Skip to main content
Log in

A Local Search Algorithm for the Single Machine Scheduling Problem with Setups and a Storage

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

We present a new mathematical model for a single machine scheduling problem originated from the tile industry. The model takes into account the sequence-dependent setup times, the minimal batch size, heterogeneous orders of customers, and a stock in storage. As the objective function we use the penalty for tardiness of the customers’ orders and the total storage cost for final products. A mixed-integer linear programming model is applied for small test instances. For real-world applications, we design a randomized tabu search algorithm. The computational results for some test instances from a Novorossiysk company are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. R. Jackson, “Scheduling a Production Line to Minimize Maximum Tardiness,” Research Report No. 43 (Univ. Calif., Los Angeles, 1955).

    Google Scholar 

  2. W. E. Smith, “Various Optimizers for Single-Stage Production,” Naval Res. Logist. Quart. 3 (1–2), 59–66 (1956).

    Article  MathSciNet  Google Scholar 

  3. L.-P. Bigras, M. Gamache, and G. Savard, “The Time-Dependent Traveling Salesman Problem and Single Machine Scheduling Problems with Sequence Dependent Setup Times,” Discrete Optim. 5 (4), 685–699 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Allahverdi, “The Third Comprehensive Survey on Scheduling Problems with Setup Times/Costs,” European J. Oper. Res. 246 (2), 345–378 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Chen, C. N. Potts, and G. J. Woeginger, “A Review of Machine Scheduling: Complexity, Algorithms, and Approximability,” in Handbook of Combinatorial Optimization, Vol. 3 (Kluwer Acad. Publ., Dordrecht, 1998), pp. 21–169.

    Google Scholar 

  6. Y. Pochet and L. A. Wolsey, Production Planning by Mixed Integer Programming (Springer, New York, 2006).

    MATH  Google Scholar 

  7. A. Dolgui, A. V. Eremeev, M. Ya. Kovalyov, and P. M. Kuznetsov, “Multi-Product Lot Sizing and Scheduling on Unrelated Parallel Machines,” IIE Trans. 42 (7), 514–524 (2010).

    Article  Google Scholar 

  8. S. L. Janak, Ch. A. Floudas, J. Kallrath, and N. Vormbrock, “Production Scheduling of a Large-Scale Industrial Batch Plant. I. Short-Term and Medium-Term Scheduling,” Indust. Eng. Chem. Res. 45, 8234–8252 (2006).

    Article  Google Scholar 

  9. P. Brucker, Scheduling Algorithms (Springer, Heidelberg, 1982).

    MATH  Google Scholar 

  10. E.-G. Talbi, Metaheuristics: From Design to Implementation (Wiley, Hoboken, NJ, 2009).

    Book  MATH  Google Scholar 

  11. N. Mladenović, J. Brimberg, P. Hansen, and J. A. Moreno-Pérez, “The p-Median Problem: A Survey of Metaheuristic Approaches,” European J. Oper. Res. 179 (3), 927–939 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  12. A. I. Erzin, N. Mladenović, and R. V. Plotnikov, “Variable Neighborhood Search Variants for Min-Power Symmetric Connectivity Problem,” Comput. Oper. Res. 78, 557–563 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  13. A. I. Erzin and R. V. Plotnikov, “Using VNS for the Optimal Synthesis of the Communication Tree in Wireless Sensor Networks,” Electron. Notes Discrete Math. 47, 21–28 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  14. Yu. A. Kochetov, A. A. Panin, and A. V. Plyasunov, “Genetic Local Search and Hardness of Approximation for the Server Load Balancing Problem,” Avtom. Telemekh. No. 3, 51–62 (2017) [Autom. Remote Control 78 (3), 425–434 (2017)].

  15. Yu. A. Kochetov and A. A. Kondakov, “VNS Matheuristic for a Bin Packing Problem with a Color Constraint,” Electron. Notes Discrete Math. 58, 39–46 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  16. S. M. Lavlinskii, A. A. Panin, and A. V. Plyasunov, “A Bilevel Planning Model for Public-Private Partnership,” Avtom. Telemekh. No. 11, 89–103 (2015) [Autom. Remote Control 76 (11), 1976–1987 (2015)].

  17. A. A. Panin, M. G. Pashchenko, and A. V. Plyasunov, “Bilevel Competitive Facility Location and Pricing Problems,” Avtom. Telemekh. No. 4, 153–169 (2014) [Autom. Remote Control 75 (4), 715–727 (2014)].

  18. S. Iellamo, E. V. Alekseeva, L. Chen, M. Coupechoux, and Yu. A. Kochetov, “Competitive Location in Cognitive Radio Networks,” 4OR 13 (1), 81–110 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  19. I. A. Davydov, P. A. Kononova, and Yu. A. Kochetov, “Local Search with an Exponential Neighborhood for the Servers Load Balancing Problem,” Diskretn. Anal. Issled. Oper. 21 (6), 21–34 (2014) [J. Appl. Indust. Math. 9 (1), 27–35 (2015)].

    MATH  Google Scholar 

  20. I. A. Davydov, A. A. Melnikov, and P. A. Kononova, “Local Search for Load Balancing Problems for Servers with Large Dimension,” Avtom. Telemekh. No. 3, 34–50 (2017) [Autom. Remote Control 78 (3), 412–424 (2017)].

  21. E. H. L. Aarts, J. H. M. Korst, and P. J. M. van Laarhoven, “Simulated Annealing,” in Local Search in Combinatorial Optimization (Wiley, Chichester, 1997), pp. 91–120.

    Google Scholar 

  22. J. Brimberg, P. Hansen, and N. Mladenović, “Attraction Probabilities in Variable Neighborhood Search,” 4OR 8 (2), 181–194 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  23. Yu. A. Kochetov, “Facility Location: Discrete Models and Local Search Methods,” in Combinatorial Optimization: Methods and Applications (IOS Press, Amsterdam, 2011), pp. 97–134.

    Google Scholar 

  24. B. H. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms (Springer, Heidelberg, 1982).

    MATH  Google Scholar 

  25. F. Glover and M. Laguna, Tabu Search (Kluwer Acad. Publ., Norwell, MA: 1997).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to P. A. Kononova or Yu. A. Kochetov.

Additional information

Russian Text © The Author(s), 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 2, pp. 60–78.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kononova, P.A., Kochetov, Y.A. A Local Search Algorithm for the Single Machine Scheduling Problem with Setups and a Storage. J. Appl. Ind. Math. 13, 239–249 (2019). https://doi.org/10.1134/S1990478919020054

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478919020054

Keywords

Navigation