Decision and discrete mathematics : maths for decision-making in business and industry /
This text offers a complete coverage in the Decision Mathematics module, also known as Discrete Mathematics, of the syllabuses of English A-level examination boards. it is a rewritten and modern version of Decision Mathematics (published by Ellis Horwood Ltd in 1986 for The Spode Group, so well know...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Chichester :
Albion,
1996.
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| Edition: | Second edition]. |
| Series: | Albion mathematics & applications series.
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| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Front Cover; Decision and Discrete Mathematics: Maths for Decision-Making in Business and Industry; Copyright Page; Table of Contents; Preface; Acknowledgements; Chapter 1. An introduction to networks; 1.1 TERMINOLOGY; 1.2 INVESTIGATIONS; 1.3 MINIMUM CONNECTOR PROBLEM (MINIMUM SPANNING TREE); 1.4 CHINESE POSTMAN PROBLEM; 1.5 TRAVELLING SALESMAN PROBLEM; 1.6 NOTES; Chapter 2. Recursion; 2.1 DEFINITION; 2.2 INVESTIGATION; 2.3 DIVISIBILITY; 2.4 HIGHEST COMMON FACTORS (EUCLID'S ALGORITHM); 2.5 NOTES; Chapter 3. Shortest route; 3.1 INVESTIGATIONS; 3.2 DIJKSTRA'S ALGORITHM; 3.3 DELAYS AT NODES.
- 3.4 CHINESE POSTMAN PROBLEM3.5 ARCS WITH NEGATIVE VALUES; 3.6 NOTES; Chapter 4. Dynamic programming; 4.1 INVESTIGATIONS; 4.2 THE METHOD OF DYNAMIC PROGRAMMING; 4.3 APPLICATIONS OF DYNAMIC PROGRAMMING; 4.4 NOTES; Chapter 5. Flows in networks; 5.1 INVESTIGATIONS; 5.2 TERMINOLOGY; 5.3 CUTSETS; 5.4 MAXIMUM FLOW, MINIMUM CUT THEOREM; 5.5 CUTSETS IN DIRECTED NETWORKS; 5.6 RESTRICTIONS ON NODES; 5.7 SEVERAL SOURCES AND/OR SINKS; 5.8 FLOW AUGMENTATION SYSTEM; 5.9 NETWORKS WITH ARCS HAVING LOWER CAPACITIES; 5.10 NOTES; Chapter 6. Critical path analysis; 6.1 ACTIVITY ON ARC : INVESTIGATIONS.
- 6.2 ACTIVITY ON ARC: DEFINITIONS AND CONVENTIONS6.3 ACTIVITY ON ARC: PROCEDURE; 6.4 ACTIVITY ON NODE: INVESTIGATIONS; 6.5 DEFINITIONS AND CONVENTIONS; 6.6 ACTIVITY ON NODE: PROCEDURE; 6.7 ACTIVITY ON NODE: TOTAL FLOAT; 6.8 ACTIVITY ON ARC: TOTAL FLOAT; 6.9 GANTT CHARTS; 6.10 RESOURCE LEVELLING; 6.11 NOTES; Chapter 7. Linear programming (graphical); 7.1 INVESTIGATION; 7.2 GRAPHICAL REPRESENTATION; 7.3 DRAWING THE OBJECTIVE FUNCTION; 7.4 NOTES; Chapter 8. Linear programming: simplex method; 8.1 INVESTIGATION; 8.2 SIMPLEX METHOD; 8.3 THE SIMPLEX TABLEAU; 8.4 e"CONSTRAINTS; 8.5 THREE DIMENSIONS.
- 8.6 MINIMISATION PROBLEMS8.7 NOTES; Chapter 9. The transportation problem; 9.1 INVESTIGATIONS; 9.2 THE TRANSPORTATION ARRAY; 9.3 MAXIMISATION PROBLEMS; 9.4 UNBALANCED PROBLEMS; 9.5 NON·UNIQUE OPTIMAL SOLUTIONS; 9.6 DEGENERACY; 9.7 NOTES; Chapter 10. Matching and assignment problems; 10.1 INVESTIGATIONS; 10.2 HALL'S MARRIAGE THEOREM; 10.3 MATCHING IMPROVEMENT ALGORITHM; 10.4 INVESTIGATIONS; 10.5 HUNGARIAN ALGORITHM; 10.6 IMPOSSIBLE ASSIGNMENTS; 10.7 MAXIMISING PROBLEMS; 10.8 NON·UNIQUE SOLUTIONS; 10.9 UNBALANCED PROBLEMS; 10.10 NOTES; Chapter 11. Game theory; 11.1 INVESTIGATION.
- 11.2 THE MINIMAX THEORY11.3 WHAT IS A ZERO·SUM GAME?; 11.4 STABLE SOLUTIONS; 11.5 ROW AND COLUMN DOMINATION; 11.6 EXPECTATION =EXPECTED PAY-OFF; 11.7 MINIMAX MIXED STRATEGY; 11.8 GAMES WITH KNOWN VALUES; 11.9 USING LINEAR PROGRAMMING; 11.10 MISCELLANEOUS EXERCISES; 11.11 NOTES; Chapter 12. Recurrence relations; 12.1 WHAT IS A RECURRENCE RELATION?; 12.2 INVESTIGATIONS; 12.3 FIRST ORDER LINEAR EQUATIONS; 12.4 COMPLEMENTARY FUNCTIONS AND PARTICULAR SOLUTIONS; 12.5 INHOMOGENEOUS; 12.6 INHOMOGENEOUS; 12.7 SECOND ORDER LINEAR; 12.8 SECOND ORDER HOMOGENEOUS; 12.9 SUMMARY.
