Building and Solving Mathematical Programming Models: 50 Practical Examples (International Series in Operations Research & Management Science, 329)

Description

This book presents the construction and resolution of 50 practical optimization problems and covers an exceptionally wide range, including games-associated problems (Unblock Me, Sudokus), logistical problems, and problems concerning plant distribution, production, operations scheduling, management and resource allocation. The problems are divided into 5 difficulty levels. Problems in the first few levels are focused on learning the model construction methodology, while those in the last level include complex optimization environments. For each problem solution, the specific steps are illustrated, promoting reader comprehension. In addition, all the models are implemented in an optimization library, LINGO, their solutions have been analyzed and their correct construction has been verified. The book also includes a simple guide to implementing models in LINGO in a straightforward manner and in any input data format (text files, spreadsheets or databases). As an ideal companion to the author’s previously published work Modelling in Mathematical Programming, the book is intended as a basic tool for students of operations research, and for researchers in any advanced area involving mathematical programming. Preface Contents Chapter 1: Introduction to Modeling Methodology 1.1 Introduction 1.2 Elements 1.2.1 Attributes of an Element 1.2.2 The Quantitative Nature of the Elements 1.2.3 Grouping of Elements in Sets 1.3 Decision Activities 1.4 Calculations 1.4.1 Auxiliary Calculations 1.4.2 Logical Calculations 1.4.3 Lower/Upper Bound Calculations 1.5 Specifications 1.5.1 Specifications Stated as Simple Propositions 1.5.1.1 Quantitative Selection Specification 1.5.1.2 Capacity Specifications 1.5.1.3 Demand Specification 1.5.1.4 Bound Imposition Specifications 1.5.1.5 Allocation or Balance Specifications 1.5.2 Specifications Stated as Compound Propositions 1.5.2.1 Modeling Operators Individually 1.5.2.2 Modeling Compound Propositions with Various Operators 1.5.2.3 Avoid the Equal Sign in Simple Propositions 1.5.2.4 Distributive Law Between Propositions and Other Equivalences 1.5.3 Data in Propositions 1.6 Objective Criterion 1.6.1 Cost According to the Interval of Values 1.6.2 Cost According to the Value of Another Variable 1.6.3 Costs Depending on the Deviation of the Variable 1.6.3.1 Penalty for Excess 1.6.3.2 Bonus for Excess 1.6.3.3 Penalty for Default 1.6.3.4 Bonus for Default 1.6.4 Balance Functions Reference Chapter 2: Building and Solving Models with LINGO 2.1 Introduction 2.2 Basic Format: The Extended Format 2.3 Compact Set-Based Format 2.3.1 SETS Section 2.3.2 DATA Section 2.3.2.1 Integrated Data in the Model File 2.3.2.2 Data in External Text File 2.3.2.3 Data in Spreadsheet File 2.3.2.4 Data in the Database File 2.3.3 Compact Definition of Constraints and Objective Function 2.3.4 Incompatibilities in the Use of Primitive Sets Instead of Derived Sets 2.3.5 CALC Section 2.4 Execution of the Solving Process 2.5 LINGO Solution Report 2.6 Output Data Format 2.6.1 Output Data in External Text Files 2.6.2 Output Data in Spreadsheet Files 2.6.3 Output Data in Database Files Reference Chapter 3: Low-Level Problems 3.1 Introduction 3.2 Problem 1: Product Manufacturing 3.3 Problem 2: Fruit Sale (Salazar 2021) 3.4 Problem 3: Securities Portfolio (Castillo et al. 2002) 3.5 Problem 4: Capital Investments (D´Auria 2008) 3.6 Problem 5: Number Partitioning (Korf 1998) 3.7 Problem 6: Installation of Parking Spaces for Electric Cars 3.8 Problem 7: Independent Edge Set (Alan 1985) References Chapter 4: Low-Medium Level Problems 4.1 Introduction 4.2 Problem 8. Power Generation Planning (Sarker and Newton 2007) 4.3 Problem 9. Purchase of Processing Machines 4.4 Problem 10. Project Selection (Castro et al. 2011) 4.5 Problem 11. Assignment of Workers to Centers 4.6 Problem 12. Warehouse Rental 4.7 Problem 13. Article and Position Planning 4.8 Problem 14: Online Sale 4.9 Problem 15. Plot Cultivation 4.10 Problem 16. Production and Distribution 4.11 Problem 17. Production of Divisible Tasks 4.12 Problem 18. Selection of Nodes and Edges References Chapter 5: Medium-Level Problems 5.1 Introduction 5.2 Problem 19. Management of Polluting Products (Castro et al. 2011) 5.3 Problem 20. Assignment of Tasks to Operators 5.4 Problem 21. Assignment of Students to Groups 5.5 Problem 22. Home Building 5.6 Problem 23. Assignment of Extracurricular Activities 5.7 Problem 24. Assignment of Subjects to Classrooms 5.8 Problem 25. Disciplines Management 5.9 Problem 26. Installation of Agencies References Chapter 6: Medium-High Level Problems 6.1 Introduction 6.2 Problem 27. Production of Pieces 6.3 Problem 28. Grouping of People 6.4 Problem 29. Task Scheduling with Precedence and Setup Times 6.5 Problem 30. Steiner Problem 6.6 Problem 31. Management of Pharmacies on Guard Duty 6.7 Problem 32. Project Task Planning 6.8 Problem 33. Product Warehouse Management 6.9 Problem 34. Assignment of Engineers to Projects 6.10 Problem 35. Excursion Planning 6.11 Problem 36. Iron Bars Production 6.12 Problem 37. Discount Management References Chapter 7: High-Level Problems 7.1 Introduction 7.2 Problem 38. Installation of City Bike Stations 7.3 Problem 39. Equipment Management in Hospitals 7.4 Problem 40. Hiring of Employees 7.5 Problem 41. Element Management 7.6 Problem 42. Creation of Sudokus 7.7 Problem 43. ``Unblock Me´´ 7.8 Problem 44. Distribution of State Aid 7.9 Problem 45. Planning of a Formula One Race 7.10 Problem 46. Ready Mixed Concrete Delivery to Construction Sites 7.11 Problem 47. Planning of a Supermarket Car Park 7.12 Problem 48. Assignment of Teacher Posts 7.13 Problem 49. Placement of Tables 7.14 Problem 50. Cutting Stock Problem (Cheng et al. 1994) References