# Scheduling parallel-machine batch operations to maximize on-time delivery performance

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## Abstract

In this paper we study the problem of minimizing total weighted tardiness, a proxy for maximizing on-time delivery performance, on parallel nonidentical batch processing machines. We first formulate the (primal) problem as a nonlinear integer programming model. We then show that the primal problem can be solved exactly by solving a corresponding dual problem with a nonlinear relaxation. Since both the primal and the dual problems are NP-hard, we use genetic algorithms, based on random keys and multiple choice encodings, to heuristically solve them. We find that the genetic algorithms consistently outperform a standard mathematical programming package in terms of solution quality and computation time. We also compare the smaller problem instances to a breadth-first tree search algorithm that gives evidence of the quality of the solutions.

## Keywords

Parallel-machine scheduling Batching Total weighted tardiness Optimal and approximate algorithms Nonlinear relaxation Genetic algorithms## Notes

### Acknowledgments

The authors would like to thank two anonymous referees and the Associate Editor for their insightful comments and constructive suggestions which significantly improved the presentation of this paper.

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