IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v246y2015i2p462-470.html
   My bibliography  Save this article

Decentral allocation planning in multi-stage customer hierarchies

Author

Listed:
  • Vogel, Sebastian
  • Meyr, Herbert

Abstract

This paper presents a novel allocation scheme to improve profits when splitting a scarce product among customer segments. These segments differ by demand and margin and they form a multi-level tree, e.g. according to a geography-based organizational structure. In practice, allocation has to follow an iterative process in which higher level quotas are disaggregated one level at a time, only based on local, aggregate information. We apply well-known econometric concepts such as the Lorenz curve and Theil’s index of inequality to find a non-linear approximation of the profit function in the customer tree. Our resulting Approximate Profit Decentral Allocation (ADA) scheme ensures that a group of truthfully reporting decentral planners makes quasi-coordinated decisions in support of overall profit-maximization in the hierarchy. The new scheme outperforms existing simple rules by a large margin and comes close to the first-best theoretical solution under a central planner and central information.

Suggested Citation

  • Vogel, Sebastian & Meyr, Herbert, 2015. "Decentral allocation planning in multi-stage customer hierarchies," European Journal of Operational Research, Elsevier, vol. 246(2), pages 462-470.
    • Handle: RePEc:eee:ejores:v:246:y:2015:i:2:p:462-470
    DOI: 10.1016/j.ejor.2015.05.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715003811
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.05.009?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. Van Zandt, Timothy, 2003. "Real-Time Hierarchical Resource Allocation with Quadratic Costs," CEPR Discussion Papers 4022, C.E.P.R. Discussion Papers.
    2. Herbert Meyr, 2012. "Demand Planning (DP)," Management for Professionals, in: Advanced Planning in Supply Chains, chapter 0, pages 67-108, Springer.
    3. Pedro Conceicao & James K. Galbraith, 2000. "Constructing Long and Dense Time-Series of Inequality Using the Theil Index," Eastern Economic Journal, Eastern Economic Association, vol. 26(1), pages 61-74, Winter.
    4. Fleischmann, B. & Meyr, H., 2003. "Planning Hierarchy, Modeling and Advanced Planning Systems," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 36714, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    5. Pedro Conceicao & James K. Galbraith & Peter Bradford, 2001. "The Theil Index in Sequences of Nested and Hierarchic Grouping Structures: Implications for the Measurement of Inequality through Time, with Data Aggregated at Different Levels of Industrial Classific," Eastern Economic Journal, Eastern Economic Association, vol. 27(4), pages 491-514, Fall.
    6. Steven F. Maier & James H. Vander Weide, 1976. "Capital Budgeting in the Decentralized Firm," Management Science, INFORMS, vol. 23(4), pages 433-443, December.
    7. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    8. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    9. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 1997. "Information Distortion in a Supply Chain: The Bullwhip Effect," Management Science, INFORMS, vol. 43(4), pages 546-558, April.
    10. Herbert Meyr, 2009. "Customer segmentation, allocation planning and order promising in make-to-stock production," Springer Books, in: Herbert Meyr & Hans-Otto Günther (ed.), Supply Chain Planning, pages 117-144, Springer.
    11. Gabriel R. Bitran & Arnoldo C. Hax, 1981. "Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables," Management Science, INFORMS, vol. 27(4), pages 431-441, April.
    12. Pibernik, Richard, 2005. "Advanced available-to-promise: Classification, selected methods and requirements for operations and inventory management," International Journal of Production Economics, Elsevier, vol. 93(1), pages 239-252, January.
    13. Nicholas Rohde, 2008. "Lorenz Curves and Generalised Entropy Inequality Measures," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 15, pages 271-283, Springer.
    14. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
    15. Meyr, H., 2009. "Customer Segmentation, Allocation Planning and Order Promising in Make-to-Stock Production," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 36061, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    16. Klaus Zoller, 1971. "Optimal Disaggregation of Aggregate Production Plans," Management Science, INFORMS, vol. 17(8), pages 533-549, April.
    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. Konstantin Kloos & Richard Pibernik & Benedikt Schulte, 2019. "Allocation planning in sales hierarchies with stochastic demand and service-level targets," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(4), pages 981-1024, December.
    2. Martin Albrecht, 2021. "Component Allocation in Make-to-stock Assembly Systems," SN Operations Research Forum, Springer, vol. 2(2), pages 1-19, June.
    3. Fleischmann, Moritz & Kloos, Konstantin & Nouri, Maryam & Pibernik, Richard, 2020. "Single-period stochastic demand fulfillment in customer hierarchies," European Journal of Operational Research, Elsevier, vol. 286(1), pages 250-266.

