Single-machine batch scheduling minimizing weighted flow times and delivery costs with job release times

Article history: Received 25 November 2011 Accepted 11 January 2011 Available online 22 January 2012 This paper addresses scheduling a set of weighted jobs on a single machine in presence of release date for delivery in batches to customers or to other machines for further processing. The problem is a natural extension of minimizing the sum of weighted flow times by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The classical problem is NP-hard and then the extended version of the problem is NP-hard. The objective function is that of minimizing the sum of weighted flow times and delivery costs. The extended problem arises in a real supply chain network by cooperation between two layers of chain. Structural properties of the problem are investigated and used to devise a branch-andbound solution scheme. Computational experiments show the efficiency of suggested algorithm for solving instances up to 40 jobs. © 2012 Growing Science Ltd. All rights reserved

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