A heuristic based on mathematical programming for a lot-sizing and scheduling problem in mold-injection production.

*(English)*Zbl 1441.90068Summary: This paper studies a lot-sizing and scheduling problem to maximize the profit of assembled products over several periods. The setting involves a plastic injection production environment where pieces are produced using auxiliary equipment (molds) to form finished products. Each piece may be processed in a set of molds with different production rates on various machines. The production rate varies according to the piece, mold and machine assignments. The novelty lies on the problem definition, where the focus is on finished products. We developed a two-stage iterative heuristic based on mathematical programming. First the lot-size of the products is determined together with the mold-machine assignments. The second stage determines if there is a feasible schedule of the molds with no overlapping. If unsuccessful, it goes back to the first stage and restricts the number of machines that a mold can visit, until a feasible solution is found. This decomposition approach allows us to deal with a more complex environment that incorporates idle times and assembly line considerations. We show the advantages of this methodology on randomly generated instances and on data from real companies. Experimental results show that our heuristic converges to a feasible solution with few iterations, obtaining solutions that the companies find competitive both in terms of quality and running times.

##### MSC:

90B35 | Deterministic scheduling theory in operations research |

90C59 | Approximation methods and heuristics in mathematical programming |

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\textit{Y. Á. Ríos-Solís} et al., Eur. J. Oper. Res. 284, No. 3, 861--873 (2020; Zbl 1441.90068)

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##### References:

[1] | Almeder, C.; Almada-Lobo, B., Synchronisation of scarce resources for a parallel machine lotsizing problem, International Journal of Production Research, 49, 24, 7315-7335 (2011) |

[2] | Beraldi, P.; Ghiani, G.; Grieco, A.; Guerriero, E., Rolling-horizon and fix-and-relax heuristics for the parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs, Computers & Operations Research, 35, 11, 3644-3656 (2008) · Zbl 1170.90386 |

[3] | Chen, J.-F.; Wu, T.-H., Total tardiness minimization on unrelated parallel machine scheduling with auxiliary equipment constraints, Omega, 34, 1, 81-89 (2006) |

[4] | Dastidar, S. G.; Nagi, R., Scheduling injection molding operations with multiple resource constraints and sequence dependent setup times and costs, Computers & Operations Research, 32, 11, 2987-3005 (2005) · Zbl 1071.90529 |

[5] | Drexl, A.; Kimms, A., Lot sizing and scheduling - survey and extensions, European Journal of Operational Research, 99, 2, 221-235 (1997) · Zbl 0923.90067 |

[6] | Fandel, G.; Stammen-Hegene, C., Simultaneous lot sizing and scheduling for multi-product multi-level production, International Journal of Production Economics, 104, 2, 308-316 (2006) |

[7] | Guimarães, L.; Klabjan, D.; Almada-Lobo, B., Modeling lotsizing and scheduling problems with sequence dependent setups, European Journal of Operational Research, 239, 3, 644-662 (2014) · Zbl 1339.90027 |

[8] | Ibarra-Rojas, O.; Ríos-Mercado, R.; Rios-Solis, Y.; Saucedo-Espinosa, M., A decomposition approach for the piece-mold-machine manufacturing problem, International Journal of Production Economics, 134, 1, 255-261 (2011) |

[9] | James, R. J.; Almada-Lobo, B., Single and parallel machine capacitated lotsizing and scheduling: New iterative mip-based neighborhood search heuristics, Computers & Operations Research, 38, 12, 1816-1825 (2011) · Zbl 1215.90027 |

[10] | Karimi, B.; Ghomi, S. F.; Wilson, J., The capacitated lot sizing problem: a review of models and algorithms, Omega, 31, 5, 365-378 (2003) |

[11] | Kim, S.-i.; Han, J.; Lee, Y.; Park, E., Decomposition based heuristic algorithm for lot-sizing and scheduling problem treating time horizon as a continuum, Computers & Operations Research, 37, 2, 302-314 (2010) · Zbl 1175.90142 |

[12] | Lin, C.; Wong, C.; Yeung, Y., Heuristic approaches for a scheduling problem in the plastic molding department of an audio company, Journal of Heuristics, 8, 5, 515-540 (2002) |

[13] | Lin, C. K.Y.; Wong, C. L.; Yeung, Y. C., Heuristic approaches for a scheduling problem in the plastic molding department of an audio company, Journal of Heuristics, 8, 5, 515-540 (2002) |

[14] | Mateus, G. R.; Ravetti, M. G.; de Souza, M. C.; Valeriano, T. M., Capacitated lot sizing and sequence dependent setup scheduling: an iterative approach for integration, Journal of Scheduling, 13, 3, 245-259 (2010) · Zbl 1193.90104 |

[15] | Meyr, H., Simultaneous lotsizing and scheduling on parallel machines, European Journal of Operational Research, 139, 2, 277-292 (2002) · Zbl 1001.90034 |

[16] | Meyr, H.; Mann, M., A decomposition approach for the general lotsizing and scheduling problem for parallel production lines, European Journal of Operational Research, 229, 3, 718-731 (2013) · Zbl 1317.90128 |

[17] | Quadt, D.; Kuhn, H., Capacitated lot-sizing with extensions: a review, 4OR: A Quarterly Journal of Operations Research, 6, 1, 61-83 (2008) · Zbl 1146.90391 |

[18] | Stadtler, H., Multi-level single machine lot-sizing and scheduling with zero lead times, European Journal of Operational Research, 209, 3, 241-252 (2011) · Zbl 1205.90112 |

[19] | Suerie, C.; Stadtler, H., The capacitated lot-sizing problem with linked lot sizes, Management Science, 49, 8, 1039-1054 (2003) · Zbl 1232.90197 |

[20] | Wolosewicz, C.; Dauzère-Pérès, S.; Aggoune, R., A lagrangian heuristic for an integrated lot-sizing and fixed scheduling problem, European Journal of Operational Research, 244, 1, 3-12 (2015) · Zbl 1346.90062 |

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