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Resource Allocation Problems

  • Chapter
Handbook of Combinatorial Optimization

Abstract

The resource allocation problem seeks to find an optimal allocation of a fixed amount of resources to activities so as to minimize the cost incurred by the allocation. A simplest form of the problem is to minimize a separable convex function under a single constraint concerning the total amount of resources to be allocated. The amount of resources to be allocated to each activity is treated as a continuous or integer variable, depending on the cases. This can be viewed as a special case of the nonlinear programming problem or the nonlinear integer programming problem.

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References

  1. C.C. Aggarwal, J.L. Wolf and P.S. Yu, On optimal batching policies for videoon-demand storage servers, Proc. of IEEE International Conference on Multimedia Computing and Systems, Hiroshima, Japan, 1996.

    Google Scholar 

  2. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin: Network Flows — Theory, Algorithms, and Applications,Prentice-Hall, 1993.

    Google Scholar 

  3. R.K. Ahuja and J.B. Orlin, A fast and simple algorithm for the maximum flow problem, Operations Research, Vol.37 (1990) 748–759.

    MathSciNet  Google Scholar 

  4. K. Ando and S. Fujishige, On structures of bisubmodular polyhedra. Mathematical Programming Vol. 74 (1996) 293–317.

    MATH  MathSciNet  Google Scholar 

  5. K. Ando, S. Fujishige and T. Naitoh, A greedy algorithm for minimizing a separable convex function over an integral bisubmodular polyhedron. Journal of the Operations Research Society of Japan Vol. 37 (1994) 188–196.

    MATH  MathSciNet  Google Scholar 

  6. K. Ando, S. Fujishige and T. Naitoh, A greedy algorithm for minimizing a separable convex function over a finite jump system. Journal of the Operations Research Society of Japan Vol. 38 (1995) 362–375.

    MATH  MathSciNet  Google Scholar 

  7. S. Baase, Computer Algorithms: Introduction to Design and Analysis,2nd Edition, Addison Wesley, 1988.

    Google Scholar 

  8. R. Baldick and F.F. Wu, Efficient integer optimization algorithms for optimal coordination of capacitators and regulators, IEEE Trans. on Power Systems, Vol. 5 (1990) 805–812.

    Google Scholar 

  9. L.M. Betts, J.R. Brown, and H. Luss, Minimax resource allocation for problems with ordering constraints, Naval Research Logistics, Vol. 41 (1994) 719–738.

    MATH  MathSciNet  Google Scholar 

  10. P.P. Bhatacharya, L. Georgiadis, P. Tsoucas, and I. Viniotis, Adaptive lexicographic optimization in multi-class M/GI/1 Queues, Mathematics of Operations Research, Vol. 18, No. 3 (1993) 705–740.

    MathSciNet  Google Scholar 

  11. G.R. Bitran and A.C. Hax, Disaggregation and resource allocation using convex knapsack problems with bounded variables, Management Science, Vol. 27 (1981) 431–441.

    MATH  MathSciNet  Google Scholar 

  12. G.R. Bitran and D. Tirupati, Tradeoff curves, targeting and balancing in manufacturing queueing networks, Operations Research, Vol. 37 (1989) 547–564.

    MATH  MathSciNet  Google Scholar 

  13. G.R. Bitran and D. Tirupati, Capacity planning in manufacturing networks, Annals of Operations Research, Vol. 17 (1989) 119–135.

    MATH  Google Scholar 

  14. K.M. Bretthauer and B. Shetty, The nonlinear resource allocation problem, Operations Research, Vol. 43, No. 4 (1995) 670–683.

    MATH  MathSciNet  Google Scholar 

  15. K.M. Bretthauer and B. Shetty, Quadratic resource allocation with generalized upper bounds, Operations Research Letters, Vol. 20 (1997) 51–57.

    MATH  MathSciNet  Google Scholar 

  16. K.M. Bretthauer, B. Shetty and S. Syam, Branch and bound algorithm for integer quadratic knapsack problem, ORSA J. Computing,Vol. 7 (1995) 109–116.

    MATH  MathSciNet  Google Scholar 

  17. K.M. Bretthauer, B. Shetty, S. Syam and S. White, A model for resource constrained production and inventory management, Decision Sciences, Vol. 25 (1994) 561–580.

    Google Scholar 

  18. J.R. Brown, Solving knapsack sharing with general tradeoff functions, Mathematical Programming, Vol. 51 (1991) 55–73.