    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. Fleischmann, Moritz & Kloos, Konstantin & Nouri, Maryam & Pibernik, Richard, 2020. "Single-period stochastic demand fulfillment in customer hierarchies," European Journal of Operational Research, Elsevier, vol. 286(1), pages 250-266.
    2. Seitz, Alexander & Grunow, Martin & Akkerman, Renzo, 2020. "Data driven supply allocation to individual customers considering forecast bias," International Journal of Production Economics, Elsevier, vol. 227(C).
    3. Konstantin Kloos & Richard Pibernik & Benedikt Schulte, 2019. "Allocation planning in sales hierarchies with stochastic demand and service-level targets," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(4), pages 981-1024, December.
    4. Quante, R. & Fleischmann, M. & Meyr, H., 2009. "A Stochastic Dynamic Programming Approach to Revenue Management in a Make-to-Stock Production System," ERIM Report Series Research in Management ERS-2009-015-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    5. Ojha, Divesh & Sahin, Funda & Shockley, Jeff & Sridharan, Sri V., 2019. "Is there a performance tradeoff in managing order fulfillment and the bullwhip effect in supply chains? The role of information sharing and information type," International Journal of Production Economics, Elsevier, vol. 208(C), pages 529-543.
    6. Raul Oltra-Badenes & Hermenegildo Gil-Gomez & Jose M Merigo & Daniel Palacios-Marques, 2019. "Methodology and model-based DSS to managing the reallocation of inventory to orders in LHP situations. Application to the ceramics sector," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-19, July.
    7. Thomas L. Magnanti, 2021. "Optimization: From Its Inception," Management Science, INFORMS, vol. 67(9), pages 5349-5363, September.
    8. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Working Papers halshs-02320110, HAL.
    9. Waßmuth, Katrin & Köhler, Charlotte & Agatz, Niels & Fleischmann, Moritz, 2023. "Demand management for attended home delivery—A literature review," European Journal of Operational Research, Elsevier, vol. 311(3), pages 801-815.
    10. Hoto, R.S.V. & Matioli, L.C. & Santos, P.S.M., 2020. "A penalty algorithm for solving convex separable knapsack problems," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    11. Alarcón, F. & Alemany, M.M.E. & Ortiz, A., 2009. "Conceptual framework for the characterization of the order promising process in a collaborative selling network context," International Journal of Production Economics, Elsevier, vol. 120(1), pages 100-114, July.
    12. Lee, Zu-Hsu & Deng, Shiming & Lin, Beixin & Yang, James G.S., 2010. "Decision model and analysis for investment interest expense deduction and allocation," European Journal of Operational Research, Elsevier, vol. 200(1), pages 268-280, January.
    13. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 2019-09, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    14. Ben Ali, M. & D’Amours, S. & Gaudreault, J. & Carle, M-A., 2018. "Configuration and evaluation of an integrated demand management process using a space-filling design and Kriging metamodeling," Operations Research Perspectives, Elsevier, vol. 5(C), pages 45-58.
    15. Patriksson, Michael & Strömberg, Christoffer, 2015. "Algorithms for the continuous nonlinear resource allocation problem—New implementations and numerical studies," European Journal of Operational Research, Elsevier, vol. 243(3), pages 703-722.
    16. Bitran, Gabriel R. & Tirupati, Devanath., 1989. "Hierarchical production planning," Working papers 3017-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    17. Ewerhart, Christian & Cassola, Nuno & Valla, Natacha, 2012. "Overbidding in fixed rate tenders: The role of exposure risk," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 539-549.
    18. Baron, Opher & Callen, Jeffrey L. & Segal, Dan, 2023. "Does the bullwhip matter economically? A cross-sectional firm-level analysis," International Journal of Production Economics, Elsevier, vol. 259(C).
    19. Martello, Silvano & Pisinger, David & Toth, Paolo, 2000. "New trends in exact algorithms for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 325-332, June.
    20. Elcio Mendonça Tachizawa & Cristina Giménez, 2005. "Drivers and sources of supply flexibility: An exploratory study," Economics Working Papers 889, Department of Economics and Business, Universitat Pompeu Fabra.

    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:ejores:v:246:y:2015:i:2:p:462-470. 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/locate/eor .

    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.