IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v185y2008i1p1-46.html
   My bibliography  Save this article

A survey on the continuous nonlinear resource allocation problem

Author

Listed:
  • Patriksson, Michael

Abstract

No abstract is available for this item.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:185:y:2008:i:1:p:1-46
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(06)01221-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Dorit S. Hochbaum, 1994. "Lower and Upper Bounds for the Allocation Problem and Other Nonlinear Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 390-409, May.
    2. Edward P. Loane, 1971. "An Algorithm to Solve Finite Separable Single-Constrained Optimization Problems," Operations Research, INFORMS, vol. 19(6), pages 1477-1493, October.
    3. Jefferson, T. R. & Scott, C. H., 1979. "The analysis of entropy models with equality and inequality constraints," Transportation Research Part B: Methodological, Elsevier, vol. 13(2), pages 123-132, June.
    4. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    5. Paul H. Zipkin, 1980. "Simple Ranking Methods for Allocation of One Resource," Management Science, INFORMS, vol. 26(1), pages 34-43, January.
    6. Elton, Edwin J & Gruber, Martin J & Padberg, Manfred W, 1976. "Simple Criteria for Optimal Portfolio Selection," Journal of Finance, American Finance Association, vol. 31(5), pages 1341-1357, December.
    7. B. O. Koopman, 1956. "The Theory of Search. I. Kinematic Bases," Operations Research, INFORMS, vol. 4(3), pages 324-346, June.
    8. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 1995. "A Branch and Bound Algorithm for Integer Quadratic Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 109-116, February.
    9. Luss, Hanan, 1992. "Minimax resource allocation problems: Optimization and parametric analysis," European Journal of Operational Research, Elsevier, vol. 60(1), pages 76-86, July.
    10. Muralidharan S. Kodialam & Hanan Luss, 1998. "Algorithms for Separable Nonlinear Resource Allocation Problems," Operations Research, INFORMS, vol. 46(2), pages 272-284, April.
    11. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    12. L. R. Ford, Jr. & D. R. Fulkerson, 1958. "A Suggested Computation for Maximal Multi-Commodity Network Flows," Management Science, INFORMS, vol. 5(1), pages 97-101, October.
    13. Jong-Shi Pang, 1980. "A New and Efficient Algorithm for a Class of Portfolio Selection Problems," Operations Research, INFORMS, vol. 28(3-part-ii), pages 754-767, June.
    14. J. M. Danskin, 1962. "A Game Theory Model of Convoy Routing," Operations Research, INFORMS, vol. 10(6), pages 774-785, December.
    15. John M. Danskin, 1962. "A Theory of Reconnaissance: I," Operations Research, INFORMS, vol. 10(3), pages 285-299, June.
    16. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    17. Samuel Zahl, 1963. "An Allocation Problem with Applications to Operations Research and Statistics," Operations Research, INFORMS, vol. 11(3), pages 426-441, June.
    18. B. O. Koopman, 1956. "Fallacies in Operations Research," Operations Research, INFORMS, vol. 4(4), pages 422-430, August.
    19. 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.
    20. Arthur M. Geoffrion, 1970. "Elements of Large-Scale Mathematical Programming Part I: Concepts," Management Science, INFORMS, vol. 16(11), pages 652-675, July.
    21. Bernard O. Koopman, 1953. "The Optimum Distribution of Effort," Operations Research, INFORMS, vol. 1(2), pages 52-63, February.
    22. Jucker, James V. & de Faro, Clovis, 1975. "A Simple Algorithm for Stone's Version of the Portfolio Selection Problem," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(5), pages 859-870, December.
    23. N. Maculan & C.P. Santiago & E.M. Macambira & M.H.C. Jardim, 2003. "An O(n) Algorithm for Projecting a Vector on the Intersection of a Hyperplane and a Box in Rn," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 553-574, June.
