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題名 二元結構動態規劃方法在多機排程問題上的應用
作者 董永寬
貢獻者 余千智
董永寬
日期 1987
上傳時間 4-May-2016 17:12:51 (UTC+8)
摘要 提要
     本論文所擬探討之對象為具有優先順序關係的隨機排程問題，包括單機、多流程機、二平行機、二平行多流程機等類型，此等問題之目的在決定工作站中一組工作執行上的先後順序，以使得其最終回應成本的期望值為最佳。
     本文使用動態規劃演算法，並以二元結構的狀態及順序表示法來求得模型的最佳序列解，並對增減優先順序限制、增減機器、增減工作、規則選用等不同的決策支擾模型作有效率的求解，同時以電腦模擬方法對決策支援環境下的解題速度與重新開始原求解模型的解題速度作一CPU時間的數值此較。
     本研究同時亦允許工作的處理時間和工作的到期日為一服從多變量常態分配函數的隨機向量，以模擬方法產生資料的樣本值來求得隨機模型的最佳期望解。
參考文獻 參考書目
     1. Adolphson, D.L., " Single machine job sequencing with precedence constraints " , SIAM J. Computing , 6(1) , 40 - 54 . (1977)
     2. Akers, S.B., " A graphical approach to production scheduling problems. " Operations Research , 4(2) , 244 - 245 , (1956)
     3. Ashour, S., Moore, T.E. and Chin, N.K., " An implicit enumeration algorithm for the nonpreemptive shop scheduling problem " . AIIE Transactions , 6(1) , 62 - 72 , (1974)
     4. Bagga, P.C.. " N-job, 2-machine sequencing problem with stochastic service times" , Opsearch , 7 , 184 - 197 , (1970)
     5. Baker, K.R., Introduction to sequencing and scheduling . John Wiely & Sons , N.Y. , (1974)
     6. Baker, K.R. and Schrage .L.E., " Finding an optimal sequence by dynamic programming : an extension to precedence related tasks " Operations Research . 26(1) , 111 - 120 . (1978a)
     7. Bakshi, M.S. and Arora, S.R.. " The sequencing problem " , Management Science , 16(4) . B247 - B263 . (1969)
     8. Bellman, R., Dynamic programming , Princeton university press , Princeton N.J. (1957)
     9. Bowman, E.H., " The schedule-sequencing problem Operations Research , 7(4) . 621 – 624 . (1959)
     10. Box, G.E.P. and Muller, M.E., " A note on the generation of random normal deviates " , Ann. Math. Stat. , 29(2) .. 610 - 611 . (1958)
     11. Brooks G.H. and White, C.R.. " An algorithm for finding optimal or near optimal solutions to the production scheduling problem " . Journal of Industrial Engineering . 16(1) : 34 - 40 . (1965)
     12. Bruno, J. and Downey, P., " Sequencing tasks with exponential service times on two machines " , Technical report, Department of electrical engineering and computer science , University of California , at Santa Barbara , (1977)
     13. Burns , R.N. and Steiner. G.. " Single machine scheduling with series - parallel precedence contraints " Research report Corr 81-5. Department of combinatories and optimization , The university of Waterloo , Waterloo , Canada . (1981)
     14. Coffman, E.G., Computer and job - shop scheduling theory . John Wiley & Sons , N.Y. (1976)
     15. Coffman, E.G. and Graham, R.L., " Optimal scheduling for two-processor system" . Acta Information , 1(3) , 200 - 213 , (1972)
     16. Conway, R.W., Maxwell. W.L. and Miller. L.W., Theory of scheduling . Addison-Wesley , Reading , Mass . (1967)
     17. Cunningham, A.A. and Dutta, S.K.. " Scheduling jobs with exponentially distributed processing times on two machines of a flow shop " . Naval Research Logistics Quarterly , 16(1) , 69 - 31 . (1973)
     18. Dempster, M.A.H. Lenstra, J.K. and Rinooy Kan, A.H.G., Deterministic and stochastic scheduling . D.Reidel Publishing Company , Holland . (1982)
     19. Denardo, E.W. Dynamic Programming : models and application . Pentice - Hall . Englewood Cliffs , N.J. (1982)
     20. Derman, C., Lieberman, G. and Ross, S., " A renewal decision problem " Management Science , 24(5) , 554 - 561 , (1978)
     21. Fisher, M.L., " A dual algorithm for the one-machine scheduling problem " Mathematical Programming , 11(2) , 458 - 481 .. (1976)
     22. French. S., Sequencing and scheduling : An introduction to the mathematics of the job-shop . John Wiely & Sons , N.Y. , (1982)
     23. Garey, M.R. " Optimal binary identification procedures " , SIAM Journal on Applied Mathematic , 23(2) , 173 - 186 . (1972)
