دانلود کتاب Stochastic programming: modeling decision problems under uncertainty

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Preface......Page 7
Contents......Page 9
1.2.1 Blending Problem......Page 0
1.2 Examples......Page 14
1.2.2 Production Planning......Page 18
Interpretation as Decision Problem......Page 19
Interpretation as Decision Problem......Page 21
2.1 Maximization of Expected Utility......Page 25
Measures of Risk Aversion......Page 29
2.2 The Mean-Variance Model......Page 31
2.2.1 Relation with Expected Utility Theory......Page 32
Objections to the Mean-Variance Model......Page 34
3.1 Models with Penalty Costs in Deterministic LP......Page 35
3.1.1 Individual Penalty Costs......Page 36
3.1.4 Penalty Costs Based on Recourse Actions......Page 37
3.2.1 Representations of Recourse Models......Page 39
Standard Formulation of Recourse Models......Page 40
Compact Formulation of Recourse Models......Page 41
Large-Scale Deterministic Equivalent Representation of Recourse Models......Page 42
3.2.2 Modeling Aspects......Page 43
3.2.3 Special Recourse Structures......Page 44
3.3.1 Fixed Recourse......Page 47
3.3.2 Simple Recourse......Page 50
3.3.3 Expected Shortage and Surplus Functions......Page 52
Expected Shortage Function H......Page 53
Expected Surplus Function G......Page 58
Expected Value Function Q......Page 59
Expected Value Problem and Value of Stochastic Solution......Page 61
Wait-and-See Problem and Expected Value of Perfect Information......Page 62
Jensen and Edmundson-Madansky Inequalities in One Dimension......Page 63
3.4 Algorithms for Recourse Models......Page 65
Discrete Distributions......Page 66
Continuous Distributions......Page 68
Simple Recourse with Random Technology Matrix......Page 70
The L-Shaped Algorithm......Page 72
Continuous Distributions......Page 76
Discrete Approximation......Page 77
4.1 Mixed-Integer Recourse Models......Page 79
4.1.1 Special Mixed-Integer Recourse Structures......Page 82
4.2.1 Fixed Mixed-Integer Recourse......Page 84
4.2.2 Simple Integer Recourse......Page 87
4.2.3 Integer Simple Recourse: Its One-Dimensional Functions......Page 89
The One-Dimensional Integer Value Function......Page 90
The One-Dimensional Integer Expected Surplus Function......Page 92
The One-Dimensional Integer Expected Shortage Function H......Page 97
The One-Dimensional Integer Expected Value Function......Page 101
4.3.1 Simple Integer Recourse......Page 105
The Convex Hull......Page 107
Convexity by Perturbation of the Distribution......Page 110
Improved Error Bound......Page 113
4.3.2 General Mixed-Integer Recourse......Page 115
L-Shaped Methods......Page 116
Dual Decomposition......Page 119
Structured Enumeration......Page 121
5.1 Modeling with Chance Constraints......Page 126
5.2.1 Different Representations of the Reliability Function......Page 129
5.2.2 Examples of Chance Constraints......Page 130
Closedness and Monotonicity of Feasibility Sets......Page 136
Convex Feasibility Sets for Fixed T......Page 138
Convex Feasibility Sets for Random T......Page 139
5.3 Discrete Distributions......Page 141
5.4 Algorithms for Models with a Joint Chance Constraint......Page 143
5.4.1 Evaluation of the Distribution Function of a Multivariate Normal Distribution......Page 144
6.1 Modeling with Integrated Chance Constraints......Page 150
6.2.1 Formulations of Single Integrated Chance Constraints......Page 152
6.2.2 Examples of Single Integrated Chance Constraints......Page 153
6.2.3 Properties of Single Integrated Chance Constraints......Page 156
Normal Distributions......Page 159
6.2.4 Discrete Distributions......Page 161
ICC for Equality (Goal) Constraints......Page 163
6.3 Joint Integrated Chance Constraints......Page 164
6.4 Conditional Surplus-at-Risk and Integrated Chance Constraints......Page 165
6.5 Integrated Chance Constraints and Recourse Models......Page 167
6.5.1 Conclusions......Page 169
6.6 Algorithms for Models with Integrated Chance Constraints......Page 170
7.1 A1: Multiperiod Inventory Control......Page 173
7.2 R1: Probabilistic Interpretations of Integrals of Distribution Functions......Page 175
7.3 R2: Complete and Sufficiently Expensive Recourse......Page 176
7.3.2 Sufficiently Expensive Recourse......Page 177
7.4 R3: Simple Recourse, Only RHS Random......Page 178
7.5 R4: Workforce Level Planning: An Example of Multiple Simple Recourse?......Page 180
7.6 C1: Chance Constraints and Integrated Chance Constraints......Page 181
7.7 C2: The Expected Shortage Function for Positive Random Variables......Page 182
7.9 C4: Relation Individual and Joint Chance Constraints......Page 183
7.10 C5: Joint Chance Constraints, Only RHS Random, Discrete Distribution......Page 185
7.11 C6: Individual Chance Constraints with One Random Variable......Page 186
7.12 U1: Stochastic Dominance and Expected Utility......Page 187
8.1 Multi-Period Production Planning......Page 190
8.2 Water Management in the Bodrog River Area......Page 194
8.3 Budgeting Cost of Nursing in a Hospital......Page 196
8.4 Growing Maize and Sorghum in Kilosa District......Page 201
8.5 Product Mix Problem......Page 204
8.6 Investment Planning for Electricity Generation......Page 206
8.7 Optimizing the Timetable of the Haarlem–Maastricht Railway Connection......Page 210
8.8 Electricity Distribution......Page 213
8.8.1 Contract with Power Plants......Page 214
8.8.2 Contract with Small Generators......Page 215
8.8.3 Modeling Uncertain Demand for Electricity......Page 216
8.8.4 Model 1: Optimizing the Contract with the Power Plants......Page 217
8.8.5 Model 2: Supply Schedule for the Next Day......Page 218
8.8.6 Future Demand for Supply from Small Generators......Page 219
8.8.7 Modeling Expected Penalty Costs......Page 220
8.8.8 Optimal Supply Schedules......Page 221
A.1 Expected Functions......Page 222
A.2 Limit Sets......Page 226
A.3 Probability Distribution and Density Functions......Page 227
B Elementary Convex Analysis......Page 229
C Deterministic LP......Page 239
D Maximum Calculus......Page 243
E Algorithms for Convex Non-linear Optimization......Page 245
E.1 Frank and Wolfe\'s Algorithm......Page 246
E.2 Veinott\'s Supporting Hyperplane Method......Page 247
Bibliography......Page 250
Index......Page 253