    MATH  Google Scholar 

  19. J.R. Brown, Bounded knapsack sharing, Mathematical Programming, Vol. 67, No. 3 (1994) 343–382.

    MATH  MathSciNet  Google Scholar 

  20. P. Brucker, An O(n) algorithm for quadratic knapsack problems, Operations Research Letters, Vol. 3 (1984) 163–166.

    MATH  MathSciNet  Google Scholar 

  21. J.A. Buzacott and J.G. Shanthikumar, Stochastic Models for Manufacturing Systems, Prentice-Hall, New Jersey, 1993.

    Google Scholar 

  22. M.A. Cohen, P.R. Kleindorfer and H.L. Lee, Near-optimal service-constrained stocking policies for spare parts, Operations Research, Vol. 37 No. 1 (1989) 104–117.

    MATH  MathSciNet  Google Scholar 

  23. W. Cook, A.M.H. Gerards, A. Schrijver, and E. Tardos, Sensitivity results in integer linear programming, Mathematical Programming, Vol. 34 (1986) 251–264.

    MATH  MathSciNet  Google Scholar 

  24. S. Cosares and D.S. Hochbaum, Strongly polynomial algorithms for the quadratic transportation problem with fixed number of sources, Mathematics of Operations Research, Vol. 19 No. 1 (1994) 94–111.

    MATH  MathSciNet  Google Scholar 

  25. G.B. Dantzig, Linear Programming and Extensions: Princeton University Press, Princeton, N.J., 1963.

    Google Scholar 

  26. M.E. Dyer and A.M. Frieze, On an optimization problem with nested constraints, Discrete Applied Mathematics,Vol. 26 (1990) 159–173.

    MATH  MathSciNet  Google Scholar 

  27. M.E. Dyer and and J. Walker, An algorithm for a separable integer programming problem with cumulatively bounded variables, Discrete Applied Mathematics, Vol. 16 (1987) 135–149.

    MATH  MathSciNet  Google Scholar 

  28. J. Edmonds and R. Giles, J. Edmonds, A mini-max relation for submodular functions on graphs, Annals of Discrete Mathematics, Vol. 1 (1977) 185–204.

    MathSciNet  Google Scholar 

  29. H.A. Eiselt, Continuous maximin knapsack problems with GLB constraints, Mathematical Programming, Vol. 36 (1986) 114–121.

    MATH  MathSciNet  Google Scholar 

  30. J.E. Eu, The sampling resource allocation problem, IEEE Trans. on Communications, Vol. 39 No. 9 (1991) 1277–1279.

    Google Scholar 

  31. A. Federguruen and H. Groenevelt, The greedy procedure for resource allocation problems - necessary and sufficient conditions for optimality, Operations Research, Vol. 34 (1986) 909–918.

    MathSciNet  Google Scholar 

  32. L.R. Ford and D.R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, New Jersey, 1962.

    Google Scholar 

  33. B.L. Fox, Discrete optimization via marginal analysis, Management Science, Vol. 13 (1966) 210–216.

    Google Scholar 

  34. G.N. Frederickson and D.B. Johnson, The complexity of selection and ranking in X + Y and matrices with sorted columns, Journal of Computer and System Sciences, Vol. 24 (1982) 197–208.

    MATH  MathSciNet  Google Scholar 

  35. S. Fujishige, Lexicographically optimal base of a polymatroid with respect to a weight vector, Mathematics of Operations Research, Vol. 21 (1980) 186–196.

    MathSciNet  Google Scholar 

  36. S. Fujishige: Linear and nonlinear optimization problems with submodular constraints. In: Mathematical Programming (M. Iri and T. Tanabe, eds., KTK Scientific Publishers, Tokyo, 1989) 203–225.

    Google Scholar 

  37. S. Fujishige, Submodular Functions and Optimization,North-Holland, 1991.

    MATH  Google Scholar 

  38. S. Fujishige, A min-max theorem for bisubmodular polyhedra, SIAM Journal on Discrete Mathematics, Vol. 10 No. 2 (1997) 294–308.

    MATH  MathSciNet  Google Scholar 

  39. S. Fujishige, N. Katoh and T. Ichimori, The fair resource allocation problem with submodular constraints, Mathematics of Operations Research, Vol. 13, No. 1 (1988) 164–173.

    MATH  MathSciNet  Google Scholar 

  40. H.N. Gabow and R.E. Tarjan, Linear time algorithm for a special case of disjoint set union, Journal of Computer and System Sciences, Vol. 30 (1985) 209–221.

