Methods and Models in Mathematical Programming by S. A. MirHassani & F. Hooshmand

Author:S. A. MirHassani & F. Hooshmand
Language: eng
Format: epub
ISBN: 9783030270452
Publisher: Springer International Publishing

2.a j ≤ b, ∀j = 1, …, n.

3.The variables are arranged such that the following non-increasing order is satisfied:

Let , and .(a)Show that the solution to the LPR problem is as follows:

and accordingly, show that U 1 is an upper bound for the optimal objective value of the zero-one knapsack problem, where

(b)Let

Show that U 2 is an upper bound for the optimal objective value of the zero-one knapsack problem and U 2 ≤ U 1, where

(c)Consider the following model:

The optimal solution to the above model is:

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