Column generation for minimizing total completion time in a parallel-batching environment

A PTAS for Minimizing the Total Weighted Completion Time on Identical Parallel Machines

We consider the problem of scheduling a set of n jobs on m identical parallel machines so as to minimize the weighted sum of job completion times. This problem is NP-hard in the strong sense. The best approximation result known so far was a 2 (1 + √ 2)-approximation algorithm that has been derived by Kawaguchi and Kyan back in 1986. The contribution of this paper is a polynomial time approximat...

Minimizing total weighted completion time approximately for the parallel machine problem with a single server

In this paper, we consider the scheduling problem of minimizing total weighted job completion time when a set of jobs has to be processed on a set of m parallel identical machines with a common server. We propose an approximation algorithm with a worst-case ratio of 3− 1 m . This result improves an existing (5− 1 m ) approximation algorithm given by Wang and Cheng (2001).

Minimizing total weighted completion

We study the special case of the m machine ow shop problem in which the processing time of each operation of job j is equal to p j ; this variant of the ow shop problem is known as the proportionate ow shop problem. We show that for any number of machines and for any regular performance criterion we can restrict our search for an optimal schedule to permutation schedules. Moreover, we show that...

On Minimizing Total Tardiness in a Serial Batching Problem

We study the problem of scheduling jobs on a serial batching machine to minimize total tardiness. Jobs of the same batch start and are completed simultaneously and the length of a batch equals the sum of the processing times of its jobs. When a new batch starts, a constant setup time s occurs. This problem 1|s-batch| P Ti is known to be NP-Hard in the ordinary sense. In this paper we show that ...

Company ON MINIMIZING TOTAL COMPLETION TIME IN BATCHMACHINE SCHEDULING