    24. William Karush, 1962. "A General Algorithm for the Optimal Distribution of Effort," Management Science, INFORMS, vol. 9(1), pages 50-72, October.
    25. Lotito, Pablo A., 2006. "Issues in the implementation of the DSD algorithm for the traffic assignment problem," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1577-1587, December.
    26. Stuart Smith & Leon Lasdon, 1992. "Solving Large Sparse Nonlinear Programs Using GRG," INFORMS Journal on Computing, INFORMS, vol. 4(1), pages 2-15, February.
    27. Lalitha Sanathanan, 1971. "On an Allocation Problem with Multistage Constraints," Operations Research, INFORMS, vol. 19(7), pages 1647-1663, December.
    28. William Karush, 1958. "On a Class of Minimum-Cost Problems," Management Science, INFORMS, vol. 4(2), pages 136-153, January.
    29. Norman Zadeh, 1970. "Note--A Note on the Cyclic Coordinate Ascent Method," Management Science, INFORMS, vol. 16(9), pages 642-644, May.
    30. Hugh Everett, 1963. "Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources," Operations Research, INFORMS, vol. 11(3), pages 399-417, June.
    31. Cote, Gilles & Laughton, Michael A., 1984. "Large-scale mixed integer programming: Benders-type heuristics," European Journal of Operational Research, Elsevier, vol. 16(3), pages 327-333, June.
    32. Paul Glasserman, 1996. "Allocating Production Capacity Among Multiple Products," Operations Research, INFORMS, vol. 44(5), pages 724-734, October.
    33. Jeff Kennington & Mohamed Shalaby, 1977. "An Effective Subgradient Procedure for Minimal Cost Multicommodity Flow Problems," Management Science, INFORMS, vol. 23(9), pages 994-1004, May.
    34. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    35. John D. Kettelle, 1962. "Least-Cost Allocations of Reliability Investment," Operations Research, INFORMS, vol. 10(2), pages 249-265, April.
    36. Arthur M. Geoffrion, 1970. "Primal Resource-Directive Approaches for Optimizing Nonlinear Decomposable Systems," Operations Research, INFORMS, vol. 18(3), pages 375-403, June.
    37. Stella Dafermos & Anna Nagurney, 1989. "Supply and Demand Equilibration Algorithms for a Class of Market Equilibrium Problems," Transportation Science, INFORMS, vol. 23(2), pages 118-124, May.
    38. Soren S. Nielsen & Stavros A. Zenios, 1993. "A Massively Parallel Algorithm for Nonlinear Stochastic Network Problems," Operations Research, INFORMS, vol. 41(2), pages 319-337, April.
    39. Arthur M. Geoffrion, 1970. "Elements of Large Scale Mathematical Programming Part II: Synthesis of Algorithms and Bibliography," Management Science, INFORMS, vol. 16(11), pages 676-691, July.
    40. Hau L. Lee & William P. Pierskalla, 1988. "Mass Screening Models for Contagious Diseases with No Latent Period," Operations Research, INFORMS, vol. 36(6), pages 917-928, December.
    41. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 1996. "Conditional subgradient optimization -- Theory and applications," European Journal of Operational Research, Elsevier, vol. 88(2), pages 382-403, January.
    42. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    43. Gabriel R. Bitran & Elizabeth A. Haas & Arnoldo C. Hax, 1981. "Hierarchical Production Planning: A Single Stage System," Operations Research, INFORMS, vol. 29(4), pages 717-743, August.
    44. B. O. Koopman, 1956. "The Theory of Search. II. Target Detection," Operations Research, INFORMS, vol. 4(5), pages 503-531, October.
    45. Bretthauer, Kurt M. & Ross, Anthony & Shetty, Bala, 1999. "Nonlinear integer programming for optimal allocation in stratified sampling," European Journal of Operational Research, Elsevier, vol. 116(3), pages 667-680, August.
    46. Gabriel R. Bitran & Susana V. Mondschein, 1996. "Mailing Decisions in the Catalog Sales Industry," Management Science, INFORMS, vol. 42(9), pages 1364-1381, September.
    47. N/A, 1959. "Current Research," Journal of Conflict Resolution, Peace Science Society (International), vol. 3(2), pages 184-187, June.
