IDEAS home Printed from https://ideas.repec.org/p/ant/wpaper/2015003.html
   My bibliography  Save this paper

D- and I-optimal design of mixture experiments in the presence of ingredient availability constraints

Author

Listed:
  • SYAFITRI, Utami
  • SARTONO, Bagus
  • GOOS, Peter

Abstract

Mixture experiments usually involve various constraints on the proportions of the ingredients of the mixture under study. In this paper, inspired by the fact that the available stock of certain ingredients is often limited, we focus on a new type of constraint, which we refer to as an ingredient availability constraint. This type of constraint substantially complicates the search for optimal designs for mixture experiments. One difficulty, for instance, is that the optimal number of experimental runs is not known a priori. We show that the optimal design problem in the presence of ingredient availability constraints is a nonlinear multidimensional knapsack problem and propose a variable neighborhood descent algorithm to identify D- and I-optimal designs for mixture experiments in case there is a limited stock of certain ingredients.

Suggested Citation

  • SYAFITRI, Utami & SARTONO, Bagus & GOOS, Peter, 2015. "D- and I-optimal design of mixture experiments in the presence of ingredient availability constraints," Working Papers 2015003, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2015003
    as

    Download full text from publisher

    File URL: https://repository.uantwerpen.be/docman/irua/ef5975/aa01755a.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. D. Quadri & E. Soutif & P. Tolla, 2009. "Exact solution method to solve large scale integer quadratic multidimensional knapsack problems," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 157-167, February.
    2. Bretthauer, Kurt M. & Shetty, Bala, 2002. "The nonlinear knapsack problem - algorithms and applications," European Journal of Operational Research, Elsevier, vol. 138(3), pages 459-472, May.
    3. Arnouts, Heidi & Goos, Peter, 2010. "Update formulas for split-plot and block designs," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3381-3391, December.
    4. Avanthay, Cedric & Hertz, Alain & Zufferey, Nicolas, 2003. "A variable neighborhood search for graph coloring," European Journal of Operational Research, Elsevier, vol. 151(2), pages 379-388, December.
    5. GARROI, Jean-Jacques & GOOS, Peter & SÖRENSEN, Kenneth, 2006. "A variable-neighbourhood search algorithm for finding optimal run orders in the presence of serial correlation and time trends," Working Papers 2006026, University of Antwerp, Faculty of Business and Economics.
    6. GOOS, Peter & JONES, Bradley & SYAFITRI, Utami, 2013. "I-optimal mixture designs," Working Papers 2013033, University of Antwerp, Faculty of Business and Economics.
    7. Fleszar, Krzysztof & Hindi, Khalil S., 2004. "Solving the resource-constrained project scheduling problem by a variable neighbourhood search," European Journal of Operational Research, Elsevier, vol. 155(2), pages 402-413, June.
    8. Thomas L. Morin & Roy E. Marsten, 1976. "An Algorithm for Nonlinear Knapsack Problems," Management Science, INFORMS, vol. 22(10), pages 1147-1158, June.
    9. Liu, Shuangzhe & Neudecker, Heinz, 1995. "A V-optimal design for Scheffé's polynomial model," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 253-258, May.
    10. JONES, Bradley & GOOS, Peter, 2012. "I-optimal versus D-optimal split-plot response surface designs," Working Papers 2012002, University of Antwerp, Faculty of Business and Economics.
    11. DE KETELAERE, Bart & GOOS, Peter & BRIJS, Kristof, 2010. "Prespecified factor-level combinations in the optimal design of mixture-process variable experiments," Working Papers 2011001, University of Antwerp, Faculty of Business and Economics.
    12. Billionnet, Alain & Calmels, Frederic, 1996. "Linear programming for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 92(2), pages 310-325, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. VÁZQUEZ-ALCOCER, Alan & GOOS, Peter & SCHOEN, Eric D., 2016. "Two-level designs constructed by concatenating orthogonal arrays of strenght three," Working Papers 2016011, University of Antwerp, Faculty of Business and Economics.