    MATH  MathSciNet  Google Scholar 

  41. Z. Galil and N. Megiddo, A fast selection algorithm and the problem of optimum distribution of effort, Journal of ACM, Vol. 26 (1979) 58–64.

    MATH  MathSciNet  Google Scholar 

  42. G. Gallo, M.E. Grigoriadis and R.E. Tarjan, A fast parametric maximum flow algorithm and applications, SIAM Journal on Computing,Vol. 18 (1989) 30–55.

    MATH  MathSciNet  Google Scholar 

  43. A. Galperin and Z. Waksman, A separable integer programming problem equivalent to its continual version, J. Comput. Appl. Math., Vol. 7 (1981) 173–179.

    MATH  MathSciNet  Google Scholar 

  44. H. Groenevelt, Two algorithms for maximizing a separable concave function over a polymatroid feasible region, European Journal of Operational Research,Vol. 54 (1991) 227–236.

    MATH  Google Scholar 

  45. O. Gross, A class of discrete type minimization problems, RM-1644, RAND-Corp., 1956.

    Google Scholar 

  46. M. Grötschel, L. Lovdsz, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization (Algorithms and Combinatorics 2), Springer-Verlag, Berlin, 1988.

    Google Scholar 

  47. O.K. Gupta and A. Ravindran, Branch and bound experiments in convex nonlinear integer programming problems, Management Science, Vol. 31 (1985) 1533–1546.

    MATH  MathSciNet  Google Scholar 

  48. S.T. Hackman and L.K. Platzman, Allocating items to an automated storage and retrieval systems, HE Transactions, Vol. 22 (1989) 7–14.

    Google Scholar 

  49. S.T. Hackman and L.K. Platzman, Near-optimal solution of generalized resource allocation problems with large capacities, Operations Research, Vol. 38, No. 5 (1990) 902–910.

    MATH  MathSciNet  Google Scholar 

  50. D.S. Hochbaum, Polynomial algorithms for convex network optimization,” in Network Optimization Problems: Algorithms, Complexity and Applications, edited by D. Du and P. M. Pardalos, World Scientific, (1993) 63–92.

    Google Scholar 

  51. D.S. Hochbaum, Lower and upper bounds for the allocation problem and other nonlinear optimization problems, Mathematics of Operations Research,Vol. 19, No. 2 (1994) 390–409.

    MATH  MathSciNet  Google Scholar 

  52. D.S. Hochbaum, A nonlinear knapsack problem, Operations Research Letters, Vol. 17 (1995) 103–110.

    MATH  MathSciNet  Google Scholar 

  53. D.S. Hochbaum and S. Hong, About strongly polynomial time algorithms for quadratic optimization over submodular constraints, Mathematical Programming Vol. 69 (1995) 269–309.

    MATH  MathSciNet  Google Scholar 

  54. D.S. Hochbaum, R. Shamir and J.G. Shanthikumar, A polynomial algorithm for an integer quadratic nonseparable transportation problem, Mathematical Programming, Vol. 55 No. 3 (1992) 359–372.

    MATH  MathSciNet  Google Scholar 

  55. D.S. Hochbaum and J.G. Shanthikumar, Nonlinear separable optimization is not much harder than linear optimization, Journal of ACM, Vol. 37, No. 4 (1990) 843–862.

    MATH  MathSciNet  Google Scholar 

  56. A.J. Hoffman, A generalization of max-flow min-cut, Mathematical Programming, Vol. 6 (1974) 352–359.

    MATH  MathSciNet  Google Scholar 

  57. T.C. Hu, Integer Programming and Network Flows,Addison-Wesley, New-York, 1969.

    MATH  Google Scholar 

  58. T. Ibaraki and N. Katoh, Resource Allocation Problems: Algorithmic Approaches, The MIT Press, Cambridge, MA, 1988.

    Google Scholar 

  59. T. Ichimori, A two-resource allocation problem with a quadratic objective function, Transactions of the Japan Society for Industrial and Applied Mathematics, Vol. 3 No. 3 (1993) 199–215 (in Japanese).

    Google Scholar 

  60. T. Ichimori and N. Katoh, A two-commodity sharing problem on networks, Networks, Vol. 21 (1991) 547–564.

    MATH  MathSciNet  Google Scholar 

  61. T. Ichimori and N. Katoh, Minimum variance discrete resource allocation problem, unpublished manuscript (in Japanese) 1997.

