Operations research handbook: standard algorithms and methods with examples
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin
de Gruyter
1977
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 398 S. zahlr. graph. Darst. |
| ISBN: | 3110070553 |
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Record in the Search Index
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| adam_text | Titel: Operations research handbook
Autor: Eiselt, Horst A
Jahr: 1977
Contents Definitions and Symbols ............................. 15 0. Summary of Matrix Algebra and Allied Topics 0.1 Definitions ........................................ 1? 0. 2 Elementary Operations ............................... 18 1. - Linear Programming 1.1 General Methods 1.1.1 The Primal Simplex-Algorithm ........................ 22 1.1.2 The Two-Phase Method ................................ 25 1.1.3 The Primal Simplex-Algorithm without Explicit Identity Matrix ............................ 30 1.1.4 The Dual Simplex-Algorithm .......................... 34 1.1.5 Sensitivity Analisys and Parametric Programming (S.A. and P.P.).......................... 38 1.1.5.1 S.A. and P.P. with Expected Alterations.............. 39 1.1.5.2 S.A. and P.P. with Unexpected Alterations 1.1.5.2.1 Subsequent Alterations of the Restriction Vector .............................................. 43 1.1.5.2.2 Subsequent Alterations of Coefficients of the Objective Function................................... 45 1.2 Shortened Methods 1.2.1 The Transportation Problem........................... 48 1.2.1.1 The Northwest-Corner Rule............................ 49 1.2.1.2 The Row Minimum Method............................... 51 1.2.1.3 The Column Minimum Method............................ 54 1.2.1.4 The Matrix Minimum Method............................ 57 1.2.1.5 The Double Preference Method......................... 60 1.2.1.6 VOGEL’s Approximation Method (VAM)................... 66 1.2.1.7 The Frequency Method................................. 71 1.2.1.8 The Stepping-Stone Method............................ 72 1.2.2 The Hungarian Method (Kuhn).......................... 75
10 Contents 1.2.3 The Decomposition Principle (Dantzig; Wolfe)............................................... 81 1.2.4 FLOOD S Technique ................................... 89 1.3 Theorems and Rules 1.3.1 The Dual Problem.................................... 91 1.3.2 Theorems of Duality................................. 93 1.3.3 The Lexicographic Selection Rule..................... 94 2. Integer Programming 2.1 Cutting Plane Methods 2.1.1 The G0M0RY- I-All Integer Method..................... 96 2.1.2 The G0M0RY-II-A11 Integer Method .................... 100 2.1.3 The GOMORY-III-Mixed Integer Method ................. 103 2.1.4 The GOMORY-III-Mixed Integer Method with Intensified Cuts ............................... 106 2.1.5 The Primal Cutting Plane Method (Young; Glover; Ben-Israel; Charnes)................. 108 2.2 Branch and Bound Methods 2.2.1 The Method of LAND and DOIG......................... HI 2.2.2 The Method of DAKIN ................................. 118 2.2.3 The Method of DRIEBEEK.............................. 122 2.2.4 The Additive Algorithm (Balas)....................... 129 2.3 Primal-Dual Methods 2.3.1 A Partitioning Procedure for Mixed Integer Problems (Benders)........................... 134 3. Theory of Graphs 3.0. 1 Definitions ......................................... 143 3.0. 2 The Determination of Rank in Graphs.................. 146 3.0. 3 The Number of Paths in a Graph....................... 148 3.0. 4 The Determination of the Strongly Connected Components of a Graph...................... 149 3.1 Shortest Paths in Graphs 3.1.1 The Algorithm of DIJKSTRA ........................... 151 3.1.2 The Algorithm of DANTZIG ............................ 154