     24. Garey, M.R. and Joshon, D.S., " Two-processor scheduling with start-times and deadlines " . Bell Laboratories , Murray Hill , N.J. (1975)
     25. Gelders, L. and Kleindorfer, P.R., " Coordinating aggregate and detailed scheduling in a one-machine job shop , part I, theory " . Operations Research, 22(1) , 46 - 60 . (1974)
     26. Geoffrion , A.M., " Duality in nonlinear programming . a simplified applications oriented development " , SIAM Review , 13(1) , 1 - 37 . (1971)
     27. Gilmore, P.C. and Gomory, R.E., " Sequencing a one-state variable machine : a solvable case of the traveling salesman problem " , Operations Research , 12(4) , 555 - 679 . (1964)
     28. Glazebrook, K.D., " On single machine sequencing with order constraints " Naval Research Logistics Quarterly , 27 . 123 -130. (1980)
     29. Gonzalez, T. and Sahni, S., " Flowshop and jobshop schedules : complexity and approximation " Operations Research , 26(1) , 36 - 52 . (1978)
     30. Graybill, F.A.. Theory and application of the linear model , Duxbury Press . North Scituate , Massachusetts . (1976)
     31. Hariri, A.M.A. and Potts.C.M., " Algorithm for two machine flow shop sequencing with precedence constraints " Europ.J.of.0ps.Res., 17(2) , 238 - 248 . (1984)
     32. Held. M., Karp, R.M., " A dynamic programming approach to sequencing problems " , J. SIAM , 10(2) , 196 -210 . (1962)
     33. Held, M., Karp, R.M. and Shareshian, R., " Assembly - line balancing : dynamic programming with precedence constraints " , Operations Research , 11(3) , 442 - 459 . (1963)
     34. Heller, J., " Some numerical experiments for an M x J flow-shop and its decision theoretical aspects " . Operations Research, 8(1) , 178 - 184 . (1960)
     35. Horn, W.A., " single-machine job sequencing with treelike precedence ordering and linear delay penalties " , SIAM J. Appl. Math , 23(2) , 189 - 202 . (1972)
     36. Hu, T.C., " Parallel sequencing and assembly line problem " , Operations Research , 9(6) , 841 -848 . (1961)
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     64. Potts, C.N., " A lagrangean based branch and bound algorithm for single machine sequencing with precedence constraints to minimizing total weighted completion time " . Management Science , 31 (10) , 1300 - 1311 . (1985)
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     66. Reddi, S.S. and Ramamoorthy, "On the flow-shop sequencing problem with no wait in process " , Operational Research Quarterly , 23 , 323 - 331 , (1972)
     67. Rinnooy Kan, A.H.G. Machine scheduling problems , Martinus Nijhoff , The Hague , (1976)
     68. Rinnooy Kan, A.H.G., Lazeweg, B.J. and Lenstra, J.K, " Minimizing total costs in one machine scheduling " , Operations Research , 23(5) , 908 -927 . (1975)
     69. Ross, S., Introduction to stochastic dynamic programming. Academic Press , N.Y. (1983)
     70. Schild, A. and Fredman, I.J., " On scheduling tasks with associated linear loss function " , Management Science , 7(3) , 280 - 285 , (1961)
     71. Schrage, L.E. and Baker, K.R., "Dynamic programming solution of sequening problem with precedence constraints " Operations Research . 26(3) . 444 - 449. (1978b)
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     83. Weiss, H., "A greedy heuristic for single machine sequencing with precedence constraints" . Management Science , 27(10) , 1209 - 1215 , (1981)
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     85. Yu, C.C.. The optimization of stochastic multiperiod systems by an implicit dynamic programming approach. Ph. D. Dissertation , J.T. Austin , (1985)
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     87. 許淑卿,多變量模擬輸出之統計分析,國立政治大學統計研究所碩士論文,(民國76年).
     88. 黃欣伸,排程的隨機動態規劃模型及其在管理上的應用,國立政治大學統計研究所碩士論文,(民國75年).
