Model building in mathematical programming

The 5th edition of Model Building in Mathematical Programming discusses the general principles of model building in mathematical programming and demonstrates how they can be applied by using several simplified but practical problems from widely different contexts. Suggested formulations and solution...

Descripción completa

Detalles Bibliográficos
Autor principal:	Williams, H. P. (-)
Formato:	Libro electrónico
Idioma:	Inglés
Publicado:	Hoboken, N.J. : Wiley 2013.
Edición:	5th ed
Materias:	Mathematical models. Programming (Mathematics)
Ver en Biblioteca Universitat Ramon Llull:	https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009684436706719

Tabla de Contenidos:

Cover
Title Page
Copyright
Contents
Preface
Part I
Chapter 1 Introduction
1.1 The concept of a model
1.2 Mathematical programming models
Chapter 2 Solving mathematical programming models
2.1 Algorithms and packages
2.1.1 Reduction
2.1.2 Starting solutions
2.1.3 Simple bounding constraints
2.1.4 Ranged constraints
2.1.5 Generalized upper bounding constraints
2.1.6 Sensitivity analysis
2.2 Practical considerations
2.3 Decision support and expert systems
2.4 Constraint programming (CP)
Chapter 3 Building linear programming models
3.1 The importance of linearity
3.2 Defining objectives
3.2.1 Single objectives
3.2.2 Multiple and conflicting objectives
3.2.3 Minimax objectives
3.2.4 Ratio objectives
3.2.5 Non-existent and non-optimizable objectives
3.3 Defining constraints
3.3.1 Productive capacity constraints
3.3.2 Raw material availabilities
3.3.3 Marketing demands and limitations
3.3.4 Material balance (continuity) constraints
3.3.5 Quality stipulations
3.3.6 Hard and soft constraints
3.3.7 Chance constraints
3.3.8 Conflicting constraints
3.3.9 Redundant constraints
3.3.10 Simple and generalized upper bounds
3.3.11 Unusual constraints
3.4 How to build a good model
3.4.1 Ease of understanding the model
3.4.2 Ease of detecting errors in the model
3.4.3 Ease of computing the solution
3.4.4 Modal formulation
3.4.5 Units of measurement
3.5 The use of modelling languages
3.5.1 A more natural input format
3.5.2 Debugging is made easier
3.5.3 Modification is made easier
3.5.4 Repetition is automated
3.5.5 Special purpose generators using a high level language
3.5.6 Matrix block building systems
3.5.7 Data structuring systems
3.5.8 Mathematical languages
3.5.8.1 SETs
3.5.8.2 DATA.
3.5.8.3 VARIABLES
3.5.8.4 OBJECTIVE
3.5.8.5 CONSTRAINTS
Chapter 4 Structured linear programming models
4.1 Multiple plant, product and period models
4.2 Stochastic programmes
4.3 Decomposing a large model
4.3.1 The submodels
4.3.2 The restricted master model
Chapter 5 Applications and special types of mathematical programming model
5.1 Typical applications
5.1.1 The petroleum industry
5.1.2 The chemical industry
5.1.3 Manufacturing industry
5.1.4 Transport and distribution
5.1.5 Finance
5.1.6 Agriculture
5.1.7 Health
5.1.8 Mining
5.1.9 Manpower planning
5.1.10 Food
5.1.11 Energy
5.1.12 Pulp and paper
5.1.13 Advertising
5.1.14 Defence
5.1.15 The supply chain
5.1.16 Other applications
5.2 Economic models
5.2.1 The static model
5.2.2 The dynamic model
5.2.3 Aggregation
5.3 Network models
5.3.1 The transportation problem
5.3.2 The assignment problem
5.3.3 The transhipment problem
5.3.4 The minimum cost flow problem
5.3.5 The shortest path problem
5.3.6 Maximum flow through a network
5.3.7 Critical path analysis
5.4 Converting linear programs to networks
Chapter 6 Interpreting and using the solution of a linear programming model
6.1 Validating a model
6.1.1 Infeasible models
6.1.2 Unbounded models
6.1.3 Solvable models
6.2 Economic interpretations
6.2.1 The dual model
6.2.2 Shadow prices
6.2.3 Productive capacity constraints
6.2.4 Raw material availabilities
6.2.5 Marketing demands and limitations
6.2.6 Material balance (continuity) constraints
6.2.7 Quality stipulations
6.2.8 Reduced costs
6.3 Sensitivity analysis and the stability of a model
6.3.1 Right-hand side ranges
6.3.2 Objective ranges
6.3.3 Ranges on interior coefficients
6.3.4 Marginal rates of substitution.
6.3.5 Building stable models
6.4 Further investigations using a model
6.5 Presentation of the solutions
Chapter 7 Non-linear models
7.1 Typical applications
7.2 Local and global optima
7.3 Separable programming
7.4 Converting a problem to a separable model
Chapter 8 Integer programming
8.1 Introduction
8.2 The applicability of integer programming
8.2.1 Problems with discrete inputs and outputs
8.2.2 Problems with logical conditions
8.2.3 Combinatorial problems
8.2.4 Non-linear problems
8.2.5 Network problems