    48. Stone, Bernell K., 1973. "A Linear Programming Formulation of the General Portfolio Selection Problemâ€," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(4), pages 621-636, September.
    49. Aardal, Karen & Larsson, Torbjorn, 1990. "A benders decomposition based heuristic for the hierarchical production planning problem," European Journal of Operational Research, Elsevier, vol. 45(1), pages 4-14, March.
    50. Smith, Adam, 1776. "An Inquiry into the Nature and Causes of the Wealth of Nations," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number smith1776.
    51. B. O. Koopman, 1979. "An Operational Critique of Detection Laws," Operations Research, INFORMS, vol. 27(1), pages 115-133, February.
    52. A. M. Geoffrion, 1969. "An Improved Implicit Enumeration Approach for Integer Programming," Operations Research, INFORMS, vol. 17(3), pages 437-454, June.
    53. Gabriel R. Bitran & Susana V. Mondschein, 1996. "Inventory Management in Catalog Sales Companies," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 274-288, August.
    54. Steven Cosares & Dorit S. Hochbaum, 1994. "Strongly Polynomial Algorithms for the Quadratic Transportation Problem with a Fixed Number of Sources," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 94-111, February.
    55. Kurt M. Bretthauer & Bala Shetty, 1995. "The Nonlinear Resource Allocation Problem," Operations Research, INFORMS, vol. 43(4), pages 670-683, August.
    56. Michael H. Schneider & Stavros A. Zenios, 1990. "A Comparative Study of Algorithms for Matrix Balancing," Operations Research, INFORMS, vol. 38(3), pages 439-455, June.
    57. Gabriel R. Bitran & Devanath Tirupati, 1989. "Tradeoff Curves, Targeting and Balancing in Manufacturing Queueing Networks," Operations Research, INFORMS, vol. 37(4), pages 547-564, August.
    58. K. S. Srikantan, 1963. "A Problem in Optimum Allocation," Operations Research, INFORMS, vol. 11(2), pages 265-273, April.
    59. F. H. Knight, 1924. "Some Fallacies in the Interpretation of Social Cost," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 38(4), pages 582-606.
    60. Harvey J. Greenberg & William P. Pierskalla, 1970. "Surrogate Mathematical Programming," Operations Research, INFORMS, vol. 18(5), pages 924-939, October.
    61. Soren S. Nielsen & Stavros A. Zenios, 1992. "Massively Parallel Algorithms for Singly Constrained Convex Programs," INFORMS Journal on Computing, INFORMS, vol. 4(2), pages 166-181, May.
    62. Bertram Klein, 1955. "Direct Use of Extremal Principles in Solving Certain Optimizing Problems Involving Inequalities," Operations Research, INFORMS, vol. 3(2), pages 168-175, May.
    63. Torbjörn Larsson & Michael Patriksson, 1992. "Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 26(1), pages 4-17, February.
    64. S M Macgill, 1979. "Convergence and Related Properties for a Modified Biproportional Matrix Problem," Environment and Planning A, , vol. 11(5), pages 499-506, May.
    65. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    66. 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.
    67. Stefan M. Stefanov, 2004. "Polynomial algorithms for projecting a point onto a region defined by a linear constraint and box constraints in â„ n," Journal of Applied Mathematics, Hindawi, vol. 2004, pages 1-23, January.
    68. Awi Federgruen & Henry Groenevelt, 1986. "Optimal Flows in Networks with Multiple Sources and Sinks, with Applications to Oil and Gas Lease Investment Programs," Operations Research, INFORMS, vol. 34(2), pages 218-225, April.
    69. Minoux, M., 1984. "A polynomial algorithm for minimum quadratic cost flow problems," European Journal of Operational Research, Elsevier, vol. 18(3), pages 377-387, December.
    70. Scott Shorey Brown, 1980. "Optimal Search for a Moving Target in Discrete Time and Space," Operations Research, INFORMS, vol. 28(6), pages 1275-1289, December.
    71. Lamond, B. & Stewart, N. F., 1981. "Bregman's balancing method," Transportation Research Part B: Methodological, Elsevier, vol. 15(4), pages 239-248, August.