描述 碩士
國立政治大學
統計學系
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002006242
資料類型 thesis
dc.contributor.advisor 余千智zh_TW
dc.contributor.author (Authors) 董永寬zh_TW
dc.creator (作者) 董永寬zh_TW
dc.date (日期) 1987en_US
dc.date.accessioned 4-May-2016 17:12:51 (UTC+8)-
dc.date.available 4-May-2016 17:12:51 (UTC+8)-
dc.date.issued (上傳時間) 4-May-2016 17:12:51 (UTC+8)-
dc.identifier (Other Identifiers) B2002006242en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/90914-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description.abstract (摘要) 提要
     本論文所擬探討之對象為具有優先順序關係的隨機排程問題，包括單機、多流程機、二平行機、二平行多流程機等類型，此等問題之目的在決定工作站中一組工作執行上的先後順序，以使得其最終回應成本的期望值為最佳。
     本文使用動態規劃演算法，並以二元結構的狀態及順序表示法來求得模型的最佳序列解，並對增減優先順序限制、增減機器、增減工作、規則選用等不同的決策支擾模型作有效率的求解，同時以電腦模擬方法對決策支援環境下的解題速度與重新開始原求解模型的解題速度作一CPU時間的數值此較。
     本研究同時亦允許工作的處理時間和工作的到期日為一服從多變量常態分配函數的隨機向量，以模擬方法產生資料的樣本值來求得隨機模型的最佳期望解。		zh_TW
dc.description.tableofcontents 目錄
     第一章 緒論………1
     第一節 模型簡介………1
     第二節 研究動機與目的………4
     第三節 研究內容與範圍………6
     第四節 本文結構………8
     第五節 研究流程………9
     第二章 排程理論及解法之回顧與分析………10
     第一節 符號說明、假設限制及分類………10
     第二節 求解的方法………19
     第三節 排程的動態規劃方法………22
     第四節 多機之排程問題………27
     第五節 隨機性之排程問題………30
     第三章 確定性之二元動態規劃模型………33
     第一節 單機的動態規劃模型………33
     第二節 多流程機的動態規劃模型………38
     第三節 二平行機的動態規劃模型………43
     第四節 二平行多流程機的動態規劃模型………47
     第五節 解題的對象………49
     第四章 隨機性之二元動態規劃模型………53
     第一節 多變量常態分配函數………53
     第二節 電腦模擬法………55
     第三節 隨機動態規劃方法………59
     第五章 排程模型之決策支援………67
     第一節 增減優先順序限制之決策支援………68
     第二節 增減一部平行機之決策支援………71
     第三節 增減流程機之決策支援………75
     第四節 增減工作之決策支援………77
     第五節 規則選取之決策支援………80
     第六節 舉例說明………81
     第六章 排程模型之數值結果與分析………88
     第一節 確定性模型之電腦模擬………88
     第二節 隨機性模型之電腦模擬………88
     第三節 決策支援模型之電腦模擬………104
     第四節 模擬結果的分析與比較………113
     第七章 結論與建議………124
     參考書目………126		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002006242en_US
dc.title (題名) 二元結構動態規劃方法在多機排程問題上的應用zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 參考書目
     1. Adolphson, D.L., " Single machine job sequencing with precedence constraints " , SIAM J. Computing , 6(1) , 40 - 54 . (1977)
     2. Akers, S.B., " A graphical approach to production scheduling problems. " Operations Research , 4(2) , 244 - 245 , (1956)
     3. Ashour, S., Moore, T.E. and Chin, N.K., " An implicit enumeration algorithm for the nonpreemptive shop scheduling problem " . AIIE Transactions , 6(1) , 62 - 72 , (1974)
     4. Bagga, P.C.. " N-job, 2-machine sequencing problem with stochastic service times" , Opsearch , 7 , 184 - 197 , (1970)
     5. Baker, K.R., Introduction to sequencing and scheduling . John Wiely & Sons , N.Y. , (1974)
     6. Baker, K.R. and Schrage .L.E., " Finding an optimal sequence by dynamic programming : an extension to precedence related tasks " Operations Research . 26(1) , 111 - 120 . (1978a)
     7. Bakshi, M.S. and Arora, S.R.. " The sequencing problem " , Management Science , 16(4) . B247 - B263 . (1969)
     8. Bellman, R., Dynamic programming , Princeton university press , Princeton N.J. (1957)
     9. Bowman, E.H., " The schedule-sequencing problem Operations Research , 7(4) . 621 – 624 . (1959)
     10. Box, G.E.P. and Muller, M.E., " A note on the generation of random normal deviates " , Ann. Math. Stat. , 29(2) .. 610 - 611 . (1958)
     11. Brooks G.H. and White, C.R.. " An algorithm for finding optimal or near optimal solutions to the production scheduling problem " . Journal of Industrial Engineering . 16(1) : 34 - 40 . (1965)
     12. Bruno, J. and Downey, P., " Sequencing tasks with exponential service times on two machines " , Technical report, Department of electrical engineering and computer science , University of California , at Santa Barbara , (1977)