8.3 Solving integer programming models
8.3.1 Cutting planes methods
8.3.2 Enumerative methods
8.3.3 Pseudo-Boolean methods
8.3.4 Branch and bound methods
Chapter 9 Building integer programming models I
9.1 The uses of discrete variables
9.1.1 Indivisible (discrete) quantities
9.1.2 Decision variables
9.1.3 Indicator variables
9.2 Logical conditions and 0-1 variables
9.3 Special ordered sets of variables
9.4 Extra conditions applied to linear programming models
9.4.1 Disjunctive constraints
9.4.2 Non-convex regions
9.4.3 Limiting the number of variables in a solution
9.4.4 Sequentially dependent decisions
9.4.5 Economies of scale
9.4.6 Discrete capacity extensions
9.4.7 Maximax objectives
9.5 Special kinds of integer programming model
9.5.1 Set covering problems
9.5.2 Set packing problems
9.5.3 Set partitioning problems
9.5.4 The knapsack problem
9.5.5 The travelling salesman problem
9.5.6 The vehicle routing problem
9.5.7 The quadratic assignment problem
9.6 Column generation
Chapter 10 Building integer programming models II
10.1 Good and bad formulations
10.1.1 The number of variables in an IP model
10.1.2 The number of constraints in an IP model
10.2 Simplifying an integer programming model.
10.2.1 Tightening bounds
10.2.2 Simplifying a single integer constraint to another single integer constraint
10.2.3 Simplifying a single integer constraint to a collection of integer constraints
10.2.4 Simplifying collections of constraints
10.2.5 Discontinuous variables
10.2.6 An alternative formulation for disjunctive constraints
10.2.7 Symmetry
10.3 Economic information obtainable by integer programming
10.4 Sensitivity analysis and the stability of a model
10.4.1 Sensitivity analysis and integer programming
10.4.2 Building a stable model
10.5 When and how to use integer programming
Chapter 11 The implementation of a mathematical programming system of planning
11.1 Acceptance and implementation
11.2 The unification of organizational functions
11.3 Centralization versus decentralization
11.4 The collection of data and the maintenance of a model
Part II
Chapter 12 The problems
12.1 Food manufacture 1
12.2 Food manufacture 2
12.3 Factory planning 1
12.4 Factory planning 2
12.5 Manpower planning
12.5.1 Recruitment
12.5.2 Retraining
12.5.3 Redundancy
12.5.4 Overmanning
12.5.5 Short-time working
12.6 Refinery optimisation
12.6.1 Distillation
12.6.2 Reforming
12.6.3 Cracking
12.6.4 Blending
12.7 Mining
12.8 Farm planning
12.9 Economic planning
12.10 Decentralisation
12.11 Curve fitting
12.12 Logical design
12.13 Market sharing
12.14 Opencast mining
12.15 Tariff rates (power generation)
12.16 Hydro power
12.17 Three-dimensional noughts and crosses
12.18 Optimising a constraint
12.19 Distribution 1
12.20 Depot location (distribution 2)
12.21 Agricultural pricing
12.22 Efficiency analysis
12.23 Milk collection
12.24 Yield management
12.25 Car rental 1
12.26 Car rental 2.
12.27 Lost baggage distribution
12.28 Protein folding
12.29 Protein comparison
Part III
Chapter 13 Formulation and discussion of problems
13.1 Food manufacture 1
13.1.1 The single-period problem
13.1.2 The multi-period problem
13.2 Food manufacture 2
13.3 Factory planning 1
13.3.1 The single-period problem
13.3.2 The multi-period problem
13.4 Factory planning 2
13.4.1 Extra variables
13.4.2 Revised constraints
13.5 Manpower planning
13.5.1 Variables
13.5.2 Constraints
13.5.3 Initial conditions
13.6 Refinery optimization
13.6.1 Variables
13.6.2 Constraints
13.6.3 Objective
13.7 Mining
13.7.1 Variables
13.7.2 Constraints
13.7.3 Objective
13.8 Farm planning
13.8.1 Variables
13.8.2 Constraints
13.8.3 Objective function
13.9 Economic planning
13.9.1 Variables
13.9.2 Constraints
13.9.3 Objective function
13.10 Decentralization
13.10.1 Variables
13.10.2 Constraints
13.10.3 Objective
13.11 Curve fitting
13.12 Logical design
13.13 Market sharing
13.14 Opencast mining
13.15 Tariff rates (power generation)
13.15.1 Variables
13.15.2 Constraints
13.15.3 Objective function (to be minimized)
13.16 Hydro power
13.16.1 Variables
13.16.2 Constraints
13.16.3 Objective function (to be minimized)
13.17 Three-dimensional noughts and crosses
13.17.1 Variables
13.17.2 Constraints
13.17.3 Objective
13.18 Optimizing a constraint
13.19 Distribution 1
13.19.1 Variables
13.19.2 Constraints
13.19.3 Objectives
13.20 Depot location (distribution 2)
13.21 Agricultural pricing
13.22 Efficiency analysis
13.23 Milk collection
13.23.1 Variables
13.23.2 Constraints
13.23.3 Objective
13.24 Yield management
13.24.1 Variables
13.24.2 Constraints
13.24.3 Objective
13.25 Car rental 1.
13.25.1 Indices.

Model building in mathematical programming

Ejemplares similares