE 
Keywords: Single machine scheduling
Batch delivery cost
Optimal algorithm
Computational complexity
Issue Date: 16-Jan-2007
Publisher: Elsevier B.V.
Source: European journal of operational research, 16 Jan. 2007, v. 176, no. 2, p. 745-755 How to cite?
Journal: European journal of operational research 
Abstract: We consider a scheduling problem in which n independent and simultaneously available jobs are to be processed on a single machine. The jobs are delivered in batches and the delivery date of a batch equals the completion time of the last job in the batch. The delivery cost depends on the number of deliveries. The objective is to minimize the sum of the total weighted flow time and delivery cost. We first show that the problem is strongly NP-hard. Then we show that, if the number of batches is B, the problem remains strongly NP-hard when B ≤ U for a variable U ≥ 2 or B ≥ U for any constant U ≥ 2. For the case of B ≤ U, we present a dynamic programming algorithm that runs in pseudo-polynomial time for any constant U ≥ 2. Furthermore, optimal algorithms are provided for two special cases: (i) jobs have a linear precedence constraint, and (ii) jobs satisfy the agreeable ratio assumption, which is valid, for example, when all the weights or all the processing times are equal.
ISSN: 0377-2217
DOI: 10.1016/j.ejor.2005.09.006
Rights: European Journal of Operational Research © 2005 Elsevier B.V. The journal web site is located at
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