Contents 11 3.1.3 The FORD Algorithm I (shortest path(s)) .................................. 159 3.1.4 The FORD Algorithm II (longest path(s)) ................................... 160 3.1.5 The Tripel Algorithm................................ 162 3.1.6 The HASSE Algorithm................................. 166 3.1.7 The Cascade Algorithm............................... 168 3.1.8 The Algorithm of LITTLE.............................. 169 3.1.9 The Method of EASTMAN............................... 174 3.2 Flows in Networks 3.2.1 The Algorithm of FORD and FULKERSON................. 178 3.2.2 The Algorithm of BUSACKER and GOWEN................. 183 3.2.3 The Method of KLEIN................................. 187 3.2.4 The Out-of-Kilter Algorithm (Ford; Fulkerson) ................................... 191 3.3 Shortest Spanning Subtrees of a Graph 3.3.1 The Method of KRUSKAL............................... 200 3.3.2 The Method of SOLLIN................................ 203 3.3.3 The Method of WOOLSEY............................... 205 3.3.4 The Method of BERGE ................................. 207 3.4 Gozinto Graphs...................................... 210 3.4.1 The Method of VAZSONYI............................... 210 3.4.2 The Method of TISCHER............................... 212 3.4.3 The Method of FLOYD................................. 213 3.4.4 The Gozinto List Method............................. 214 4. Planning Networks 4.0. 1 The Critical Path Method (CPM)....................... 217 4.0. 2 The CPM Project Acceleration........................ 220 4.0. 3 The Program Evaluation and Review Technique (PERT) .................................... 224 4.0. 4 The Metra Potential Method (MPM) .................... 227 4.0. 5 The Graphical Evaluation and Review Technique (GERT) .................................... 230
12 Contents 5. Game Theory 5.1 Non Matrix Games 5.1.1 The Normal Form..................................... 236 5.1.2 NASH s Solution of the Bargaining Problem........... 241 5.1.3 The Extensive Form.................................. 242 5.2 Matrix Games 5.2.1 A Method for Determining Pure Strategy Pairs for Two-Person Zero-Sum Games ....................... 251 5.2.2 A Method for Solving Two-Person Zero-Sum Games with the Simp!ex-Algorithm................. . 253 5.2.3 An Approximization Method for Two-Person Zero-Sum Games ( learning method ; Gale; Brown)...... 256 5.2.4 The LEMKE-HOWSON Algorithm for the Solution of Bimatrix Games................................... 260 5.3 Decisions under Uncertainty (games against nature) .............................. 264 5.3.1 The Solution of WALD................................ 265 5.3.2 The Solution of HURWICZ............................. 266 5.3.3 The Solution of SAVAGE and NIEHANS.................. 266 5.3.4 The Solution of BAYES............................... 267 5.3.5 The Solution of LAPLACE............................. 268 5.3.6 The Solution of HODGES and LEHMANN.................. 268 6. Dynamic Programming 6.0. 1 The n-Period Model .................................. 270 6.0. 2 The Infinite-Period Model (policy iteration routine) ............................................ 276 7. Queueing Models................:...... 280 7.0. 1 The 1-Channel, 1-Stage Model ........................ 282 7.0. 2 The 1-Channel, r-Phase Model ........................ 284 7.0. 3 The k-Channel, 1-Stage Model ........................ 285 8. Nonlinear Programming 8.1 Theorems and Special Methods 8.1.1 The Theorem of KUHN and TUCKER...................... 288
Contents 13 8.1.2 The Method of LAGRANGE.............................. 289 8.1.3 A Method for the Optimization of Nonlinear Separable Objective Functions under Linear Constraints......................................... 292 8.2 General Methods 8.2.1 The Method of WOLFE (short form).................... 296 8.2.2 The Method of FRANK and WOLFE....................... 302 8.2.3 The Method of BEALE................................. 307 8.2.4 An Algorithm for the Solution of Linear Complementarity Problems (Lemke) .................... 312 8.2.5 The Gradient Projection Method (Rosen) .............. 315 9. Generation of Random Numbers (simulation)........ 321 9.0. 1 The AWF-Cubes (Graf)................................ 321 9.0. 2 The Midsquare Method (J.v.Neumann) .................. 322 9.0. 3 A Mixed Congruence Method........................... 323 9.0. 4 A Multiplicative Congruence Method.................. 324 10. Replacement Models 10.1 Replacement Models with Respect to Gradually Increasing Maintenance Costs 10.1.1 A Model Disregarding the Rate of Interest........... 325 10.1.2 A Model Regarding the Rate of Interest.............. 326 10.2 Replacement Models with Respect to Sudden Failure 10.2.1 A Model Disregarding the Rate of Interest........... 328 10.2.2 A Model Regarding the Rate of Interest.............. 331 11. Inventory Models .................................... 333 11.0. 1 The Classical Inventory Model (Andler) .............. 333 11.0. 2 An Inventory Model with Penalties for Undersupplied Demands............................... 334 11.0. 3 An Inventory Model with Terms for Delivery.......... 335 11.0. 4 An Inventory Model with Damage to Stock............. 337 11.0. 5 An Inventory Model with Rebates (different price intervals) ......................... 338
