IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v57y2015ipbp212-216.html
   My bibliography  Save this article

Approximate solution of a profit maximization constrained virtual business planning problem

Author

Listed:
  • Dolgui, Alexandre
  • Kovalev, Sergey
  • Pesch, Erwin

Abstract

A virtual business problem is studied, in which a company-contractor outsources production to specialized subcontractors. Finances of the contractor and resource capacities of subcontractors are limited. The objective is to select subcontractors and distribute a part of the demanded production among them so that the profit of the contractor is maximized. A generalization of the knapsack problem, called Knapsack-of-Knapsacks (K-of-K), is used to model this situation, in which items have to be packed into small knapsacks and small knapsacks have to be packed into a large knapsack. A fully polynomial time approximation scheme is developed to solve the problem K-of-K.

Suggested Citation

  • Dolgui, Alexandre & Kovalev, Sergey & Pesch, Erwin, 2015. "Approximate solution of a profit maximization constrained virtual business planning problem," Omega, Elsevier, vol. 57(PB), pages 212-216.
    • Handle: RePEc:eee:jomega:v:57:y:2015:i:pb:p:212-216
    DOI: 10.1016/j.omega.2015.05.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048315000912
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2015.05.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kellerer, Hans & Strusevich, Vitaly, 2013. "Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product," European Journal of Operational Research, Elsevier, vol. 228(1), pages 24-32.
    2. Balachandran, Kashi R. & Wang, Hsiao-Wen & Li, Shu-Hsing & Wang, Taychang, 2013. "In-house capability and supply chain decisions," Omega, Elsevier, vol. 41(2), pages 473-484.
    3. Magazine, M. J. & Oguz, Osman, 1981. "A fully polynomial approximation algorithm for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 8(3), pages 270-273, November.
    4. Gomes da Silva, Carlos & Figueira, José & Lisboa, João & Barman, Samir, 2006. "An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming," Omega, Elsevier, vol. 34(2), pages 167-177, April.
    5. Danese, Pamela, 2013. "Supplier integration and company performance: A configurational view," Omega, Elsevier, vol. 41(6), pages 1029-1041.
    6. Eugene L. Lawler, 1979. "Fast Approximation Algorithms for Knapsack Problems," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 339-356, November.
    7. Wang, Xiuli & Zhu, Qianqian & Cheng, T.C.E., 2015. "Subcontracting price schemes for order acceptance and scheduling," Omega, Elsevier, vol. 54(C), pages 1-10.
    8. Martello, Silvano & Toth, Paolo, 1985. "Approximation schemes for the subset-sum problem: Survey and experimental analysis," European Journal of Operational Research, Elsevier, vol. 22(1), pages 56-69, October.
    9. Mikhail Y. Kovalyov & Marie-Claude Portmann & Ammar Oulamara, 2006. "Optimal testing and repairing a failed series system," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 279-295, November.
    10. Shabtay, Dvir & Arviv, Kfir & Stern, Helman & Edan, Yael, 2014. "A combined robot selection and scheduling problem for flow-shops with no-wait restrictions," Omega, Elsevier, vol. 43(C), pages 96-107.
    11. Imrie, R, 1994. "'A strategy of the last resort'? Reflections on the role of the subcontract in the United Kingdom," Omega, Elsevier, vol. 22(6), pages 569-578, November.
    12. Sartaj Sahni, 1977. "General Techniques for Combinatorial Approximation," Operations Research, INFORMS, vol. 25(6), pages 920-936, December.
    13. Shabtay, Dvir & Bensoussan, Yaron & Kaspi, Moshe, 2012. "A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 67-74.
    14. Heese, H. Sebastian, 2015. "Single versus multiple sourcing and the evolution of bargaining positions," Omega, Elsevier, vol. 54(C), pages 125-133.
    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. Dolgui, Alexandre & Hashemi-Petroodi, S. Ehsan & Kovalev, Sergey & Kovalyov, Mikhail Y., 2021. "Profitability of a multi-model manufacturing line versus multiple dedicated lines," International Journal of Production Economics, Elsevier, vol. 236(C).
    2. Banda, Juan & Velasco, Jonás & Berrones, Arturo, 2017. "Dual mean field search for large scale linear and quadratic knapsack problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 158-167.
    3. Caserta, Marco & Voß, Stefan, 2019. "The robust multiple-choice multidimensional knapsack problem," Omega, Elsevier, vol. 86(C), pages 16-27.