    Google Scholar 

  62. S. Karabati, P. Kouvelis, and G. Yu, The discrete allocation problem in flow lines, Management Science, Vol. 41 No. 9 (1995) 1417–1430.

    MATH  Google Scholar 

  63. S. Karabati, P. Kouvelis, and G. Yu, A min-max-sum resource allocation problem and its application, Working Paper 1996–08, Koc University, Istanbul, Turkey, 1996.

    Google Scholar 

  64. A.V. Karzanov and S.T. McCormick, Polynomial methods for separable convex optimization in totally unimodular linear spaces with applications, SIAM J. on Computing, Vol. 26 No. 4 (1997) 1245–1275.

    MATH  MathSciNet  Google Scholar 

  65. N. Katoh, An e-approximation scheme for minimum variance problems, Journal of the Operations Research Society of Japan, Vol. 33 No. 1 (1990) 46–65.

    MATH  MathSciNet  Google Scholar 

  66. N. Katoh, T. Ibaraki and H. Mine, A polynomial time algorithm for the resource allocation problem with a convex objective function, Journal of Operational Research Society, Vol. 30 (1979) 449–455.

    MATH  MathSciNet  Google Scholar 

  67. W. Kim, A new way to compute the product and join of relations, Proc. of the ACM SIGMOD Conference, Santa Monica, 1980.

    Google Scholar 

  68. J.H. King, Allocation of scarce resources in manufacturing facilities, AT&T Technical Journal, Vol. 68, No. 3 (1989) 103–113.

    Google Scholar 

  69. V. King, S. Rao and R. Tarjan, A faster deterministic maximum flow algorithm, Proc. of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, (1992) 157–163.

    Google Scholar 

  70. R.S. Klein and H. Luss, Minimax resource allocation with tree structured substitutable resources, Operations Research, Vol. 39 No. 2 (1991) 285–295.

    MATH  Google Scholar 

  71. R.S. Klein, H. Luss, and U.G. Rothblum, Minimax resource allocation problems with resource-substitutions represented by graphs, Operations Research Vol. 41 (1993) 959–971.

    MATH  MathSciNet  Google Scholar 

  72. R.S. Klein, H. Luss, and U.G. Rothblum, Relaxation-based algorithms for minimax optimization problems with resource allocation applications, Mathematical Programming, Vol. 64 (1994) 337–363.

    MATH  MathSciNet  Google Scholar 

  73. R.S. Klein, H. Luss, and U.G. Rothblum, Multiperiod allocation of substitutable resources, European J. of Operational Research, Vol. 85 (1995) 488–503.

    MATH  Google Scholar 

  74. R.S. Klein, H. Luss, and D.R. Smith, A lexicographic minimax algorithm for multiperiod resource allocation, Mathematical Programming, Vol. 55 (1992) 213–234.

    MATH  MathSciNet  Google Scholar 

  75. M.S. Kodialam and H. Luss, Algorithms for separable nonlinear resource allocation problems, to appear in Operations Research.

    Google Scholar 

  76. B.O. Koopman, The optimum distribution of effort, Operations Research, Vol. 1 (1953) 52–63.

    MathSciNet  Google Scholar 

  77. P. Kubat and H.S. Koch, Managing test-procedures to achieve reliable software, IEEE Transactions on Reliability, Vol. R-32 (1983) 299–303.

    Google Scholar 

  78. T. Kuno, H. Konno and E. Zemel, A linear time algorithm for solving continuous knapsack problems, Operations Research Letters, Vol. 10 (1991) 23–26.

    MATH  MathSciNet  Google Scholar 

  79. H.L. Lee and W.P. Pierskalla, Mass screening models for contagious diseases with no latent period, Operations Research, Vol. 36 No. 1 (1988) 917–928.

    MATH  MathSciNet  Google Scholar 

  80. D. Li and Y. Y. Haimes, A decomposition method for optimization of large-system reliability, IEEE Trans. on Reliability, Vol. 41 No. 2, (1992) 183–189.

    MATH  Google Scholar 

  81. L. Lovász, Submodular functions and convexity, in: A. Bachem, M. Grötschel and B. Korte, eds., Mathematical Programming - The State of the Art (Springer-Verlag, Berlin, 1983) 235–257.

    Google Scholar 

  82. H. Luss, An algorithm for separable nonlinear minimax problems, Operations Research Letters, Vol. 6 (1987) 159–162.

    MATH  MathSciNet  Google Scholar 

  83. H. Luss, A nonlinear minimax allocation problem with multiple knapsack constraints, Operations Research Letters, Vol. 10 (1991) 183–187.

