## Model building in mathematical programmingReview of previous editions 'Such a text - and this is the only one of this type I know of - should be the basis of all instruction in Mathematical Programming.' Journal of the Royal Statistical Society 'An excellent introduction ... for students of business administration and people who want to see the utility of operations research.' European Journal of Operational Research 'It will be appreciated very much by practitioners who already have knowledge in the field of mathematical programming.' Mathematical Programming Society Newsletter Model Building in Mathematical Programming Fourth Edition H. Paul Williams Faculty of Mathematical Studies, University of Southampton, UK This extensively revised fourth edition of this well-known and much praised book contains a great deal of new material. In particular sections and new problems have been added covering Revenue Management. Hydro Electric Generation, Date Envelopment (efficiency) Analysis, Milk Distribution and Collection and Constraint Programming. The book discusses the general principles of model building in mathematical programming and shows how they can be applied by using simplified but practical problems from widely different contexts. Suggested formulations and solutions are given in the latter part of the book together with computational experience to give the reader a feel for the computation difficulty of solving that particular type of model. Aimed at undergraduates, postgraduates, research students and managers, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpretation of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject. |

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### Contents

Introduction | 3 |

Solving Mathematical Programming Models | 10 |

Building Linear Programming Models | 17 |

Copyright | |

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### Common terms and phrases

0-1 integer 0-1 variables application arcs arise blending problem branch and bound clearly condition considered convex hull corresponding depot described in Section dual Economy example extra constraints factory feasible region Figure following constraints formulation given grinding capacity HPROD imposed industry infeasible input integer programming models integer variables involving IP model knapsack problem limited linear programming model logical conditions LP problem manpower mathematical programming model Maximize method minimize minimum cost month naphtha necessary network flow nodes non-convex non-linear non-zero objective coefficients objective function objective value obtained optimal solution output package programs period planning possible PROD profit contribution programming problems quantities ranges redundant represent right-hand side coefficient scenarios Section 1.2 semi-skilled separable programming set covering problem shadow prices simple upper bounds simplex algorithm solve sometimes specialized algorithm straints submodels subset surplus variables SVEG tion tons OIL tons VEG travelling salesman problem type of model unit valuations workers