14 Contents 11.0. 6 An Inventory Model with Respect to Transportation Capacity.................................. 340 12. Sequencing Models 12.0. 1 JOHNSON S Algorithm for Two Machines ................ 343 12.0. 2 JOHNSON S Algorithm for Three Machines (special case) ...................................... 345 12.0. 3 A Heuristic Solution for a Sequencing Problem.......347 13. Plant Location Models 13.1 Exact Methods 13.1.1 The Optimal Plant Location in a Transportation Network I................................. 350 13.1.2 The Optimal Plant Location in a Transportation Network II................................ 351 13.1.3 The Optimal Plant Location on a Straight Line ....... 353 13.1.4 The Optimal Plant Location with Respect to Rectangular Transportation Movements ................ 354 13.2 Heuristic Methods 13.2.1 The Center of Gravity-Method ........................ 356 13.2.2 A Solution by Vector Summation ...................... 358 13.2.3 An Iterative Method ................................. 363 Appendix............................................ 367 Table 1 : q k = (1 + i) k ........................... 367 Table 2 : q‘ k = (1 + i) _k ........................... 367 Table 3 : e k ....................................... 368 Table 4 : Random numbers with an equal distribution.............................. 370 Table 5 : Area under the standardized normal distribution function..................... 372 Bibliography ........................................ 373
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| spelling | Eiselt, Horst A. 1950- Verfasser (DE-588)133413780 aut Operations research handbook standard algorithms and methods with examples Horst A. Eiselt ; Helmut von Frajer Berlin de Gruyter 1977 398 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Recherche opérationnelle - Guides, manuels, etc Operations research -- Handbooks, manuals, etc Operations Research (DE-588)4043586-6 gnd rswk-swf Operations Research (DE-588)4043586-6 s DE-604 Frajer, Helmut von 1948- Verfasser (DE-588)1145387594 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000583131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eiselt, Horst A. 1950- Frajer, Helmut von 1948- Operations research handbook standard algorithms and methods with examples Recherche opérationnelle - Guides, manuels, etc Operations research -- Handbooks, manuals, etc Operations Research (DE-588)4043586-6 gnd |
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| title | Operations research handbook standard algorithms and methods with examples |
| title_auth | Operations research handbook standard algorithms and methods with examples |
| title_exact_search | Operations research handbook standard algorithms and methods with examples |
| title_full | Operations research handbook standard algorithms and methods with examples Horst A. Eiselt ; Helmut von Frajer |
| title_fullStr | Operations research handbook standard algorithms and methods with examples Horst A. Eiselt ; Helmut von Frajer |
| title_full_unstemmed | Operations research handbook standard algorithms and methods with examples Horst A. Eiselt ; Helmut von Frajer |
| title_short | Operations research handbook |
| title_sort | operations research handbook standard algorithms and methods with examples |
| title_sub | standard algorithms and methods with examples |
| topic | Recherche opérationnelle - Guides, manuels, etc Operations research -- Handbooks, manuals, etc Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Recherche opérationnelle - Guides, manuels, etc Operations research -- Handbooks, manuals, etc Operations Research |
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