    MATH  MathSciNet  Google Scholar 

  84. H. Luss, Minimax resource allocation problems: Optimization and parametric analysis, European J. of Operational Research Vol. 60 (1992) 76–86.

    MATH  Google Scholar 

  85. H. Luss and M.B. Rosenwein, Multiperiod resource allocation with a smoothing objective, Naval Research Logistics,Vol. 42 (1995) 1007–1020.

    MATH  Google Scholar 

  86. H. Luss and D.R Smith, Resource allocation among competing activities: A lexicographic minimax approach, Operations Research Letters,Vol. 5 (1986) 227–231.

    MATH  MathSciNet  Google Scholar 

  87. H. Luss and D.R Smith, Multiperiod allocation of limited resources: A mini-max approach, Naval Research Logistics, Vol. 35 (1988) 493–501.

    MATH  MathSciNet  Google Scholar 

  88. N. Megiddo and A. Tamir, Linear time algorithms for some separable quadratic programming problems, Operations Research Letters, Vol. 13 (1993) 203–211.

    MATH  MathSciNet  Google Scholar 

  89. J.J. Moré and S.A. Vavadis, On the solution of concave knapsack problems, Mathematical Programming, Vol. 49 (1991) 397–411.

    MATH  Google Scholar 

  90. K. Murota, Convexity and Steinitz’s exchange property, Advances in Mathematics, Vol. 124 (1996) 272–311.

    MATH  MathSciNet  Google Scholar 

  91. K. Murota, Discrete convex analysis, to appear in Mathematical Programming.

    Google Scholar 

  92. K. Murota, Discrete convex analysis, to appear in Discrete Structure and Algorithms V, edited by S. Fijishige, Kindai-Kagakusha, 1998 (in Japanese).

    Google Scholar 

  93. K. Namikawa and T. Ibaraki, An algorithm for the fair resource allocation problem with a submodular constraint, Japan J. of Industrial and Applied Mathematics, Vol. 8 (1991) 377–387.

    MATH  MathSciNet  Google Scholar 

  94. Q.C. Nguyen and R.E. Stone, A multiperiod resource allocation problem with storable and substitutable resources, Management Science, Vol. 39 (1993) 964–974.

    MATH  Google Scholar 

  95. S.S. Nielsen and S.A. Zenious, Massively parallel algorithms for singly constrained convex program, ORSA J. Computing, Vol. 4 (1992) 166–181.

    MATH  Google Scholar 

  96. H. Ohtera and S. Yamada, Optimal allocation & control problems for software-testing resources, IEEE Trans. on Reliability,Vol. 39 No. 2, (1990) 171–176.

    MATH  Google Scholar 

  97. J.-S. Pang and C.-S. Yu, A min-max resource allocation problem with substitutions, European Journal of Operational Research, Vol. 41 (1989) 218–223.

    MATH  MathSciNet  Google Scholar 

  98. C.H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, N.J., 1982.

    MATH  Google Scholar 

  99. P.M. Pardalos and N. Kovoor, An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds, Mathematical Programming, Vol. 46 (1990) 321–328.

    MATH  MathSciNet  Google Scholar 

  100. P.M. Pardalos, Y. Ye and C.G. Han, Algorithms for the solution of quadratic knapsack problems, Linear Algebra Appl., Vol. 152 (1991) 69–91.

    MATH  MathSciNet  Google Scholar 

  101. J. Renegar, On the worst case arithmetic complexity of approximation zeroes of polynomials, Journal of Complexity, Vol. 3 (1987) 9–113.

    MathSciNet  Google Scholar 

  102. A.G. Robinson, N. Jiang and C.S. Lerme, On the continuous quadratic knapsack problem, Mathematical Programming, Vol. 55 (1992) 99–108.

    MATH  MathSciNet  Google Scholar 

  103. J.G. Shanthikumar and D.D. Yao, Second-order stochastic properties in queueing systems, Proceedings of IEEE, Vol. 77 No. 1 (1989) 162–170.

    Google Scholar 

  104. J.G. Shanthikumar and D.D. Yao, Multiclass queueing systems: Polymatroidal structure and optimal scheduling control, Operations Research, Vol. 40 No. 2 (1992) 293–299.

    MathSciNet  Google Scholar 

  105. W. Shih, A new application of incremental analysis in resource allocations, Operational Research Quarterly, Vol. 25 (1974) 587–597.