    72. Vidal, ReneVictor Valqui, 1984. "A graphical method to solve a family of allocation problems," European Journal of Operational Research, Elsevier, vol. 17(1), pages 31-34, July.
    73. Bretthauer, Kurt M., 1996. "Capacity planning in manufacturing and computer networks," European Journal of Operational Research, Elsevier, vol. 91(2), pages 386-394, June.
    74. Awi Federgruen & Paul Zipkin, 1984. "A Combined Vehicle Routing and Inventory Allocation Problem," Operations Research, INFORMS, vol. 32(5), pages 1019-1037, October.
    75. D. J. Laughhunn, 1970. "Quadratic Binary Programming with Application to Capital-Budgeting Problems," Operations Research, INFORMS, vol. 18(3), pages 454-461, June.
    76. Gabriel R. Bitran & Elizabeth A. Haas & Arnoldo C. Hax, 1982. "Hierarchical Production Planning: A Two-Stage System," Operations Research, INFORMS, vol. 30(2), pages 232-251, April.
    77. Bernard O. Koopman, 1957. "The Theory of Search," Operations Research, INFORMS, vol. 5(5), pages 613-626, October.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Zhang, Bin & Hua, Zhongsheng, 2008. "A unified method for a class of convex separable nonlinear knapsack problems," European Journal of Operational Research, Elsevier, vol. 191(1), pages 1-6, November.
    4. Syam, Siddhartha S., 1998. "A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals," European Journal of Operational Research, Elsevier, vol. 108(1), pages 196-207, July.
    5. 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.
    6. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 2003. "A specially structured nonlinear integer resource allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 770-792, October.
    7. DePaolo, Concetta A. & Rader, David Jr., 2007. "A heuristic algorithm for a chance constrained stochastic program," European Journal of Operational Research, Elsevier, vol. 176(1), pages 27-45, January.
    8. De Waegenaere, A.M.B. & Wielhouwer, J.L., 2001. "A Partial Ranking Algorithm for Resource Allocation Problems," Other publications TiSEM 8b2e0185-36f9-43df-8a3d-d, Tilburg University, School of Economics and Management.
    9. Kameshwaran, S. & Narahari, Y., 2009. "Nonconvex piecewise linear knapsack problems," European Journal of Operational Research, Elsevier, vol. 192(1), pages 56-68, January.
    10. 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.
    11. Bretthauer, Kurt M. & Ross, Anthony & Shetty, Bala, 1999. "Nonlinear integer programming for optimal allocation in stratified sampling," European Journal of Operational Research, Elsevier, vol. 116(3), pages 667-680, August.
    12. Friedrich, Ulf & Münnich, Ralf & de Vries, Sven & Wagner, Matthias, 2015. "Fast integer-valued algorithms for optimal allocations under constraints in stratified sampling," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 1-12.
    13. De Waegenaere, A.M.B. & Wielhouwer, J.L., 2001. "A Partial Ranking Algorithm for Resource Allocation Problems," Discussion Paper 2001-40, Tilburg University, Center for Economic Research.
    14. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    15. 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.
    16. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    17. K. C. Kiwiel, 2008. "Variable Fixing Algorithms for the Continuous Quadratic Knapsack Problem," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 445-458, March.
    18. Thomas L. Magnanti, 2021. "Optimization: From Its Inception," Management Science, INFORMS, vol. 67(9), pages 5349-5363, September.
    19. Torrealba, E.M.R. & Silva, J.G. & Matioli, L.C. & Kolossoski, O. & Santos, P.S.M., 2022. "Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 46-59.
    20. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.

    More about this item

    Statistics

    Access and download statistics

    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:185:y:2008:i:1:p:1-46. 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.