    2. VÁZQUEZ-ALCOCER, Alan & XU, Hongquan, 2018. "Construction of two-level nonregular designs of strength three with large run sizes," Working Papers 2018003, University of Antwerp, Faculty of Business and Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. VÁZQUEZ-ALCOCER, Alan & GOOS, Peter & SCHOEN, Eric D., 2016. "Two-level designs constructed by concatenating orthogonal arrays of strenght three," Working Papers 2016011, University of Antwerp, Faculty of Business and Economics.
    2. HERREMANS, Dorien & WEISSER, Stéphanie & SÖRENSEN, Kenneth & CONKLIN, Darrell, 2014. "Generating structured music using quality metrics based on Markov models," Working Papers 2014019, University of Antwerp, Faculty of Business and Economics.
    3. Mohammadivojdan, Roshanak & Geunes, Joseph, 2018. "The newsvendor problem with capacitated suppliers and quantity discounts," European Journal of Operational Research, Elsevier, vol. 271(1), pages 109-119.
    4. X. J. Zheng & X. L. Sun & D. Li, 2010. "Separable Relaxation for Nonconvex Quadratic Integer Programming: Integer Diagonalization Approach," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 463-489, August.
    5. AgralI, Semra & Geunes, Joseph, 2009. "Solving knapsack problems with S-curve return functions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 605-615, March.
    6. HERREMANS, Dorien & SÖRENSEN, Kenneth, 2013. "FuX, an android app that generates counterpoint," Working Papers 2013003, University of Antwerp, Faculty of Business and Economics.
    7. GARROI, Jean-Jacques & GOOS, Peter & SÖRENSEN, Kenneth, 2006. "A variable-neighbourhood search algorithm for finding optimal run orders in the presence of serial correlation and time trends," Working Papers 2006026, University of Antwerp, Faculty of Business and Economics.
    8. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    9. Federico Della Croce & Dominique Quadri, 2012. "Improving an exact approach for solving separable integer quadratic knapsack problems," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 21-28, January.
    10. HERREMANS, Dorien & SÖRENSEN, Kenneth, 2012. "Composing Fifth Species Counterpoint Music With Variable Neighborhood Search," Working Papers 2012020, University of Antwerp, Faculty of Business and Economics.
    11. David Bergman, 2019. "An Exact Algorithm for the Quadratic Multiknapsack Problem with an Application to Event Seating," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 477-492, July.
    12. Zhang, Chongqi & Wong, Weng Kee, 2013. "Optimal designs for mixture models with amount constraints," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 196-202.
    13. Bretthauer, Kurt M. & Shetty, Bala, 2002. "The nonlinear knapsack problem - algorithms and applications," European Journal of Operational Research, Elsevier, vol. 138(3), pages 459-472, May.
    14. GOOS, Peter & JONES, Bradley & SYAFITRI, Utami, 2013. "I-optimal mixture designs," Working Papers 2013033, University of Antwerp, Faculty of Business and Economics.
    15. Janssens, Jochen & Talarico, Luca & Sörensen, Kenneth, 2016. "A hybridised variable neighbourhood tabu search heuristic to increase security in a utility network," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 221-230.
    16. Zhang, Jianzhong & Xu, Chengxian, 2010. "Inverse optimization for linearly constrained convex separable programming problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 671-679, February.
    17. JANSSENS, Jochen & TALARICO, Luca & SÖRENSEN, Kenneth, 2014. "A hybridised taboo search heuristic to increase security in a utility network," Working Papers 2014023, University of Antwerp, Faculty of Business and Economics.
    18. Tom S. Clark & Aaron B. Strauss, 2010. "The Implications of High Court Docket Control for Resource Allocation and Legal Efficiency," Journal of Theoretical Politics, , vol. 22(2), pages 247-268, April.
    19. Zhang, Chongqi & Peng, Heng, 2012. "D-optimal designs for quadratic mixture canonical polynomials with spline," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1095-1101.
    20. ten Eikelder, S.C.M. & van Amerongen, J.H.M., 2023. "Resource allocation problems with expensive function evaluations," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1170-1185.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ant:wpaper:2015003. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joeri Nys (email available below). General contact details of provider: https://edirc.repec.org/data/ftufsbe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.