    Google Scholar 

  106. A. Shioura, Minimization of an M-convex function, to appear in Discrete Applied Mathematics.

    Google Scholar 

  107. H.S. Stone, J. Turek, and J.L. Wolf, Optimal partitioning of cache memory, IEEE Transactions on Computers, Vol. 41 No. 9 (1992) 1054–1068.

    Google Scholar 

  108. A. Tamir, A strongly polynomial algorithm for minimum convex separable quadratic cost flow problems on series-parallel networks, Mathematical Programming, Vol. 59 (1993) 117–132.

    MATH  MathSciNet  Google Scholar 

  109. C.S. Tang, A max-min allocation problem: Its solutions and applications, Operations Research, Vol. 36 (1988) 359–367.

    MATH  MathSciNet  Google Scholar 

  110. A.N. Tantawi, D. Twosely, and J.L. Wolf, An algorithm for a class constrained resource allocation problem, 1987.

    Google Scholar 

  111. D. Thiébaut, H.S. Stone, and J.L. Wolf, Improving disk cache hit-ratios through cache partitioning, IEEE Transactions on Computers, Vol. 41 No. 9, (1992) 665–676.

    Google Scholar 

  112. J. Turek, W. Ludwig, J.L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelsohn, and P.S. Yu, Scheduling parallelizable tasks to minimize average response time, Proc. of ACM Symp. on Parallel Algorithms and Architectures, 1994.

    Google Scholar 

  113. J. Turek, J.L. Wolf, K.R. Pattipati, and P.S. Yu, Scheduling parallelizable tasks: Putting it all on the shelf, Proc. of ACM SIGMETRICS ’92, 225–236, June 1992.

    Google Scholar 

  114. J. Turek, J.L. Wolf, and P.S. Yu, Approximate algorithms for scheduling parallelizable tasks, Proc. of the 4 th Annual Symposium on Parallel Algorithms and Architectures, San Diego, 323–332, June 1992.

    Google Scholar 

  115. J.A. Ventura and C.M. Klein, A note on multi-item inventory systems with limited capacity, Operations Research Letters, Vol. 7 (1988) 71–75.

    MATH  MathSciNet  Google Scholar 

  116. J.L. Wolf, D.M. Dias, and P.S. Yu, A parallel sort merge join algorithm for managing data skew, IEEE Trans. on Parallel and Distributed Systems,Vol. 4 No. 1 (1993) 70–86.

    Google Scholar 

  117. J.L. Wolf, B.R. Iyer, K.R. Pattipati, and P.S. Yu, Optimal buffer partitioning for the nested block join algorithm, Proc. of 7th International Conference on Data Engineering, 1991, 510–519.

    Google Scholar 

  118. J.L. Wolf, P.L. Yu, and H. Shachnai, DASD dancing: A disk load balancing optimization scheme for video-on-demand computer systems, Proc. of ACM Sigmetrics Conference, Ottawa, Canada, 1995.

    Google Scholar 

  119. D.D. Yao, Optimal run quantities for an assembly system with random yields, IIE Transactions,Vol. 20 No. 4 (1988) 399–403.

    Google Scholar 

  120. G. Yu and P. Kouvelis, On min-max optimization of a collection of classical discrete optimization problems, in Minimax and Applications,D.-Z. Du and P.M. Pardalos (eds.), (1995) 157–171.

    Google Scholar 

  121. U. Yüceer, Marginal allocation algorithm for nonseparable functions, unpublished manuscript 1995.

    Google Scholar 

  122. Tak-S. Yum, Mon-S. Chen, and Yiu-W. Leung, Bandwidth allocation for multimedia teleconferences, Proc. of ICC’91, 1991, 852–858.

    Google Scholar 

  123. P.H. Zipkin, Simple ranking methods for allocation of one resource, Management Science, Vol. 26 (1980) 34–43.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Architecture and Architectural Systems Graduate School of Engineering, Kyoto University, Sakyo, Kyoto, Japan, 606-8501

    Naoki Katoh

  2. Department of Applied Mathematics and Physics Graduate School of Informatics, Kyoto University, Sakyo, Kyoto, Japan, 606-8501

    Toshihide Ibaraki

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  1. Naoki Katoh
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Editors and Affiliations

  1. University of Minnesota, Minneapolis, USA

    Ding-Zhu Du

  2. University of Florida, Gainesville, USA

    Panos M. Pardalos

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Katoh, N., Ibaraki, T. (1998). Resource Allocation Problems. In: Du, DZ., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0303-9_14

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