Rounding heuristics

If one can determine a p that solves minp>o Vp N), one would have a procedure for computing Vlp(N). The resulting solution (values of the y variables) while integral need not be feasible for CAPl. To produce a feasible solution one can round (heuristically) the final solution into a feasible one. 

Between these two extremes lies a region where relaxations may be helpful but branch and bound is unlikely to be effective. Here, bounds from relaxations at least delimit the suboptimahty of solutions found through heuristic search or other means. Relaxation may also provide a good source of feasible discrete solutions when the problem admits easy rounding of relaxation optima. 

NB-hard. LP relaxation rounds down and can be strengthened with the ineqimlities discussed in the Valid Inequalities section above. Solutionbuilding heuristics based on ratios of Cj to weighted sums of Ay are common. 

Heuristic 49 Crushing of coarse solids. Use a jaw crusher to reduce lumps of hard, abrasive, and/or sticky materials of 4 inches to 3 feet in diameter to slabby particles of 1 to 4 inches in she. Use a gyratory crusher to reduce slabby materials of 8 inches to 6 feet in size to rounded particla of 1 to 10 inches in diameter. Use a cone crusher to reduce less hard and less sticky materials of 2 inches to 1 foot in diameter to particles of 0.2 inch (4 mesh) to 2 inches in diameter. 

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