Model Building in Mathematical ProgrammingThis extensively revised and updated edition discusses the general principles of model building in mathematical programming and shows how they can be applied by using twenty simplified, but practical problems from widely different contexts. Suggested formulations and solutions are given in the latter part of the book, together with some computational experience to give the reader some feel for the computational difficulty of solving that particular type of model. |
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Page 117
... objective value does of course change if we alter this coefficient within its ranges . Since x , has a value of 1 in the optimal solution , each unit of increase or decrease in its objective coefficient will obviously provide an ...
... objective value does of course change if we alter this coefficient within its ranges . Since x , has a value of 1 in the optimal solution , each unit of increase or decrease in its objective coefficient will obviously provide an ...
Page 159
... objective value of 146.84 . This is clearly the best known integer solution so far obtained . Obviously there are no more variables left to branch on at this node so we can terminate the branch . Since the objective value can get no ...
... objective value of 146.84 . This is clearly the best known integer solution so far obtained . Obviously there are no more variables left to branch on at this node so we can terminate the branch . Since the objective value can get no ...
Page 218
... objective value of P and the maximum objective of P ' ( or minimum objective of Q ' ) is sometimes known as a duality gap . It can be regarded ( rather loosely ) as a measure of how inadequate any dual values will be when used as shadow ...
... objective value of P and the maximum objective of P ' ( or minimum objective of Q ' ) is sometimes known as a duality gap . It can be regarded ( rather loosely ) as a measure of how inadequate any dual values will be when used as shadow ...
Contents
Introduction 335 | 3 |
Solving Mathematical Programming Models | 10 |
Building Linear Programming Models | 20 |
Copyright | |
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Common terms and phrases
0-1 variables application arise assignment problem blending problem branch and bound clearly condition considered convex hull depot described in Section drilling example extra constraints factory feasible region Figure following constraints formulation given grinding capacity impose increase indicate industry infeasible input input-output models integer solution integer variables involving IP model knapsack problem LIMIT linear programming model logical conditions manpower master model mathematical programming model matrix minimize minimum cost MPSX naphtha necessary network flow nodes non-convex non-linear non-zero objective coefficient objective function objective value obtained optimal solution output package programs piecewise planning possible practical problems procedure PROD product mix profit contribution quantities ranges redundant represented result right-hand side coefficient rows Section 1.2 set covering problem set packing shadow prices SIGMA simplex algorithm sometimes structure submodels subproblem SVEG tion tons OIL tons VEG total profit totally unimodular transportation problem type of model valuations x₁ y₁ zero