    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. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    2. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria combinatorial optimization," Working papers 3756-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Halman, Nir & Kellerer, Hans & Strusevich, Vitaly A., 2018. "Approximation schemes for non-separable non-linear boolean programming problems under nested knapsack constraints," European Journal of Operational Research, Elsevier, vol. 270(2), pages 435-447.
    4. Rui Diao & Ya-Feng Liu & Yu-Hong Dai, 2017. "A new fully polynomial time approximation scheme for the interval subset sum problem," Journal of Global Optimization, Springer, vol. 68(4), pages 749-775, August.
    5. Hans Kellerer & Ulrich Pferschy, 1999. "A New Fully Polynomial Time Approximation Scheme for the Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 59-71, July.
    6. Arnaud Fréville & SaÏd Hanafi, 2005. "The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects," Annals of Operations Research, Springer, vol. 139(1), pages 195-227, October.
    7. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria flow, knapsack, and scheduling problems," Working papers 3757-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Caprara, Alberto & Kellerer, Hans & Pferschy, Ulrich & Pisinger, David, 2000. "Approximation algorithms for knapsack problems with cardinality constraints," European Journal of Operational Research, Elsevier, vol. 123(2), pages 333-345, June.
    9. Aardal, Karen & van den Berg, Pieter L. & Gijswijt, Dion & Li, Shanfei, 2015. "Approximation algorithms for hard capacitated k-facility location problems," European Journal of Operational Research, Elsevier, vol. 242(2), pages 358-368.
    10. Haris Aziz & Sujit Gujar & Manisha Padala & Mashbat Suzuki & Jeremy Vollen, 2022. "Coordinating Monetary Contributions in Participatory Budgeting," Papers 2206.05966, arXiv.org, revised Feb 2023.
    11. Daria Dzyabura & Srikanth Jagabathula, 2018. "Offline Assortment Optimization in the Presence of an Online Channel," Management Science, INFORMS, vol. 64(6), pages 2767-2786, June.
    12. Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.
    13. Hifi, Mhand & M'Hallah, Rym, 2006. "Strip generation algorithms for constrained two-dimensional two-staged cutting problems," European Journal of Operational Research, Elsevier, vol. 172(2), pages 515-527, July.
    14. Zhong, Xueling & Ou, Jinwen & Wang, Guoqing, 2014. "Order acceptance and scheduling with machine availability constraints," European Journal of Operational Research, Elsevier, vol. 232(3), pages 435-441.
    15. Sim, Jeongeun & Kim, Bosung, 2021. "Sourcing decision in the presence of a complementary component," Omega, Elsevier, vol. 101(C).
    16. Yuan Li & William J. Kettinger, 2022. "Testing the Relationship Between Information and Knowledge in Computer-Aided Decision-Making," Information Systems Frontiers, Springer, vol. 24(6), pages 1827-1843, December.
    17. Zhong, Weiya & Dosa, Gyorgy & Tan, Zhiyi, 2007. "On the machine scheduling problem with job delivery coordination," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1057-1072, November.
    18. Li, Siyu & Huo, Baofeng & Han, Zhaojun, 2022. "A literature review towards theories and conceptual models of empirical studies on supply chain integration and performance," International Journal of Production Economics, Elsevier, vol. 250(C).
    19. Tanveer Ahsan & Sultan Sikandar Mirza & Ammar Ali Gull & Muhammad Ansar Majeed, 2023. "How to deal with customer and supplier concentration to attain sustainable financial growth? The role of business strategy," Business Strategy and the Environment, Wiley Blackwell, vol. 32(7), pages 4600-4619, November.
    20. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.

    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:eee:jomega:v:57:y:2015:i:pb:p:212-216. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    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.