no. 3
Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources
RAIRO. Operations Research, Tome 55 (2021) no. 3, pp. 1949-1970

The purpose of this paper is to propose mathematical models to represent a lot sizing and scheduling problem on multiple production lines that share scarce resources and to investigate the computational performance of the proposed models. The main feature that differentiates this problem from others in the literature is that the decision on which lines to organize should be taken considering the availability of the necessary resources. The optimization criterion is the minimization of the costs incurred in the production process (inventory, backlogging, organization of production lines, and sequence-dependent setup costs). Nine mixed integer optimization models to represent the problem are given and, also, the results of an extensive computational study carried out using a set of instances from the literature. The computational study indicates that an efficient formulation, able to provide high quality solutions for large sized instances, can be obtained from a classical model by making the binary production variables explicit, using the facility location reformulation as well as the single commodity flow constraints to eliminate subsequences. Moreover, from the results, it is also clear that the consideration of scarce resources makes the problem significantly more difficult than the traditional one.

DOI : 10.1051/ro/2021084
Classification : 90C11
Keywords: Lot sizing and scheduling, parallel production lines, scarce resources, mixed integer programming models 
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     title = {Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources},
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Alves de Oliveira Soler, Willy; Oliveira Santos, Maristela; Rangel, Socorro. Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources. RAIRO. Operations Research, Tome 55 (2021) no. 3, pp. 1949-1970. doi: 10.1051/ro/2021084

[1] M. Afzalirad and J. Rezaeian, Resource-constrained unrelated parallel machine scheduling problem with sequence dependent setup times, precedence constraints and machine eligibility restrictions. Comput. Ind. Eng. 98 (2016) 40–52. | DOI

[2] Z. Alipour, F. Jolai, E. Monabbati and N. Zaerpour, General lot-sizing and scheduling for perishable food products. RAIRO-Oper. Res. 54 (2020) 913–931. | MR | Zbl | Numdam | DOI

[3] B. Almada-Lobo, A. Clark, L. Guimarães, G. Figueira and P. Amorim, Industrial insights into lot sizing and scheduling modeling. Pesquisa Operacional 35 (2015) 439–46. | DOI

[4] C. Almeder and B. Almada-Lobo, Synchronisation of scarce resources for a parallel machine lotsizing problem. Int. J. Prod. Econ. 49 (2011) 7315–7335. | DOI

[5] A. R. Clark and S. J. Clark, Rolling-horizon lot-sizing when set-up times are sequence-dependent. Int. J. Prod. Econ. 38 (2000) 2287–2307. | Zbl | DOI

[6] K. Copil, M. Wörbelauer, H. Meyr and H. Tempelmeier, Simultaneous lotsizing and scheduling problems: a classification and review of models. OR Spec. 39 (2017) 1–64. | MR | Zbl | DOI

[7] E. D. Dolan and J. J. Moré, Benchmarking optimization software with performance profiles. Math. Program. 91 (2002) 201–213. | MR | Zbl | DOI

[8] G. D. Eppen and R. K. Martin, Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper. Res. 35 (1987) 832–848. | Zbl | DOI

[9] B. Fleischmann and H. Meyr, The general lotsizing and scheduling problem. Oper. Res. Spek. 19 (1997) 11–21. | MR | Zbl | DOI

[10] H. Y. Fuchigami and S. Rangel, A survey of case studies in production scheduling: Analysis and perspectives. J. Comput. Sci. 25 (2018) 425–436. | DOI

[11] B. Gavish and S. C. Graves, The travelling salesman problem and related problems (1978).

[12] C. H. Glock, E. H. Grosse and J. M. Ries, The lot sizing problem: A tertiary study. Int. J. Prod. Econ. 155 (2014) 39–51. | DOI

[13] L. Guimarães, D. Klabjan and B. Almada-Lobo, Modeling lotsizing and scheduling problems with sequence dependent setups. Eur. J. Oper. Res. 239 (2014) 644–662. | MR | Zbl | DOI

[14] M. Güngör, A. T. Ünal and Z. C. Taşkın, A parallel machine lot-sizing and scheduling problem with a secondary resource and cumulative demand. Int. J. Prod. Econ. 56 (2018) 3344–3357. | DOI

[15] K. Haase, Capacitated lot-sizing with sequence dependent setup costs. Oper. Res. Spek. 18 (1996) 51–59. | MR | Zbl | DOI

[16] K. Haase and A. Kimms, Lot sizing and scheduling with sequence-dependent setup costs and times and efficient rescheduling opportunities. Int. J. Prod. Econ. 66 (2000) 159–169. | DOI

[17] R. J. W. James and B. Almada-Lobo, Single and parallel machine capacitated lotsizing and scheduling: New iterative mip-based neighborhood search heuristics. Comput. Oper. Res. 38 (2011) 1816–1825. | Zbl | DOI

[18] G. M. Kopanos, L. Puigjaner and C. T. Maravelias, Production planning and scheduling of parallel continuous processes with product families. Ind. Eng. Chem. Res. 50 (2010) 1369–1378. | DOI

[19] E. L. Lawler, The traveling salesman problem: a guided tour of combinatorial optimization. Wiley-Interscience Series Discrete Mathematics (1985). | Zbl

[20] H. Meyr, Simultaneous lotsizing and scheduling by combining local search with dual reoptimization. Eur. J. Oper. Res. 120 (2000) 311–326. | MR | Zbl | DOI

[21] H. Meyr, Simultaneous lotsizing and scheduling on parallel machines. Eur. J. Oper. Res. 139 (2002) 277–292. | MR | Zbl | DOI

[22] C. E. Miller, A. W. Tucker and R. A. Zemlin, Integer programming formulation of traveling salesman problems. JACM 7 (1960) 326–329. | MR | Zbl | DOI

[23] W. A. Oliveira and M. O. Santos, A new branching rule to solve the capacitated lot sizing and scheduling problem with sequence dependent setups. TEMA (São Carlos) 18 (2017) 515–529. | MR | DOI

[24] W. A. O. Soler, M. O. Santos and K. Akartunali, Mip approaches for a lot sizing and scheduling problem on multiple production lines with scarce resources, temporary workstations, and perishable products. J. Oper. Res. Soc. (2019) 1–16.

[25] L. A. Wolsey, Mip modelling of changeovers in production planning and scheduling problems. Eur. J. Oper. Res. 99 (1997) 154–165. | Zbl | DOI

[26] J. Xiao, H. Yang, C. Zhang, L. Zheng and J. N. D. Gupta, A hybrid lagrangian-simulated annealing-based heuristic for the parallel-machine capacitated lot-sizing and scheduling problem with sequence-dependent setup times. Comput. Oper. Res. 63 (2015) 72–82. | MR | Zbl | DOI

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