     13. Burns , R.N. and Steiner. G.. " Single machine scheduling with series - parallel precedence contraints " Research report Corr 81-5. Department of combinatories and optimization , The university of Waterloo , Waterloo , Canada . (1981)
     14. Coffman, E.G., Computer and job - shop scheduling theory . John Wiley & Sons , N.Y. (1976)
     15. Coffman, E.G. and Graham, R.L., " Optimal scheduling for two-processor system" . Acta Information , 1(3) , 200 - 213 , (1972)
     16. Conway, R.W., Maxwell. W.L. and Miller. L.W., Theory of scheduling . Addison-Wesley , Reading , Mass . (1967)
     17. Cunningham, A.A. and Dutta, S.K.. " Scheduling jobs with exponentially distributed processing times on two machines of a flow shop " . Naval Research Logistics Quarterly , 16(1) , 69 - 31 . (1973)
     18. Dempster, M.A.H. Lenstra, J.K. and Rinooy Kan, A.H.G., Deterministic and stochastic scheduling . D.Reidel Publishing Company , Holland . (1982)
     19. Denardo, E.W. Dynamic Programming : models and application . Pentice - Hall . Englewood Cliffs , N.J. (1982)
     20. Derman, C., Lieberman, G. and Ross, S., " A renewal decision problem " Management Science , 24(5) , 554 - 561 , (1978)
     21. Fisher, M.L., " A dual algorithm for the one-machine scheduling problem " Mathematical Programming , 11(2) , 458 - 481 .. (1976)
     22. French. S., Sequencing and scheduling : An introduction to the mathematics of the job-shop . John Wiely & Sons , N.Y. , (1982)
     23. Garey, M.R. " Optimal binary identification procedures " , SIAM Journal on Applied Mathematic , 23(2) , 173 - 186 . (1972)
     24. Garey, M.R. and Joshon, D.S., " Two-processor scheduling with start-times and deadlines " . Bell Laboratories , Murray Hill , N.J. (1975)
     25. Gelders, L. and Kleindorfer, P.R., " Coordinating aggregate and detailed scheduling in a one-machine job shop , part I, theory " . Operations Research, 22(1) , 46 - 60 . (1974)
     26. Geoffrion , A.M., " Duality in nonlinear programming . a simplified applications oriented development " , SIAM Review , 13(1) , 1 - 37 . (1971)
     27. Gilmore, P.C. and Gomory, R.E., " Sequencing a one-state variable machine : a solvable case of the traveling salesman problem " , Operations Research , 12(4) , 555 - 679 . (1964)
     28. Glazebrook, K.D., " On single machine sequencing with order constraints " Naval Research Logistics Quarterly , 27 . 123 -130. (1980)
     29. Gonzalez, T. and Sahni, S., " Flowshop and jobshop schedules : complexity and approximation " Operations Research , 26(1) , 36 - 52 . (1978)
     30. Graybill, F.A.. Theory and application of the linear model , Duxbury Press . North Scituate , Massachusetts . (1976)
     31. Hariri, A.M.A. and Potts.C.M., " Algorithm for two machine flow shop sequencing with precedence constraints " Europ.J.of.0ps.Res., 17(2) , 238 - 248 . (1984)
     32. Held. M., Karp, R.M., " A dynamic programming approach to sequencing problems " , J. SIAM , 10(2) , 196 -210 . (1962)
     33. Held, M., Karp, R.M. and Shareshian, R., " Assembly - line balancing : dynamic programming with precedence constraints " , Operations Research , 11(3) , 442 - 459 . (1963)
     34. Heller, J., " Some numerical experiments for an M x J flow-shop and its decision theoretical aspects " . Operations Research, 8(1) , 178 - 184 . (1960)
     35. Horn, W.A., " single-machine job sequencing with treelike precedence ordering and linear delay penalties " , SIAM J. Appl. Math , 23(2) , 189 - 202 . (1972)
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