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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/103910


    Title: 背包問題之研究
    Authors: 莊照明
    Contributors: 姚興台
    莊照明
    Date: 1984
    Issue Date: 2016-11-14 15:02:20 (UTC+8)
    Abstract: 第一章 緒論1
    第一節 前言1
    第二節 研究動機與目的1
    第三節 內容結構2
    第二章 背包問題5
    第一節 簡介5
    第二節 求解法則6
    第三節 週期性質16
    第四節 將整數規劃問題化為背包問題20
    第五節 背包問題在裁紙問題上之應用24
    第三章 0 - 1背包問題31
    第一節 縮減法則32
    第二節 分支定界法36
    第三節 將0 - 1背包問題應用到一般化的分派問題43
    第四節 電腦實例47
    第四節 摺疊的0 - 1背包問題57
    第一節 簡介57
    第二節 一些定理59
    第三節 求解決則65
    第四節 實例68
    第五章 連續的摺疊背包問題71
    第一節 簡介71
    第二節 一些性質72
    第三節 分解定理78
    第四節 子問題及其一些性質80
    第五節 求解法則89
    第六節 實例92
    第六章 結論與建議95
    註解97
    參考資料99
    Reference: 1. Balas. E. “An additive algorithm for solving linear programs with zero-one variables”, Oper. Res. 13 ( 1965 ) : 517-546.
    2. Cabot, V. A. “ An enumeration algorithm for knapsack problems ” , Oper. Res. 18 ( 1970 ) : 306-311.
    3. Cooper. L. & D. I. Steinberg, Methods and Applications of Linear Programming, Philadelphia, London, Toronto, (1974 ).
    4. Dantzig, G. B. “Discrete variable extremum problems ” , Oper. Res. 5 ( 1957 ) 266-277.
    5. Denardo, E. V. Dynamic Programming : Models and Applications, Prentice-Hall, Englewood Cliffs, New Jersey, ( 1982 ).
    6. Garfinkel, R. & G. Nemhauser, Integer Programming , J. Wiley, New York, ( 1970 ).
    7. Gilmore. P. C. & R. E. Gomory, “ A linear programming approach to the cutting stock problem ” , Oper. Res. 11 ( 1961 ) : 849-859.
    8. Greenberg, H. & R. L. Hegerich, “ A branch search algorithm for the knapsack problem ” , Management Sci. 16 ( 1971 ) : 327-332.
    9. Hu. T. C. Integer Programming and Network Flows, Addison-Wesley, Reading, Massachusetts, ( 1969 ).
    10. Ingargiola, G. P. & J. F. Korsh, “ Reduction algorithm for zero-one single knapsack problems” , Management Sci. 20 ( 1973 ) 460-463.
    11. Kolesar, P. J. “ A branch and bonnd algorithm for the knapsack problem ”, Management Sci. 22 ( 1967 ) : 723-735.
    12. Posner, M. E. “The decomposition of nonlinear problems”, Mathematical Programming. 15 ( 1978 ) : 360-362.
    13. Posner. M. E. “The continuous collapsing knapsack problem” , Mathematical Programming 26 ( 1983 ) : 76-86.
    14. Posner, M. E. & M. Guignard, “The 0-1 collapsing knapsack problem” , Mathematical Programming 15 ( 1978 ) : 155- 161.
    15. Rochafellar, R. T. , Convex Analysis, Princeton U. Press, N. J. ( 1969 ).
    16. Ross, C. T. “ A branch and bound algorithm for the generalized assignment problem ”, Mathematical Programming 8 ( 1975 ) : 91-103.
    17. Taha, H. A., Integer Programming : Theory, Applications, and Computations, University of Arkansas Fayetteville. Arkansas, ( 1975 ).
    Relation: 國立政治大學
    統計研究所
    碩士
    72
    Data Type: thesis
    Appears in Collections:[Department of Statistics] Theses

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